The political agenda effect and state centralization

Abstract

We provide a potential explanation, based on the “political agenda effect”, for the absence of, and unwillingness to create, centralized power in the hands of a national state. State centralization induces citizens of different backgrounds, interests, regions or ethnicities to coordinate their demands in the direction of more general-interest public goods, and away from parochial transfers. This political agenda effect raises the effectiveness of citizen demands and induces them to increase their investments in conflict capacity. In the absence of state centralization, citizens do not necessarily band together because of another force, the escalation effect, which refers to the fact that elites from different regions will join forces in response to the citizens doing so. Such escalation might hurt the citizen groups that have already solved their collective action problem (though it will benefit others). Anticipating the interplay of the political agenda and escalation effects, under some parameter configurations, political elites strategically opt for a non-centralized state. We show how the model generates non-monotonic comparative statics in response to the increase in the value or effectiveness of public goods (so that centralized states and public good provision may be absent precisely when they are more beneficial for society). We also suggest how the formation of a social democratic party may sometimes induce state centralization (by removing the commitment value of a non-centralized state), and how elites may sometimes prefer partial state centralization.

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Journal of Comparative Economics
journal homepage: www.elsevier.com/locate/jce
The political agenda effect and state centralization
Daron Acemoglu
a
, James A. Robinson
b
, Ragnar Torvik
⁎,c
a
Massachusetts Institute of Technology, Department of Economics, E52-380, 50 Memorial Drive, Cambridge MA 02142, USA
b
Harris School of Public Policy, University of Chicago, 1155 East 60th Street, Chicago, 60637, IL USA
c
Department of Economics, Norwegian University of Science and Technology, Trondheim N-7491, Norway
ARTICLE INFO
Keywords:
Conflict
Escalation effect
Political agenda effect
Public good provision
State capacity
State centralization
JEL classification:
D70
H11
P48
ABSTRACT
We provide a potential explanation, based on the “political agenda effect”, for the absence of, and
unwillingness to create, centralized power in the hands of a national state. State centralization
induces citizens of different backgrounds, interests, regions or ethnicities to coordinate their
demands in the direction of more general-interest public goods, and away from parochial
transfers. This political agenda effect raises the effectiveness of citizen demands and induces
them to increase their investments in conflict capacity. In the absence of state centralization,
citizens do not necessarily band together because of another force, the escalation effect, which
refers to the fact that elites from different regions will join forces in response to the citizens doing
so. Such escalation might hurt the citizen groups that have already solved their collective action
problem (though it will benefit others). Anticipating the interplay of the political agenda and
escalation effe cts, under some parameter configurations, political elites strategically opt for a
non-centralized state. We show how the model generates non-monotonic comparative statics in
response to the increase in the value or effectiveness of public goods (so that centralized states
and public good provision may be absent precisely when they are more beneficial for society). We
also suggest how the formation of a social democratic party may sometimes induce state cen-
tralization (by removing the commitment value of a non-centralized state), and how elites may
sometimes prefer partial state centralization.
1. Introduction
There is a great deal of variation across societies both historically and today in the degree to which a national state has
achieved the Weberian monopoly of violence over its territory, developed the authority and the capacity to enforce laws, maintain
law and order, and raise taxes and provide public goods — a vector of attributes that social scientists call “state capacity”. A
growing literature has documented the importance of state capacity for economic outcomes (e.g., Johnson, 1982; Amsden, 1989;
Evans, 1995; Evans and Rauch, 1999, 2000; Besley and Persson, 2009, 2011; Acemoglu et al., 2015, 2016, and Acemoglu and
Robinson, 2019).
Fundamental for establishing capacity is whether or not a state has managed to centralize authority and moved from various
systems of “indirect rule” to a situation where a national state actually directly organizes these activities. The extent to which this
process, which we refer to as state centralization, has been undertaken, varies greatly as well. At one end of the scale there are
countries such as most Western European ones, as well as China and Japan, with a high degree of state centralization, while at the
other end, the Afghan, Somali, Pakistani, Philippine, and Colombian states, among many others, are very far from having forged such
https://doi.org/10.1016/j.jce.2020.03.004
Received 4 February 2020; Received in revised form 25 March 2020; Accepted 27 March 2020
⁎
Corresponding author.
E-mail addresses: daron@mit.edu (D. Acemoglu), jamesrobinson@uchicago.edu (J.A. Robinson), ragnar.torvik@ntnu.no (R. Torvik).
Journal of Comparative Economics xxx (xxxx) xxx–xxx
0147-5967/ © 2020 The Authors. Published by Elsevier Inc. on behalf of Association for Comparative Economic Studies. This is an open access
article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).
Please cite this article as: Daron Acemoglu, James A. Robinson and Ragnar Torvik, Journal of Comparative Economics,
https://doi.org/10.1016/j.jce.2020.03.004

centralization. In non-centralized states, rule and authority are delegated to other entities, such as traditional elites in the Philippines,
tribal elites in Pakistan and various types of warlords in Colombia. Though state centralization appears to be a critical prerequisite for
establishing capacity,
1
and is mostly taken for granted (e.g. in the literature on East Asian development), we are far from a consensus
as to why many states have not centralized power or even attempted to establish the monopoly of violence over their territories. This
question is particularly puzzling since it would appear that all power-holders should want to monopolize power in their countries
(e.g., North, 1981, Chapter 3). If so, why is the state so hard to centralize?
This paper investigates political economic causes of lack of state centralization — and thus one of the factors keeping state
capacity perennially low in many societies. We model state centralization as the decision of different elites to coordinate their actions
and delegate their control over (local) violence to a national state. Critical to our explanation is the political agenda effect, which is the
name we give to the possibility that state centralization changes the dynamics of political action and conflict in society. The an-
ticipation of the political agenda effect may discourage elites from coordinating their actions and centralizing the state. More spe-
cifically, when citizens from different regions, sectors, interests, backgrounds, or ethnicities organize jointly, their agenda will change
in a direction that makes their demands from power-holders (elites) focus more on (general-interest) public goods. The greater
efficiency of public goods — relative to transfers — encourages them to invest more in their conflict capacity, increasing the ef-
fectiveness of their demands.
2
In turn, state centralization induces citizens to organize nationally as well — rather than at the local or
the ‘parochial’ level. It is this indirect effect of state centralization that makes elites often prefer a non-centralized state. Herein lies
the main mechanism of our model: the elites may strategically opt for a non-centralized state so as not to induce the citizens to
organize nationally and thus avert the political agenda effect.
The process of centralization and strengthening of the national state in Britain between 1758 and 1834 (see, e.g., Brewer, 1990;
Hardling, 1996) illustrates the political agenda effect — the changes in the societal equilibrium accompanying state centralization.
Charles Tilly’s (1995) classic study emphasizes that this process “... brought eighteenth century Britons into open confrontation with
one another...” (p. 5). At the start of the period, Tilly notes, contention was about
“local people and local issues, rather than nationally organized programs and parties” (p. 5),
[but] “between 1758 and 1833 a new variety of claim-making had taken shape in Britain... Mass popular politics had taken hold
on a national scale” (p. 13).
Tilly observes how the forms of collective action that emerged were completely new. For example, the open meeting became “a
kind of demonstration... a coordinated way of publicizing support for a particular claim on holders of power. Frequently a special
purpose association, society or club called the meeting. What is more, meetings recurrently concerned national issues, emphatically
including issues that the government and Parliament were on their way to deciding” (p. 10). Tilly further points out that “the means
by which ordinary people made collective claims... underwent a deep transformation: increasingly they involved large scale, co-
ordinated interaction that established direct contact between ordinary people and agents of the national state” (p. 14).
Tilly also argues that the driving force of this changing nature of contention and increasing coordination of civil society was
indeed the development of the national state:
“an expansion of taxes, national debt, and service bureaucracies, which increased not only the state’s size but also its weight
within the economy.. These changes... promoted a shift towards collective action that was large in scale and national in scope”
[and] “the expansion of the state pushed popular struggles from local arenas and from significant reliance on patronage towards
autonomous claim-making in national arenas” (Tilly, 1995, p. 49, 53).
This was precisely because, according to Tilly, the state gained “increasing importance... for the fates of ordinary people” (p. 16),
and that this
3
“generated threats and opportunities. Those threats and opportunities in turn stimulated interested parties to attempt new sorts of
defense and offense; to match association with association, to gain electoral power, to make direct claims on their national
government. Through long strenuous interaction with authorities, enemies and allies, those ordinary people fashioned new ways
of acting together in their interests and forced their interlocutors to change their own ways of making and responding to claims.
Cumulatively, struggles of ordinary people with power-holders wrought great changes in the British structure of power”
(Tilly, 1995, p. 16).
Our model formalizes and further elucidates these interactions by considering a society with Nregions, with location being the
only dimension of heterogeneity across groups of citizens.
4
Each region is also inhabited by a group of elites. Citizens can make
demands from elites backed up by their ability to engage in conflict. If they are not able to engage in conflict, the elites will not
1
For the link between different aspects of state centralization and the capacity of the state to effectively provide public goods and regulate
economic activity, see the historical accounts by Jean-Laurent (1990),Epstein (2000) and Nye (2007), and empirical work by Dincecco and
Katz (2016),Gennaioli and Rainer (2007),Michalopoulos and Papaioannou (2013), and Osafo-Kwaako and Robinson (2013).
2
Here ‘citizens’ stands for members of civil society, distinguished from those who are the political elite or the power-holders (or their direct
agents, such as the police or the military). The citizens could be acting as peasants, workers or civil society members in formulating demands and
participating in potential conflict with the state and its agents.
3
Johnson (2015) presents a similar argument to Tilly’s in the French case.
4
This is for specificity, and working with other dimensions of heterogeneity would lead to essentially identical results.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
2

respond to their demands and provide any redistribution. When they are able to engage in conflict, the elites will placate their
demands with the cheapest form of redistribution — consisting of a combination of direct transfers and public good provision — to
convince them not to engage in costly conflict.
The effectiveness of the demands of citizens is determined by two factors: they need to invest in their conflict capacity, which is
costly, and moreover, only some groups of citizens (in our model, for simplicity, citizens from one region only) are able to solve their
collective action problem and invest. These “strong” citizens then have a choice — either engage in local demands (backed up by the
threat of local conflict), or organize other “weak citizens” and engage in demands and conflict at a national (or at the very least supra-
local) level. In our model, when the demands are local, the cheapest way of placating them for the local elite is to make parochial,
local transfers. However, when the demands are at the supra-local (or national) level, general-interest public goods become a better
option, because different types of public goods benefit all citizen groups — not just the local group. This formalizes the political
agenda effect: when the conflict is at the supra-local level, citizens will invest more in their conflict capacity because they recognize
that a successful outcome in the conflict will lead to public good provision, which is more beneficial for them (and in the absence of
redistribution from the elite, they themselves will be able to invest in public goods in case they win the conflict). This argument
further shows that the political agenda effect also provides a mechanism for why, as documented by the studies cited in footnote 1,
public good provision will be associated with centralized states — parochial transfers emerge as the most economical way of meeting
citizen demands in the absence of state centralization.
Weighing against a national organization, however, is the escalation effect: if the citizens band together in a national organization,
this will escalate the fight by inducing the elites to also form a national organization and pool their resources to fight against the
citizens. The escalation effect features prominently in the calculus of strong citizens: by forming a national organization, they will
directly benefit the weak citizen groups (who would have otherwise remained unorganized), but they may face a lower probability of
success and thus lower transfers because of the escalation of the conflict.
5
We show that for an interesting part of the parameter space, in the absence of a centralized state, the escalation effect is potent
enough that strong citizens do not initiate a national organization, and as a result, the elites are able to avoid the political agenda
effect. Crucially, if the elites were to choose a centralized state, this would induce citizens to also join up in a national coalition,
putting in motion the political agenda effect. As a result, the elites strategically choose a non-centralized state in order to avoid such
political escalation, and prefer to deal with demands from their local citizens, if any, by making parochial transfers.
6
Several important, and in some cases surprising, conclusions follow from this theory. First, in the relevant region, citizens benefit
ex ante from a centralized state, because it enables all of them to organize and make demands, and as already noted, these demands
will be met via the provision of general-interest public goods. In contrast, with a non-centralized state, only strong citizens are able to
do so (and they do not internalize the positive impact they have on other citizen groups). Second, and paradoxically, a greater value
of public goods — and similarly, lower heterogeneity in the preferences of citizens — can make the provision of public goods and
state centralization less likely. This is because more valuable public goods, by making citizens more likely to coordinate under state
centralization, may further discourage elites from building a centralized state, thus push in the direction of parochial, location- or
issue-specific transfers. Third, we show how a social democratic party may change the nature of equilibrium. This happens when such
a party induces citizens to band together before the identity of the strong group is revealed, wrestling away from the elites the first
mover advantage (which enabled the elites to effectively commit to not banding together as long as the citizens did not do so also).
Put differently, once citizens commit to acting in a nationally coordinated manner, the strong citizen groups will always organize the
weak groups, and in response, elites now prefer the centralized state. In the relevant part of the parameter space, this option always
increases the ex ante utility of citizens. Finally, we show how elites may opt for partial state centralization, which enables them to
increase their power in the conflict and thus reduce the transfer they need to make, while still making use of the escalation effect to
discourage strong citizens from forming coalitions with weak citizens.
The escalation and political agenda effect are evident in many experiences of political centralization, particularly in Post-World
War II Southeast Asia. For example, Malaysia was split by the British prior to World War II into the Crown colony of the Straights
Settlement, (consisting of Singapore, Melaka, Penang and Province Wellesley), the Federated Malay States and the Unfederated
Malay States. The states were ruled indirectly through the traditional rulers (Emerson, 1937). In addition there was a Chinese
Protectorate which dealt with any issues related to the Chinese people. This patchwork of polities meant that Malaya was politically
highly non-centralized (e.g., (Andaya and Andaya, 1982, p. 245)). This changed after World War II. During the war, the Japanese
took over Singapore as a colony and united the rest of the country as a protectorate, weakening traditional rulers and fomenting a
Malay national identity in opposition to the British. Andaya and Andaya argue that “Malays increasingly began to see themselves as
belonging to a Malaya-wide entity, rather than to their individual states,” (1982, p. 248), which was a very different situation from
the types of parochialism evident previously. This national identity came together with the rapid growth of the Malayan Communist
Party (MCP), which was armed during the war by the British to fight the Japanese, and thereafter assumed virtual de facto control of
the country when the Japanese surrendered. The response of the British was to propose to merge all of the polities into a Malayan
Union in a way that implied equal treatment for Malays and Chinese. But this policy, in turn, triggered a response akin to our political
agenda effect: “For the first time in history, the Malays rose in one movement to fight against the formation, putting aside parochial
5
Such escalation may not always harm the strong citizens, but will always do so at the margin when they are indifferent between engaging in
conflict by themselves and forming a broader coalition.
6
This strategic lack of state centralization may further contribute to the low capacity of the state: the elites do not provide public goods, and do
not need to build the capacity of the state to increase the efficiency of public goods.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
3

sentiments relating to individual states, districts or clans” (Hooper, 2003, p. 8). This reaction led to a compromise Federation of
Malaya, and to strengthened state institutions to contain the Communist rebellion. (Harper, 1999, pp. 195-196), notes that “During
the Emergency the classic functions of the state — military, fiscal, administrative — were greatly extended and new ones adopted. A
centralized federal government grew in strength — The state became for the first time a physical presence in the lives of many of its
subjects.”. Slater’s summary of the situation thus emphasizes how the elites had to centralize the state in response to this bottom-up
conflict. He states: “Malaysia’s strong central state” has its roots in “elite responses to especially challenging pressures from below”
(Slater, 2010, p. 59), and
“endemic and unmanageable threats from below inspired the construction of a strong and centralized state apparatus in Malaya in
the decade following World War II. By the time of independence in 1957, the Malayan state was already noteworthy for the
effectiveness of its coercive and administrative institutions. The initial processes of state-building were compounded and ac-
celerated in the early 1970s, as the racial riots of May 1969 provided a powerful impetus for government leaders to strengthen
their coercive grip and increase their fiscal demands upon the Malaysian population” (Slater, 2010, p. 147).
The situation in Indonesia in the 1960s was also very similar. Once again, the significant strengthening of state institutions (in the
context of the transition from Sukarno to Suharto and the emergence of the so-called New Order, e.g., Anderson 2001) came in
response to the communist insurgency. Slater’s assessment of this case further illustrates our escalation effect: “it was the dramatic
rise of contentious class politics in the mid-1960s, via the mobilization of a powerful, grassroots communist party with a massive
rural and urban membership, that spurred a remarkable increase in elite collective action upon the birth of the Suharto regime”
(2010, pp. 26-27). He then generalizes these two cases to the entirety of Southeast Asia, again underscoring our escalation effect:
“Mass movements preceded the rise of authoritarian Leviathans... New elite coalitions arose in active support of... increased state
centralization” (Slater, 2010, p. 23).
That the anticipation of the political agenda effect can inhibit state-building is well illustrated by the history of European colonial
rule as well. Most colonial powers, like the British ruled “indirectly” and delegated a large number of tasks, such as taxation and the
provision of justice, to local traditional rulers. They saw little benefit from providing public services, and all the dangers of building a
capable administration, which would just increase demands from society and put further roadblocks on their plans to run a profitable
colony. Sir Donald Cameron, the governor of Tanganyika in the 1920s, clearly identified the political agenda effect when he noted
“If we set up a European form of administration, the day will come when the people of the Territory will demand the British form
of administration shall pass into their hands... If we aim at indirect administration through the appropriate Native Authority... we
shall be building an edifice... capable of standing the shock which will inevitably come when the educated native seeks to gain
possession of the machinery of government and to run it on Western lines... If we treat them properly, moreover, we shall have the
members of the Native Administration on our side” (Iliffe, 1979, p. 322).
Hechter (2000) notes more broadly how shifts from indirect to direct rule led to large reactions from society in the face of much
more direct centralized administration, with this reaction often taking the form of nationalism.
Our paper is related to the growing literature in economics and political science on the role of state capacity, political cen-
tralization and the formation of the state, mentioned already above. Some of this literature has developed political mechanisms that
deter elites from building states. Acemoglu (2005) suggests that states with strength beyond a certain level will make citizens worse
off and may be resisted (unless a “consensually strong state” that is effectively monitored by the citizens emerges). Besley and
Persson (2009),Besley and Persson (2011) emphasize that if incumbent elites are threatened with the loss of power then they may
refrain from building a state because the capacity can be subsequently used against them. Our model develops a very different
mechanism, with different predictions. For instance, in these previous studies, when public goods become more valuable, this makes
it more attractive to build a state, but this is not necessarily the case in our model. Acemoglu et al. (2011) develop a model where
incumbent elites face democratization and create an inefficient state in order to favorably influence the democratic political equi-
librium. The large literature on civil war can also be interpreted in terms of state formation, for example political factors may deter
states from eliminating rebel groups and establishing a monopoly of violence (e.g., Acemoglu et al., 2010; Acemoglu et al., 2013).
Our results on the political agenda effect are also related to the large literature on clientelism which has emphasized how
politicians target transfers to their supporters (Bates, 1981; Shefter, 1977, 1993; Lizzeri and Persico, 2001; Kitschelt and Wilkinson,
2007; Robinson and Verdier, 2013; Stokes et al., 2013) and to the long-standing puzzle in political science of when politics focus on
the provision of general-interest public goods as opposed to patronage, clientelism and parochial benefits (see Kitschelt, 2000, for an
overview). We provide a new argument here based on the political agenda effect — public goods politics emerge when citizens
organize collectively, a process which leads to a demand for public as opposed to parochial transfers. This argument also provides a
potential explanation for the findings of Anderson et al. (2015), which document how local elites in Maharashtra, India are able to
dominate politics and curtail the provision of public goods, among other things, by clientelism, particularly aimed at preventing
coordination by non-elite citizens. Our main result is related to, but distinct from, Lizzeri and Persico’s (2004) argument that when
politicians need to appeal to a larger number of voters (due to democratization), it becomes more cost-effective for them to do this by
providing public goods. Our emphasis on the roles of the political agenda effect and state centralization in curtailing clientelism is
also different from one of Shefter’s (1977) suggestions that clientelism is weakened when new political parties mobilize outside the
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
4

existing political system.
7
Several strands of the literature on state formation in the sociology and political science literatures are connected to our theory as well.
One branch emphasizes the role of social movements, which the state may influence by using its resources or by other means (Tilly 1978), or
by favoring some specific groups, for example, through selective policy or repression (McAdam et al. 1988). Another important branch, also
due to Tilly (1990), emphasizes the connection between war-making and state-building. According to this argument, bureaucratic state
structures emerge in order to coordinate taxation, conscription and requisitioning necessary for large armies. Wittfogel’s (1957) famous
Oriental despotism thesis can be viewed as a precursor of this argument. Wittfogel claimed that early state formation originated from the
desire to establish large-scale irrigation systems in places where non-irrigated agriculture was infeasible or less productive. Yet another
branch builds on Scott’s (1998) seminal work highlighting efforts of states to make society “legible”, for example, by collecting census data,
imposing uniform language and standardizing weights and measures. Several other scholars also emphasize that state formation or cen-
tralization is specifically motivated by the desire to control society, such as in Anderson’s (1974) and Hechter and Brustein’s (1980) theories
of the emergence of absolutism in early modern Europe, or Saylor’s (2014) examination of contemporary state-building in several developing
countries. Our approach is complementary to all of these arguments, but emphasizes how state efforts to gain control over society, regardless
of their exact motivation, tend to trigger the political agenda effect and thus may sometimes end up threatening.
Finally, our model is connected to the literature on federalism as well. The seminal work by Riker (1964) argued that federalism
emerged from a bottom-up process of autonomous political units ceding authority to a federal government to exploit the potential
benefits of coordinating on such things as national defense. Subsequent research has focused on how federal systems can deal with
specific challenges, for example externalities and public good provision (e.g., Lockwood, 2002; Besley and Coate, 2003), and with the
exception of Crémer and Palfrey (1999), there has been little work on the endogenous emergence of federalism. Closer to our paper
are models of the circumstances under which federal systems may decentralize authority or even break into component parts (e.g.,
Bolton and Roland 1997;Filippov et al. 2004;de Figueiredo and Weingast 2005;O’Neill 2005). Though such positive theories can
explain why centralization may not occur, we are not aware of other works that have studied the impact of centralization on the
organization of society or argued that this is an important disincentive to centralization.
The rest of the paper is organized as follows. In Section 2 we introduce our model of state centralization. In Section 3 we study the
equilibrium political power and political agendas with and without state centralization. The equilibrium emergence of state cen-
tralization is discussed in Section 4. In Section 5 we extend the model to deal with a case where the citizens can coordinate into a
national political movement ahead of an eventual centralization of the state, and in Section 6 we extend the model to discuss a case
where the elites may centralize the state only in parts of the territory. Section 7 concludes. We present some omitted proofs and
discuss several additional extensions of the model in the Appendix.
2. Model
In this section, we present our basic model of state centralization. The ideas discussed in the Introduction are conceptualized in the
context of a model consisting of regional heterogeneity though, as noted there, other dimensions of heterogeneity would be entirely ana-
logous.
2.1. Preferences and technology
We consider a society consisting of Nregions, and we use
i N{1, ..., }
to denote a particular region. Each region is inhabited by a set
of homogeneous citizens and homogeneous elites, each with measure normalized to 1. Throughout, there will be no conflict of interest among
citizens or elites within a given region, and we will not distinguish between the group and a particular element thereof, and use the
superscripts c(respectively, e) to denote the entire group of citizens (respectively, elites) or an individual member.
8
Elite preferences depend only on their consumption, denoted for an elite agent of region iby
C,
i
e
where
C0
i
e
. Since the total measure of elites within each region is normalized to 1,
Ci
e
also denotes total consumption expenditure
of elites in region i.
Citizen preferences depend both on their consumption and on public goods (such as public schooling or the quality of roads,
which may matter less for elites who are able to afford their own private alternatives). However, reflecting the potential conflict of
interest across regions, the quality of these public goods within an individual’s own region matters more for her than those in other
regions. Namely, the utility of a citizen from region iis
7
The emphasis on the state shapes society and vice versa is also related to the work of Habermas (1991), who suggested the notion of a ‘public
sphere’ as an inclusive place in society where people come together to discuss and deliberate and form opinions. Habermas viewed this as related to
state formation, noting that “Civil society came into existence as the corollary of a depersonalized state authority” (1989, p. 19). Other scholars,
such as Katznelson (1985),Evans (1995), and Migdal (1988, 2001), have also emphasized the interaction between the state and society, but have
tended to treat both the strength of the state and society as historically determined.
8
As noted above, ‘region’ here stands for either locational heterogeneity, ethnic or religious heterogeneity, or heterogeneity in terms of other
preferences. An important application of the model is to ethnic heterogeneity, which would imply that the conflict in the non-centralized state is
between elites and citizens of a certain ethnicity, and state centralization involves elites of different ethnicities banding together.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
5

+ +C G G(1 ) ,
i
ci
j i
j
where
C0
i
c
is the private consumption of citizen i, G
i
≥ 0 is the total quantity of public goods in the individual’s own region, and
λ∈[0, 1] parameterizes the extent of heterogeneity in preferences among citizens: when λis close to zero, an individual cares about
public goods in other regions equally (e.g., because this facilitates trading or an individual can get easy access to these public goods),
and conversely when λis close to 1, an individual only cares about public goods in her region.
Total output of the consumption good within each region is Y, and we simplify the setup by assuming that this is inelastically
produced and initially accrues to the elite (e.g., it is their endowment of land or natural resources). It can also be taxed without any
distortions. One unit of this consumption good can be converted into μunits of any of the regional public goods.
Let us next define, for future reference, Φ(n) as the marginal utility of funds for citizens. Namely, this is the maximum symmetric
citizen utility that a coalition of citizens from a coalition with
=n
can achieve from one unit of the consumption good per
region. To compute this, note that if we convert a fraction xof the unit of consumption from each region into the public good from
that region (by the symmetry requirement), then each citizen will have a utility of
+ + = + +n µx x n µx x(1 (1 ) ( 1)) 1 ((1 ) ) 1
. Clearly, this expression always has a corner maximizer in x, thus en-
abling us to write
+n n µ( ) max{1, ( (1 ) ) } .
(1)
It is also straightforward to see that Φ(n) is nondecreasing in n. We next impose our first parametric assumption on this Φfunction:
Assumption 1.
=(1) 1
and Φ(N) > 1.
The first part of this assumption imposes that μ< 1, which ensures that when in isolation, a single group prefers not to invest in
the public good. The second part implies that when all Nregions are combined, it is worthwhile to invest in public goods. In
particular, the second part requires that λis not too large. Substantively, this assumption restricts attention to situations in which the
demand for public goods will be greater when all regions are simultaneously investing in public goods.
9
This assumption thus restricts
attention to the part of the parameter space that is of interest for our analysis. Since Φ(n) is nondecreasing, Assumption 1also implies
that there exists a unique n* such that Φ(n) > 1 for n>n* but
=n(*) 1
.
Remark 1. Our analysis below will show that the functional form of Φ(n)plays no major role in our results. Thus we could generalize (1) to
= +n f n n µ( ) ( ) max{1, ((1 ) ) },
where f(n)is a nondecreasing function reflecting the greater effectiveness of using funds when resources are deployed at the more centralized
level or in a more coordinated fashion. For instance, the case where
=f n( ) 1
for all n <N , and f(N) > 1 can be interpreted as capturing the
greater efficiency of a “centralized state” allocating funds for all regions.
2.2. Policies, political power and state centralization
Policies in this economy concern how much of each region’s output Ywill be taxed and how much of this will be provided as
direct transfers to citizens and how much of it will be invested in public goods. These policies are decided by the group which has
local or national political power. Initially, political power in region irests with the elite from that region, but may be contested by
citizens. We next describe how this conflict takes place and the technology for conflict. The key is whether the state is “centralized”.
As described in the Introduction, our focus is whether political power and fiscal policy are determined entirely at the local level or are
centralized to the national level.
The two cases we initially consider are total lack of state centralization, denoted by
=s0,
and full centralization, analogously
denoted by
=s1
. Under a non-centralized state, each local elite acts entirely autonomously, without any coordination, whereas
under full centralization, they commit to transfer power to a national political body that represents their collective preferences as we
describe next.
Under both centralized and non-centralized state structures, citizens can contest political power. We assume that the extent to
which they can do so depends on whether they are able to solve their within-region collective action problem, and for simplicity we
assume that only one of the Nregions (drawn uniformly at random) will be able to do so, and the remaining
N1
regions will not.
We refer to the citizens that have solved their collective action problem as “strong”, and the citizens in the remaining regions as
“weak”. Strong citizens can contest local political power, while weak citizens cannot unless they join up in a coalition or “organi-
zation” with the strong region.
10
Suppose, without loss of any generality, that it is citizens in region 1 that are strong. An additional decision for this group of
citizens is whether to form a coalition with other regions. We denote by
=Z0
c
the decision not to form such a coalition, and by
=Z1
c
the decision to offer to form a coalition to citizens from other regions. We ignore for now the decision to offer to form a
9
Many public goods, such as infrastructure or public health investments, would have this property.
10
The interpretation here is that when weak groups are part of an organization with a strong group that has already solved its collective action
problem, they can also de facto solve their own collective action problem, thus becoming capable of contesting power in their region or in a national
conflict.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
6

coalition with a subset of this homogeneous set of citizens from other regions; we return to this issue in the Appendix and show that
this simplification is without consequence. Following the choice of
=Z1,
c
citizens from all other regions decide whether to join this
coalition, denoted by
z{0, 1}
i
c
for i≠ 1. Let us also designate
=i{ :
z1
c
=i1
or
=z1}
i
c
(and note that region 1 is always in
=z1
c
). If
=Z0,
c
it means that citizens from region 1 will engage only in local conflict and present local demands from their elites. If
=Z1
c
and
=z1
i
c
for all i≥ 2, then citizens from different regions will have formed a national organization, and engage in national conflict and
present national demands.
Under a non-centralized state (
=s0
), after observing the realization of the strength of citizens of different regions and
=,
z1
c
each
regional elite also decides whether to join up in a coalition. We use a similar notation,
z,
i
e
to denote the decision of the elite from
region ito form a coalition with the elite from region 1 (ignoring coalitions excluding region 1 is without loss of any generality as will
become apparent). We denote by
=i{ :
z1
e
=i1
or
=z1}
i
e
the coalition of the elite.
Under a centralized state (
=s1
), on the other hand, the elites pool their resources and delegate these to a national organization,
which then confronts all demands and conflict from the citizens.
Subsequent to the state centralization decision and the coalition formation decisions, each region within this citizen-side coalition
decides how much to invest in the conflict technology (e.g., armaments or organizational capital), denoted by
,
i
c
with the collection
of these investments being
=
{ }
i
c
izc1
. We assume that the cost of investment in terms of the final good is given by
( ),
i
c
which is
continuously differentiable and satisfies
=(0) 0,
>( ) 0,
i
c
( ) 0
i
c
for all
0,
i
c
and
=lim ( )
i
c
i
c
. Each regional elite has
conflict capacity given by θ
e
≥ 0. We take this elite-side capacity as exogenous to simplify the discussion and show in the Appendix
that endogenizing it does not affect our main results.
Finally, each regional elite facing the threat of conflict — i.e., those with indices belonging to the set
= =z z1 1
c e
— decides on
a transfer-public good package to encourage peaceful settlement with the citizens. We denote the package offered by elites in region i
by (T
i
, G
i
), where
+T G µ Y/
i i
(with
Y
T G µ/
i i
being left for the consumption of the elite in region i). No concession can be simply
captured by setting
=T G( , ) (0, 0)
i i
. More specifically, there are three possibilities to consider. Either (i)
=
={1},
z1
e
in which case the
elite in region 1 individually offer a policy package. Or (ii)
={1},
z1
e
in which case the elites in this coalition jointly decide on a
policy package, which they will each offer.
11
The fact that they all offer the same policy package is natural, since at this point, there is
no conflict of interest among regional elites in
=z1
e
for in case this offer is rejected, they will all have exactly the same probability of
losing the conflict and suffering the same consequences (as we describe next). Or finally (iii)
= =
i,
z z1 1
c e
in which case this elite
group is facing the organized coalition
=z1
c
but is not part of
=,
z1
e
so will have to make an individual offer again. Following the
offer
=
T G( , )
i i ize1
or (T
i
, G
i
)
i
, the corresponding group of citizens decide whether to accept this concession or to fight
=
f( {0, 1}
e
zc1
or
f{0, 1}
i
e
). If
=f1,
e
there will be fighting, and the winner of the conflict is determined stochastically.
To explain how conflict takes place, first consider the case in which
=s0
(i.e., no state centralization) and
= =
= = {1},
z z1 1
e c
so that conflict is local. Then there will be a single conflict in region 1, and no conflict with any other region, since all other citizen
groups are weak. The outcome of the conflict in region 1 depends on whether
> + ,
c e
1 1
where σis a random variable drawn from a cumulative distribution H( · ). If this inequality holds, then the citizen side wins and
determines the taxes, transfers and the public good provision level. If it does not, the elite side wins and makes all the policy
decisions.
Given this specification, the probability that citizens in region 1 win this conflict is simply
H( ).
ce
1
Let us next turn to the case in which still
=s0
and at least one of
=z1
c
and
=z1
e
is not a singleton, so that conflict is not purely
local. Then, analogously, the outcome of the conflict depends on whether
> +
=
=
.
i
i
cz e1
zc
e
1
(2)
If this inequality holds, the coalition of citizens wins, and otherwise the elite coalition wins, and makes the policy choices. Intuitively,
the left-hand side involves the investments of all citizen groups that are in a coalition with a strong partner, and thus able to take part
in a conflict. The right-hand side involves the strength of all elite groups that have joined the coalition involving region 1. The right-
hand side thus reflects the fact that all their resources are pooled. Notice that this expression also applies when
=z1
e
is not equal to
=z1
c
. If some region
=
jz1
e
but
=
j,
z1
c
it means that they are contributing to the elite side of this fight, and since
=
j,
z1
c
citizens from this region are not contributing to the citizen side. The cost to the elite from region jis that if the citizen side wins, they
will have also lost, whereas if they had not joined this coalition, because their citizens are weak, they would have never lost the
conflict. Conversely, if
=
jz1
c
but
=
j,
z1
e
then the outcome of the conflict in region jis determined depending on whether
> +
=
,
i
i
ce
zc1
implying that the elite in this region are facing the full strength of the citizen coalition
=z1
c
.
11
There is no interesting possibility that
=ze1
is a singleton but not equal to {1}, since in this case the citizens are not organized, and thus there is
no need to make any concessions.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
7

Finally, consider the case in which
=s1,
so that there is state centralization, and the citizen coalition is given by
=z1
c
. Because
state centralization has already pooled all elite resources, the outcome of the conflict now depends on whether
> +
=
N.
i
i
ce
zc1
In all of this, the conflict always destroys a fraction
1 (0, 1)
of the total output, representing the fact that conflict is costly.
Hence, the party that wins the conflict will have access to a regional output in the amount of αY. This cost can be avoided if the elite
in question choose to make an offer (T
i
, G
i
) that the citizen side prefers to fighting, and thus chooses
=f0
i
e
.
Finally, in what follows we will also impose:
Assumption 2. The density of the distribution function H, h, exists over its entire support
N[ , ¯)
e
where
>
¯0,
is continuously
differentiable and is nonincreasing. Moreover,
>h N Y( ) (0)
e
.
This assumption is useful for several reasons. First, it ensures that the second-order condition in the conflict choice of citizens is
satisfied. Second it guarantees that the density of the distribution function H, which shapes the marginal incentives of citizens in their
investment decisions, is well-defined and positive over the range in which these investments will take place (
¯
is an arbitrary positive
constant, making sure that the support of the distribution does not stop exactly at 0). Third, it also ensures that starting at zero
conflict capacity, citizens have an incentive for investment in this capacity. This assumption is the weaker version of the oft-imposed
requirement that
=(0) 0
.
2.3. Timing of events and equilibrium
To summarize, the timing of events is as follows.
1. The elites decide whether to centralize the state (i.e., choose between
=s0
and
=s1
). Note that at this stage, all regional elites
have the same preferences over state centralization.
2. It becomes common knowledge in which region citizens are strong. Suppose, without loss of any generality that this is region 1.
Then citizens in region 1 decide whether to form a coalition with other regions (i.e., choose between
=Z0
c
and
=Z1
c
). If
=Z0,
c
then there is no coalition of citizens from different regions. If
=Z1,
c
then other regions decide whether to join the coalition of the
strong citizens from region 1 (i.e., they choose
=z0
i
c
or
=z1
i
c
for
= …i N2, ,
). In region 1 and those in
=
iz1
c
(or equiva-
lently, those where
=z1
i
c
) citizens choose
0
i
c
.
3. Then elites from different regions decide whether to join in a coalition with the elite from region 1, which are the ones facing the
strong citizens (i.e., they decide
=z0
i
e
or
=z1
i
e
for
= …i N2, ,
). Then:
(a) In regions
= =
iz z1 1
c e
(or equivalently those with i≥ 2 and
= =z z 0
i
c
i
e
) political power is not contested and the elites
decide the policy vector (T
i
, G
i
).
(b) Elites that are in
=z1
e
jointly decide what offer
=
T G( , )
i i ize1
to make to the citizens they are facing, and those in
= =z z1 1
c e
individually make such offers.
4. If the state is centralized (
=s1
), then elites from different regions will have already formed their grand coalition, i.e.,
=
=z1
e
.
Then, all of the elites jointly decide what offer
=
T G( , )
i i ize1
to make to the citizens they are facing.
5. Following these offers, citizens decide whether to accept the offers they have received or not (
=
f{0, 1}
e
zc1
or
f{0, 1}
i
e
). If the
offer is accepted, it is implemented. Otherwise, there is fighting and whether the citizens or the elite win is determined according
to (2), and the winner sets the policies with the value of output reduced to αY.
6. Policies are implemented, and all payoffs are realized.
In what follows, we focus on pure-strategy subgame perfect equilibria. This detailed timing of events also specifies citizen and elite
strategies, and a subgame perfect equilibrium is defined, in the usual fashion, as a strategy profile in which all actions are best
responses to other strategies in all histories. When this will cause no confusion, we refer to pure-strategy subgame perfect equilibria
simply as “equilibria”.
Remark 2. The timing of events also clarifies that there are two different ways in which the elites can “centralize the state” (form their grand
coalition and coordinate their actions). The first is by choosing
=s1
in stage 1, and the second one is by choosing
=
=
N N
z1
e
in stage 3. As we
have specified the payoffs, these two options are entirely equivalent. It is straightforward, but cumbersome, to introduce a slight cost advantage
for the first option, so that elites explicitly choose
=s1
when this is in their interest rather than wait for stage 4. In what follows, we simplify the
discussion by assuming that when state centralization is in their interest, the elites will do so by setting
=s1
.
3. Equilibrium
Pure-strategy subgame perfect equilibria are characterized by backward induction. We start by the policy offer of elites under
threat of conflict and the response of citizens.
Lemma 1. Regardless of whether
=s0
or
=s1,
any equilibrium always involves
=
=
f0,
e
zc1
i.e., there will always be an offer from the elite
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
8

that induces no fighting. Moreover, this offer will give citizens exactly the same utility as they would obtain with fighting.
Proof. See the Appendix. □
The intuition for this is simple. Since α< 1, conflict is costly, and the elites can always benefit by offering the policy mix that
makes citizens as well off as they would be with conflict. Moreover, since the elite have the possibility to make such an offer, they will
never propose a policy mix that gives citizens strictly greater utility than the latter could obtain by fighting. This last observation also
implies that in the previous stages of the game in our analysis of the decisions of citizens, we could always use the utility that they
would obtain under fighting.
The next question is what policy mix the elites will use, what coalitions will form along the equilibrium path, and whether the
elites will choose state centralization. To investigate these issues, we first characterize the equilibria in subgames starting first
without state centralization, and then with state centralization.
3.1. Equilibrium without a centralized state (
=s0
)
Suppose that the elites have decided not to form a centralized state, designated by
=s0
.
3.1.1. The escalation effect
Our next result formalizes the escalation effect in a society without state centralization. It shows that when there has been no state
centralization, the coalition formation of elites will mimic that of citizens. Throughout, we continue to suppose, without loss of any
generality, that region 1 is the one where citizens are strong.
Lemma 2. Suppose
=s0
(there has been no state centralization) and citizens have formed a coalition
=z1
c
(∋1). Then
=
= = .
z z1 1
e c
Proof. See the Appendix. □
Intuitively, no elite in a region where the citizens have not joined the coalition
=z1
c
would want to join the coalition
=,
z1
e
since
they are facing weak, unorganized citizens that cannot make any demands, but if they join the coalition, this will force them to make
concessions or be included in the fight with positive probability of losing (because at least some other members of the coalition are
facing organized citizens). Conversely, elites in the regions where citizens have joined the coalition
=z1
c
will be facing organized
demands, and are better off pooling their resources with other elites.
The anticipation of this behavior highlights the escalation effect mentioned in the Introduction: when citizens in region 1 decide to
form a coalition with citizens from other regions, they will escalate the conflict, inducing other elite groups to join the fight as well.
12
3.1.2. Choice of conflict capacity
Suppose now that a coalition
=z1
c
of citizens has formed. How will they choose their conflict capacity? First, we know from
Lemma 2that
=
= =z z1 1
e c
. Next recall that even though the group of citizens will make their fighting decisions jointly, the level of
conflict capacity is the purview of each region.
13
Hence, it will be the solution to a maximization problem in which each group iof
citizens in the coalition
=z1
c
chooses
i
c
recognizing that they will be facing an identical coalition of elites. Setting
=
=n,
z1
c
this
maximization problem for each
=
iz1
c
is:
=
H n n Ymax ( ) ( ).
j
j
cei
c
0
i
c
zc1
(3)
Intuitively,
=
H n
jj
ce
zc1
is the probability that the citizens will win the conflict — since their total conflict capacity will be
=
jj
c
zc1
and the exogenous conflict capacity of the elite they are facing is nθ
e
. If they lose in the conflict, then the regional elites
choose the policies and naturally set zero taxes, yielding zero utility to citizens. If the citizens succeed, they can tax the entire income
that is not destroyed in conflict, αY, and they can use this either for the direct transfers or public good investments, and the term Φ(n)
12
As already noted in the Introduction, the escalation effect does not always harm the strong citizens (citizens from region 1). For instance, if the
strength of elites, θ
e
, is small and the level of investment of citizens, θ
c
, is large, the likelihood that citizens prevail in the conflict when both sides
have formed their grand coalitions (given by the probability that
> +
c e
) will be greater than the likelihood that citizens from region 1
win against elites from region 1 (given by the probability that
> +
ce
1
). However, as we will see below, the escalation effect will always harm
citizens from region 1 at the margin when they are indifferent between engaging in conflict by themselves and forming a larger coalition (e.g., their
grand coalition). This is because for them to be indifferent in this fashion, we have to be in the case where θ
e
is relatively large compared to θ
c
.
13
This assumption is made so as to ensure that forming a coalition does not automatically increase their investments in conflict capacity by
removing the free-rider effect (which thus prevents us from mixing two potentially distinct benefits of forming a larger coalition, the first coming
from the political agenda effect, and the second one from the wrecked coordination to remove the free-rider effect). In the Appendix we characterize
the equilibrium of the model when citizens solve the free-rider effect in their investment in conflict capacity, and show that all of our results apply
identically in this case (though the exact thresholds are different).
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
9

captures the marginal utility of these funds when they are optimally used. Finally,
( )
i
c
is the cost that this group of citizens faces
from their investments.
The first-order condition for this problem is (for each
=
iz1
c
)
=
=
h n n Y( ) ( ) 0,
j
j
ceic
zc1
(4)
with the second-order condition
<
=
h n n Y( ) ( ) 0.
j
j
ceic
zc1
Assumption 2ensures that the first-order condition (4) will always hold, thus removing the need to write this in complementary
slackness form, and also that there will be a unique solution where the second-order condition holds (since h′ ≤ 0).
One important implication of (4) is that citizens from all regions will choose the same investment in conflict capacity, and this will
depend only on n(and not on the exact identity of the regions in
=z1
c
).
14
We denote this investment level by
= = =
( )
*( , , ),
z z z1 1 1
c e c
where the first argument is the conditioning on the size of the coalition of citizens, the second
argument is the size of the coalition of elites the citizens will be facing, and the term
=
( )
z1
c
highlights the other major effect
discussed in the Introduction, the political agenda effect. The presence of this term, and thus the political agenda effect, both directly
increases the utility of citizens from conflict in (3) and raises their level of investment in conflict capacity in (4). Since we are in the
case of no state centralization and
= =
= = n
z z1 1
c e
(from Lemma 2), the equilibrium level of conflict capacity can be simply
denoted θ*(n, n,Φ(n)).
Indeed, because Γ″ > 0 everywhere, the level of investment in conflict capacity is always (strictly) increasing in whatever in-
creases the marginal utility of additional investments, given by
=
h n n Y( ) ( )
ii
ce
zc1
. The political agenda effect then follows
straightforwardly from this observation, since
>n n n n
*( , , ( ) )/ ( ) 0,
and dΦ(n)/dn ≥ 0. Intuitively, a higher Φ(n) implies that the marginal utility of the funds that citizens can capture following a
successful conflict is greater, and this will encourage them to invest more in conflict. In turn, larger coalitions of citizens can use funds
more productively to provide public goods, thus explaining why Φ(n) is increasing in n.
More specifically, substituting these equilibrium conflict investments in the utility functions of citizens, we can observe that the
utility of citizens from each region
=
iz1
c
under a non-centralized state (
=s0
) is
= =U n s H n n n n n n Y n n n
*[ | 0] ( *( , , ( ) ) ) ( ) ( *( , , ( )) ).
i
ce
(5)
From Lemma 1, the elite will make an offer to citizens that just convinces them not to fight, and at this point they have already paid
the cost of investments in conflict capacity. Hence, the utility of citizens from each region
=
iz1
c
entering conflict will be
H n n n n n n Y(*( , , ( ) ) ) ( )
e
. With the same logic that citizens can use their funds most effectively by providing public goods,
elites in the coalition
=
= =z z1 1
e c
can also deliver this utility most effectively by providing public goods, since one unit of the
consumption good invested in the public good equally across each region in
=z1
c
yields the utility of Φ(n) to each group of citizens.
Hence, the cost of delivering a utility of
H n n n n n n Y(*( , , ( ) ) ) ( )
e
to citizens in this coalition is
H n n n n n Y(*( , , ( ) ) )
e
.
Thus the utility of elites in
=
iz1
e
can be written as
= =U n s H n n n n n Y
*[ | 0] [1 ( *( , , ( ) ) ) ] .
i
ee
(6)
Because of the political agenda effect,
=U n s
*[ | 0]
i
c
is increasing in Φ(n), while
=U n s
*[ | 0]
i
e
is decreasing in Φ(n). The latter is true
despite the fact that, when the citizens have formed a coalition of size n, each dollar that the elite decides to redistribute is also worth
more by exactly the same amount, Φ(n), since in this case a higher Φ(n) also raises the investment of citizens in their conflict capacity.
Second, because h′ ≤ 0, the marginal utility of funds is decreasing in the investments of other citizens in the coalition and in the
size of the coalition, making investments of different groups of citizens strategic substitutes. For the same reason, the marginal utility
of funds is increasing in the size of the coalition of elites, creating a force towards greater investments when citizens are facing a
larger coalition of elites.
3.1.3. Coalition decision of citizens
Let us now consider the coalition decision of citizens. If
=Z1,
c
then clearly
=z1
i
c
for all
= …i N2, ,
. This is because when they
do not join a coalition with citizens from region 1, these unorganized groups of citizens cannot contest power and thus receive zero
transfers in public goods, whereas once they do so, they will receive positive transfers in the next stage of the game.
This then implies that if
=Z1,
c
the grand coalition of all citizens will form. Consequently, the choice for citizens from region 1 is
14
This applies to citizens from region 1 as well, since, after joining the coalition, the problem facing all citizens, including those from region 1, are
identical.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
10

to choose
=Z0
c
and act by themselves, or initiate the formation of this grand coalition.
15
Suppose first that
=
={1}
z1
c
. Then with the same notation as above and noting that in this case the size of the coalition is 1 and
(also from Assumption 1)
=(1) 1,
(5) becomes
= =U s H Y
*[1| 0] ( *(1, 1, 1) ) ( *(1, 1, 1) ).
ce
1
(7)
For future reference, we also write the utility of elites from region 1 in this case, which follows readily from (6):
= =U s H Y
*[1| 0] [1 ( *(1, 1, 1) )] .
ee
1
(8)
Note also that in this case, the most efficient way of transferring resources for the elite is a direct transfer, so there will be no
investment in public goods. That is,
=T H Y(*(1, 1, 1) )
e
1
and
=G0
1
.
Suppose next that
=
=z1
c
. Then because the equilibrium is symmetric and thus citizens from different regions will choose the
same investment level, (5) becomes
= =U N s H N N N N N N Y N N N
*[ | 0] ( *( , , ( ) ) ) ( ) ( *( , , ( ))),
c e
(9)
and similarly, (6) becomes
= =U N s H N N N N N Y
*[ | 0] [1 ( *( , , ( )) ) ]
e e
(10)
Since from Assumption 1,Φ(N) > 1, we also know that all transfers from elites to citizens in this case will take the form of public
good provision. That is,
=T0
i
and
=G µ H N N N N N Y(*( , , ( ) ) )
ie
for all i.
We can conclude that citizens from region 1 will prefer to form the grand coalition of citizens when their utility from the grand
coalition, (9), is strictly greater than their utility from standing alone, (7). The former, (9), is increasing in Φ(N),
16
while the latter,
(7), does not depend on Φ(N). Therefore, there exists a value of Φ(N), Φ*(N), such that
=
H N N N N N N Y N N N
H Y
(*( , , *( ) ) ) *( ) ( *( , , *( )) )
(*(1, 1, 1) ) ( *(1, 1, 1)).
e
e
(11)
Then whenever Φ(N) > Φ*(N), citizens from region 1 (the strong citizens) prefer a grand coalition, and whenever Φ(N) < Φ*(N),
they prefer to act by themselves. This conclusion is intuitive. Forming a coalition with citizens from other regions is costly because of
the escalation effect: the fight will escalate because, in response, the grand coalition of elites will form and fight against them (this is
captured by the fact that θ
e
is now multiplied by Non the left-hand side). The benefit, on the other hand, is related to the political
agenda effect as well as to the fact that now all citizens are coordinated (captured by the fact that θ*(N, N,Φ(N)) is multiplied by N).
The latter effect corresponds to the more effective use of funds in case of victory in the conflict, and exhibits itself in the presence of
the term Φ(N) multiplying the probability of success on the left-hand side, and the greater level of investment in conflict capacity of
all citizens (i.e., the fact that θ*(N, N,Φ(N)) > θ*(N, N, 1)).
Another important point is worth noting: equation (11) is purely from the viewpoint of citizens in region 1, trading off the
escalation effect against the coordination of all citizens and the political agenda effect. However, when citizens from region 1 form a
coalition with other citizens, they create a positive externality on these citizens, who would have otherwise not contested power and
obtained zero transfers and public goods, and a commensurate negative externality on elites from other regions, which now will have
to make transfers to their citizens. The ex ante expectation of this externality plays an important role in interpreting our results below.
The coalition formation decision of citizens, and the resulting utility levels for citizens and elites, are summarized in the next proposition.
Proposition 1. Suppose the elites have not formed a centralized state (i.e.,
=s0
), and suppose without loss of any generality that it is citizens
from region 1 that are strong. Then there exists Φ*(N)such that the following are true:
1. If Φ(N) < Φ*(N), then citizens from region 1 choose
=Z0
c
and act independently. There is no redistribution in regions
= …i N2, , ,
and in
region 1, there is redistribution in the form of direct transfers to convince citizens in this region not to fight. That is,
=T H Y(*(1, 1, 1) )
e
1
and
=G0
1
.
2. If Φ(N) > Φ*(N), then citizens from region 1 choose
=Z1
c
and all of the regions choose
=z1,
i
c
joining the coalition of citizens from
region 1. In this case, there will be redistribution in all regions in the form of public good provision. That is,
=T0
i
and
=G µ H N N N N N Y(*( , , ( ) ) )
ie
for all i.
Proof. The existence of the threshold Φ*(N) follows from (11). Then by the definition of Φ*(N), when Φ(N) < Φ*(N), the right-hand
side of (11) is greater and thus citizens from region 1 prefer
=Z0,
c
and the rest of part 1 follows straightforwardly. When
15
As already noted, in the Appendix we discuss the case in which citizens from region 1 can restrict the coalition to a certain number of regions,
thus inducing the formation of a smaller coalition, and show that when H( · ) is uniform and Γ( · ) is quadratic, they will never choose to do this. We
also establish that when Nis sufficiently large, even if citizens choose to form a smaller coalition, the elites will opt for a non-centralized state.
16
The derivative is given by:
+H N N N N N Y Nh N N N N N N Y N N N(*( , , ( ) ) ) [ ( *( , , ( ) ) ) ( ) ( *( , , ( ) )) ].
eN N N
N
e
*( , , ( ) )
( )
The
first term is clearly positive. We can further see that the second term is positive by the following argument. First,
>0
N N N
N
*( , , ( ))
( )
with a
straightforward application of the implicit function theorem. Second, the term in square brackets in the second line is also strictly positive, since the
first-order condition (4) implies that
=h N N N N N N Y N N N(*( , , ( )) ) ( ) ( *( , , ( ) ) ),
e
and thus this term is equal to
>N h N N N N N N Y( 1) ( *( , , ( )) ) ( ) 0
e
.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
11

Φ(N) > Φ*(N), the left-hand side of (11) is greater, and citizens from region 1 prefer
=Z1
c
. The rest of part 2 once again follows
readily. □
An important point, related to our discussion in the Introduction, is that when Φ(N) < Φ*(N) and conflict is local, elites placate
the citizens by making direct transfers to them instead of providing public goods. Instead, when Φ(N) > Φ*(N) and conflict is
national, there will be public good provision instead of direct transfers. This emphasizes the link between the nature of conflict and
demands from citizens and whether the responses from elites are “patrimonial”.
We can also readily determine the expected utility of elites before the identity of the citizens that are strong is determined. When
Φ(N) < Φ*(N), there is only 1/Nprobability that they will have to redistribute income to their citizens as specified in Proposition 1,
whereas when Φ(N) > Φ*(N), all elites will necessarily make transfers as specified in Proposition 1. Therefore, the following cor-
ollary to Proposition 1follows immediately (proof in the text).
Corollary 1. When Φ(N) < Φ*(N), the expected utility of elites is
= =U s
N
H Y
*[ 0] 1 ( *(1, 1, 1) ) .
e e
(12)
When Φ(N) > Φ*(N), the expected utility of elites is
= =U s H N N N N N Y
*[ 0] [1 ( *( , , ( ) ) ) ] .
e e
(13)
These expressions make it clear that, as shown in Figure 1, when Φ(N) crosses the threshold of Φ*(N), there is a downward jump
in the utility of elites due to the change in the equilibrium coalition of citizens.
17
This discontinuous behavior at the threshold Φ*(N)
reflects the political agenda effect, and highlights the advantage of a non-centralized state for the elites when the marginal utility of
funds for citizens is not too high (i.e., is less than Φ*(N)). It is this advantage (in the political agenda effect), as we will see next, that
will induce elites to opt for a non-centralized state for a range of values of Φ(N).
3.2. Equilibrium under a centralized state
We next present the analogous analysis for the case in which there is a centralized state, i.e.,
=s1
.
3.2.1. Choice of conflict capacity
The choice of conflict capacity is very similar to that under the non-centralized state, except that now the elite have already
committed to nationally-coordinated action. Therefore, when the coalition of citizens is
=,
z1
c
the optimization problem for citizens
from region
=
iz1
c
becomes
=
H N n Ymax ( ) ( ),
j
j
cei
c
0
i
c
zc1
where
=
=n
z1
c
. Here we have used the fact that because of state centralization, the baseline includes a greater amount of elite
resources being deployed against the citizens. The first-order conditions are then identical to (4), with the nθ
e
term replaced by Nθ
e
,
Fig. 1.
17
That the jump is downward follows from the same argument as the one we use in step 1 of the proof of Proposition 3.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
12

and we do not write them out to conserve space. One important implication is that the escalation effect which played an important
role in our analysis without state centralization is no longer present — the elites have already banded together and there will be no
further escalation of conflict on the elite side even if citizens form a non-local coalition.
3.2.2. The coalition formation decision of citizens
The coalition decision of citizens can be analyzed similarly to the one without state centralization. First, it is again straightforward
to see that when citizens from region 1, who we have again set as the ones that are strong without loss of any generality, choose
=Z1,
c
then citizens from all other regions will choose
=z1
i
c
. Thus the choice for citizens from region 1 is once more simply between
=
={1}
z1
c
and
=
=z1
c
. When they choose
=
={1},
z1
c
we again have
=(1) 1,
and thus their overall utility under state
centralization (
=s1
) will be
= =U s H N N Y N
*[1| 1] ( *(1, , 1) ) ( *(1, , 1)).
ce
1
(14)
Conversely, when they choose
=
=,
z1
c
their overall utility under state centralization will be
= =U N s H N N N N N N Y N N N
*[ | 1] ( *( , , ( ) ) ) ( ) ( *( , , ( ))).
c e
(15)
The comparison of these two expressions boils down to
>
H N N N N N N Y N N N
H N N Y N
(*( , , ( )) ) ( ) ( *( , , ( )))
(*(1, , 1) ) ( *(1, , 1)).
e
e
(16)
When evaluated at
=N N( ) *( ),
the left-hand side of (16) is identical to the left-hand side of (11), while its right-hand side is
strictly smaller than the right-hand side of (11) because of the presence of Nmultiplying θ
e
inside the Hfunction. Intuitively, this
reflects the absence of the escalation effect mentioned above — citizens can now make their coalition formation decision without
worrying about how this will escalate the conflict by inducing the elites to form a coalition, and therefore they are more likely to form
such a coalition. These observations also establish the next proposition.
Proposition 2. Suppose the elites have formed a centralized state (i.e.,
=s1
), and suppose without loss of any generality that citizens from
region 1 are strong. Then citizens from region 1 choose
=Z1
c
and all the regions choose
=z1,
i
c
joining the coalition of citizens from region 1.
There will be redistribution in all regions in the form of public good provision. That is,
=T0
i
and
=G µ H N N N N N Y(*( , , ( ) ) )
ie
for
all i.
Proof. The proof is straightforward by observing that (16) is always satisfied. To see this note that since Φ(N) ≥ 1 and the left-hand
side of (16) is increasing in Φ(N) while the right-hand side is independent of Φ(N), a stronger (more demanding) condition than (16)
is that
>H N N N N Y N N H N N Y N(*( , , 1) ) ( *( , , 1)) ( *(1, , 1) ) ( *(1, , 1) ).
e e
(17)
To see that this must always hold, we first prove that
>H N N N N Y H N N Y(*( , , 1) ) ( *(1, , 1) ) .
e e
(18)
Suppose, to obtain a contradiction, that this is not the case. From (4), we have
=
=
h N N N N Y N N
h N N Y N
(*( , , 1) ) ( *( , , 1)
(*(1, , 1) ) ( *(1, , 1) ).
e
e
But since his nonincreasing from Assumption 2,
h N N N N h N N(*( , , 1) ) ( *(1, , 1) ).
e e
Then, given that Γ″ > 0, θ*(N, N, 1) > θ*(1, N, 1). This in turn implies that
>N N N N N N
*( , , 1) *(1, , 1) ,
e e
and thus
>H N N N N Y H N N Y(*( , , 1) ) ( *(1, , 1) ) ,
e e
yielding a contradiction.
Next, since (18) holds, we must have from (4) and Assumption 2that Γ′(θ*(N, N, 1) < Γ′(θ*(1, N, 1)), and hence that Γ(θ*(N, N,
1) < Γ(θ*(1, N, 1)), establishing that (17), and thus (16), is always satisfied. □
Intuitively, because the escalation effect is entirely absent, citizens simply gain additional strength by joining together without
any cost of doing so. This means that when elites form a centralized state, citizens will also respond by forming their grand coalition.
This result thus highlights the cost of state centralization from the viewpoint of elites. It implies that citizens will necessarily form a
coalition in their potential conflict against the elites.
18
18
The result that citizens will form their grand coalition under a centralized state is due to the assumption that the escalation effects disappear
entirely under state centralization. If we relax this, for example, by assuming that the centralized state is equivalent to elites pooling some fraction of
their resources (thus giving them a strength Kθ
e
, where K∈(1, N)), and their remaining power will be pooled in response to citizens joining together
in conflict, then there will exist another threshold,
<N N
˜( ) *( )
such that the citizens will form their grand coalition under state centralization
only if
>N N( ) ˜( )
.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
13

The next corollary once again characterizes the expected utility of elites.
Corollary 2. When there is state centralization (
=s1
), the equilibrium utility of elites is given by
= =U s H N N N N N Y
*[ 1] [1 ( *( , , ( ) ) ) ] .
e e
(19)
4. Equilibrium state centralization
In this section, we study the state centralization decision of elites by combining the results from Corollaries 1and 2. We will first
provide a sharp result under Assumption 2, which ensures that his nonincreasing (i.e., h′( · ) ≤ 0), and then in the next subsection we
will generalize this result to the case in which his single-peaked, which will reveal an additional strategic interplay.
4.1. Main result
Proposition 3. Let Φ*(N)be as defined in Proposition 1, and suppose that Assumptions 1and 2hold. Then there exists a Φ
*
(N)such that we
have the following characterization of the unique equilibrium:
1. If Φ(N) < Φ
*
(N), then the elites choose state centralization (
=s1
).
2. If Φ
*
(N) < Φ(N) < Φ*(N), then the elites choose a non-centralized state (
=s0
).
3. If Φ*(N) < Φ(N), then the elites choose state centralization (
=s1
).
19
Proof. We will proceed in several steps.
Step 1: We first prove that for Φ*(N) ≥ 1
H N N N N N N Y H Y(*( , , *( ) ) ) *( ) ( *(1, 1, 1) ) .
e e
(20)
Suppose, to obtain a contradiction, that this is not the case. From (4), we have
=
=
h N N N N N N Y N N N
h Y
(*( , , *( ) ) ) ) *( ) ( *( , , *( ))
(*(1, 1, 1) ) ( *(1, 1, 1)).
e
e
(21)
But since his nonincreasing from Assumption 2,
h h N N N N N N(*(1, 1, 1) ) ( *( , , *( ) ) ) *( ).
e e
But then, given that Γ″ > 0, θ*(N, N,Φ*(N)) ≥ θ*(1, 1, 1). This immediately implies that, Γ(θ*(N, N,Φ*(N))) ≥ Γ(θ*(1, 1, 1)), and
thus
H N N N N N N Y H Y(*( , , *( ) ) ) *( ) ( *(1, 1, 1) ) ,
e e
yielding a contradiction, establishing step 1.
Step 2: Define Φ
*
(N) such that
=H N N N N N
N
H(*( , , *( ) ) ) 1(*(1, 1, 1) ).
e e
Since θ*(N, N,Φ
*
(N)) is increasing in Φ
*
(N) (from (4)), for all Φ(N) > Φ
*
(N), the elite prefer non-state centralization, and for all
Φ(N) < Φ
*
(N), they prefer state centralization.
Step 3: We next prove that in the relevant region where Φ*(N) ≥ 1, we have Φ
*
(N) < Φ*(N) (if Φ*(N) ≤ 1, then we could not have
Φ(N) > Φ*(N)).
Recall from step 1 that
H N N N N N N H(*( , , *( ) ) ) *( ) ( *(1, 1, 1) )
e e
. Dividing both sides by N, we have
H N N N N N N
N N
H(*( , , *( )) ) *( ) 1 (*(1, 1, 1) ).
e e
Since from (1) and Assumption 1,
= = <N N N N µ N
*( ) ( ) ( ( 1) ) ,
this implies
>H N N N N N
N
H(*( , , *( ) ) ) 1(*(1, 1, 1) ),
e e
which yields that for
=N N( ) *( ),
(12) is strictly greater than (19). Since Φ(N) > Φ
*
(N) and (12) is strictly greater than (19), we
must have that Φ*(N) > Φ
*
(N).
We now proceed to prove the three claims in the proposition.
Part 1: If Φ(N) < Φ
*
(N), (12) is strictly less than (19), and thus the elites prefer a centralized state with citizens forming their
19
Throughout we simplify the statement of the propositions by omitting the case where
=N N( ) *( ),
which involves the citizens being in-
different between joining up in a coalition and not.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
14

grand coalition to a non-centralized state where there is no coalition formation among citizens. Therefore they choose
=s1
.
Part 2: If Φ
*
(N) < Φ(N) < Φ*(N), then (12) is strictly greater than (19), and thus the elites prefer a non-centralized state to
forming a centralized state and having citizens form their grand coalition against it. Therefore, they opt for
=s0
.
Part 3: In this case, because Φ(N) > Φ*(N), the citizens will always form their grand coalition, thus the elites also prefer to do the
same, and thus again
=s1
Finally, note also that this part covers the remaining case where Φ*(N) < 1, since then by Assumption 1
Φ(N) > Φ*(N). □
The most interesting part of Proposition 3is the second one, establishing that when Φ
*
(N) < Φ(N) < Φ*(N), the elites prefer a
non-centralized state. The logic for this result goes via the escalation and political agenda effects discussed above and the externality
that citizens from region 1 create on other citizens when they form a coalition with them. Because Φ(N) < Φ*(N), when the state is
not centralized, citizens from region 1 prefer not to form a coalition with other citizens because of the escalation effect — when they
form a coalition, they know that the elites will respond by forming their own coalition and thus escalate the conflict. Because
Φ(N) > Φ
*
(N), this reluctance to form a citizen coalition is, from an ex ante point of view, highly beneficial for elites, because of the
aforementioned externality and the political agenda effect: whenever citizens form this coalition, other citizens benefit and elites lose
out. Each elite group, therefore, benefits from this externality with probability
N N( 1)/
. In addition, because of the political agenda
effect, if the state were centralized, they would have to endure higher levels of citizen investments in conflict capacity. In contrast,
when the state is centralized, citizens from region 1 will form a coalition with other regions, obviating these benefits on elites. This
can be thought of as a reverse escalation effect, reflecting the desire of elites to avoid the political agenda effect that arises when
citizens form the grand coalition in response to state centralization — the centralization of the state this time escalates the conflict on
the side of the citizens, who recognize that they are facing a national, unified elite and thus become more willing to form their own
grand coalition, which then puts in motion the political agenda effect. In what follows, to make the discussion more specific, we do
not use the term reverse escalation effect, and simply refer to the wish of the elite to avoid citizens forming a coalition as the political
agenda effect.
Parts 1 and 3 are straightforward in this light: when Φ(N) < Φ
*
(N), the elites actually prefer citizens to form their grand coalition
because they are sufficiently powerful against the citizens that the conflict being between Nregions is advantageous for them.
20
Conversely, when Φ(N) > Φ*(N), the agenda effect is sufficiently powerful that citizens will always form a coalition with other
regions, and consequently, the elites prefer
=s1
.
21
Moreover, in this case, any transfers from the elites to citizens take the form of
public goods.
Parts 1-3 together imply a nonmonotonic relationship between Φ(N) and state centralization. Note a limitation of this result,
however. We do not know whether Φ
*
(N) is greater than one or less than one. In the latter case, part 1 can never take place, and thus
the relationship becomes monotonic. This nonmonotonic relationship also implies nonmonotone comparative statics, which are
summarized in the next corollary. In this and the subsequent corollaries, the references to “more likely” or “less likely” stand for
expanding or contracting the part of the parameter space where the result applies.
Corollary 3. The likelihood of a centralized state and any public goods being provided is potentially nonmonotone in the productivity of public
good provision, μ, and in the heterogeneity of the preferences of different regions over public goods, λ.
Proof. Suppose we are in the case in which 1 < Φ
*
(N) < Φ*(N). Then a higher μincreases
=N N N µ( ) ( ( 1) ) ,
thus contracting
the region of the space of the remaining parameters for which Φ(N) < Φ
*
(N). This makes state centralization and the provision of
public goods less likely (the latter since when we are in part 2 of Proposition 3, any payments from the elite to citizens take the form
of direct transfers, not the provision of public goods). Further increases in Φ(N) ultimately take society out of the region where
Φ
*
(N) < Φ(N) < Φ*(N), thus again inducing state centralization and public good provision. The nonmonotonicity with respect to λis
similar. □
This corollary shows that, somewhat paradoxically, an increase in the productivity or value of public goods can make them less
likely to be provided and the centralized state that can effectively provide them less likely to emerge.
22
This is because a higher μ
raises the marginal value of funds to citizens, Φ(N), which may then shift from the region in which Φ(N) < Φ
*
(N) to the one where
Φ
*
(N) < Φ(N) < Φ*(N). This shift would induce a stronger political agenda effect, and the desire of elites to avoid this political
agenda effect would push them towards not establishing a centralized state, which would in turn discourage citizens from forming a
national coalition. Intuitively, a higher productivity of public goods makes the political agenda effect more powerful, and this further
increases the strategic value of choosing a non-centralized state for the elites. Similarly, lower heterogeneity in the preference of
different regions also has a nonmonotonic effect (whereas one might have expected that greater heterogeneity would always make
public good provision less likely). The intuition is the same as for the comparative static for the productivity of public goods: as λ
20
In particular, in this region of the parameter space θ
e
is sufficiently large relative to θ* that
H N N N N N(*( , , *( )) )
e
is much smaller than
H(*(1, 1, 1) ) ,
e
making the elite prefer the conflict to be between their grand coalition and the grand coalition of the citizens. Thus, as in e.g.
Wittfogel (1957), it is the elites that gain from state centralization.
21
Notice that here we are making use of the convention we introduced in Remark 2that whenever the elites prefer to form their grand coalition,
we will refer to this as
=s1,
even though they could alternatively achieve this by choosing
=s0,
and then ex post forming their grand coalition
(with entirely equivalent consequences to
=s1
).
22
If we adopted the generalization suggested in Remark 1, an increase in f(N) relative to f(1), reflecting a greater (cost) advantage of the
centralized state in providing public goods, we would also have nonmonotonic effects.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
15

decreases, we may shift from the region in which Φ(N) < Φ
*
(N) to the one where Φ
*
(N) < Φ(N) < Φ*(N).
4.2. Extension: Multiple equilibria
In this subsection, we relax Assumption 2and replace it with the following:
Assumption 2′. The density of the distribution function H, h, exists over its entire support
N[ , 0],
e
is continuously
differentiable and single-peaked.
There are two generalizations in Assumption 2′ relative to Assumption 2. First, it allows hto be single-peaked rather than
nonincreasing everywhere. Second, the assumption that
>h N Y( ) (0)
e
is dropped (we will analyze both this and the converse
case in the next proposition).
Now the first-order condition of citizens in their conflict capacity, (4), may no longer have a unique solution. The next proposition
delineates the circumstances under which this will be the case. When there is a unique equilibrium, the results are similar to those
highlighted in Proposition 3. When there are multiple solutions, these translate into multiple equilibria, some of which have greater
investments in conflict capacity by citizens. In this case, the patterns of state centralization are somewhat richer, but have the same
overall intuition. To limit attention to the more interesting cases, whenever there are multiple equilibria, we focus on symmetric
equilibria (when the equilibrium is unique, it is always symmetric as already characterized).
Proposition 4. Let Φ*(N)be as defined in Proposition 1, and suppose that Assumption 1and 2′ hold.
1. Suppose also that
>h N Y( ) (0),
e
h( · ) is concave to the left of its peak, and Γ′( · ) is weakly convex. Then, there exists a unique
equilibrium. In this unique equilibrium, there exists
N( )
such that
(a) If
<N N N( ) min{ *( ) , *( ) },
then the elites choose state centralization (
=s1
).
(b) If Φ
*
(N) < Φ*(N)and
< <N N N
*( ) ( ) *( ),
then the elites choose a non-centralized state (
=s0
).
(c) If
<N N
*( ) ( ),
then the elites choose state centralization (
=s1
).
2. Suppose instead that
<h N Y( ) (0),
e
h( · ) is concave to the left of its peak and Γ′( · ) is weakly convex. Then, generically, there are
either one or three symmetric equilibria. One equilibrium involves the elites choosing state centralization (i.e.,
=s1
) and no investment by
the citizens in their conflict capacity, and is stable under best-response dynamics. In addition, when there are three equilibria, there is also a
middle equilibrium, which is unstable under best-response dynamics, and an equilibrium with the highest level of citizen investment in their
conflict capacity, which is also stable under best-response dynamics. Assuming that there are no equilibrium switches in response to changes
in Φ(N), the equilibrium with the highest level of citizen investment is identical to the one described in part 1.
3. If h( · ) is not concave to the left of its peak or Γ″( · ) is not weakly convex, there is generically an odd number of equilibria. If
<h N Y( ) (0),
e
there always exists an equilibrium with state centralization and no investment by citizens in their conflict capacity.
Assuming that there are no equilibrium switches in response to changes in Φ(N), the equilibrium with the highest level of citizen investment
is identical to the one described in part 1.
Proof. First suppose that
>h N Y( ) (0)
e
(which was imposed as part of Assumption 2before) and that h( · ) is concave to the left
of its peak and Γ′( · ) is weakly convex. Then, Figure 2a shows the marginal benefit and cost for additional investment for citizens that
are part of the active coalition of citizens. The figure makes it clear that in this case there will be a single intersection, and thus the
uniqueness result continues to hold. The rest of the proof is similar to that of Proposition 3, with the major difference that when
h′ > 0, we can no longer deduce that Φ
*
(N) < Φ*(N) when Φ*(N) ≥ 1 (but the case where Φ
*
(N) > Φ*(N) does not generate
additional equilibrium outcomes, since when
>N N( ) *( ),
the citizens will form their grand coalition with or without a centralized
state, and whether (12) is strictly greater than (19) becomes irrelevant).
Second, note that when
<h N Y( ) (0),
e
h( · ) is concave to the left of its peak, and Γ′( · ) is weakly convex, Figure 2b shows that
the marginal cost of investment may be everywhere above the marginal benefit for citizens from a given region, in which case there
will be a unique equilibrium with no citizen investment. Figure 1c illustrates how, when this is not the case, there will exist three
symmetric equilibria under state centralization, one of which is again the corner equilibrium with no citizen investment. In this
corner equilibrium, because under state centralization (
=s1
), citizens choose no investment in their conflict capacity, and thus their
probability of success is always lower under state centralization than any other coalition configuration (i.e.,
<h N h n n n n N( ) ( *( , , ( )) )
e e
for any n), centralizing the state is a strict best response for the elites. The fact that the middle
equilibrium is unstable under best-response dynamics follows from standard arguments (from the fact that marginal cost is less steep
than marginal benefits). The equilibrium with the highest level of investment in citizen conflict capacity satisfies exactly the same
first-order conditions for citizens as the unique equilibrium in part 1 under the usual assumption that there are no switches across
equilibria in response to changes in parameters (compare Figures 2a and 2c).
Figure 2d shows how there might exist two equilibria in the non-generic case in which the Γ′ schedule is tangent to h( · ). Our
notion of genericity rules out such tendencies (any small perturbation of either the Γ′ or the hschedule in this case would restore the
existence of one or three equilibria).
Finally, Figure 2e depicts a case with five equilibria when h( ·) is not concave to the left of its peak. The fact that the number of
equilibria is generically odd follows from standard arguments. The equilibrium with the highest level of investment in their conflict
capacity again satisfies the same first-order conditions for citizens. □
There are several senses in which this proposition is a generalization of Proposition 3. First, under the assumption that
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
16

>h N Y( ) (0)
e
(which was imposed via Assumption 2previously), the result that there exists a unique equilibrium also holds
when the density his increasing provided that it is concave to the left of its peak and Γ′( · ) is weakly convex. However, in this case the
threshold Φ
*
(N) may be greater than the threshold Φ*(N) even when Φ*(N) ≥ 1 (when the unique equilibrium is in the range where
h′ > 0). When this is so, we also need to consider some additional configurations. In particular, we might have that
< <N N N( ) *( ) *( ),
but the implications of this are identical to the configuration where
<N( )
Φ
*
(N) < Φ*(N) (as summarized
in part 1 of Proposition 3). Or we might have that
< <N N N
*( ) ( ) *( ) ,
and yet the proposition shows that in this case the
implications are identical to the third part of Proposition 3, because citizens will form their grand coalition regardless (because
<N N
*( ) ( )
).
Second and more radically, when
<h N Y( ) (0),
e
we are likely to have multiple equilibria, at least under state centraliza-
tion.
23
In this case, as already noted, we focus on symmetric equilibria (where all regions that are part of the active coalition choose
the same level of investment). The proposition shows that, unless the marginal cost of investment is everywhere above the marginal
benefit, there will be three such equilibria when h( · ) is again concave to the left of its peak and Γ′( · ) is weakly convex. One of these
equilibria will feature zero investment by the citizens under state centralization, and because this is the best configuration for the
elites, they will have no incentive to deviate from state centralization. There will also exist a middle equilibrium which is unstable.
Finally, the third symmetric equilibrium, the one with the highest level of investment by citizens in their conflict capacity, is similar
to the equilibrium characterized in the first part of the proposition (and once again does not allow us to rank the thresholds Φ*(N)
and Φ
*
(N)).
Third, when h( · ) is not concave to the left of its peak or Γ′( · ) is not weakly convex, there can be more equilibria, though these
have a similar structure to those characterized in part 2.
Overall, we interpret these results as showing the general robustness of the results highlighted in Proposition 3, but they also point
out to additional insights. In particular, the multiplicity of equilibria might be one of the factors in play in accounting for the
variation across societies in the patterns of state centralization and effectiveness of the state in social conflict.
Fig. 2.
23
There may not be multiple equilibria without state centralization, since we may have that
>h Y( ) (0),
e
even though
<h N Y( ) (0)
e
.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
17

5. The role of a social democratic party
The main reason why there is no state centralization when Φ
*
(N) < Φ(N) < Φ*(N) is because the elites are using lack of state
centralization as a strategic tool to discourage citizens from banding together in a national organization. They are able to do so
because of two features of the setup studied here: first, they have the first mover advantage in choosing state centralization; and
second, they recognize that once the identity of the region where citizens are strong is realized, those citizens (citizens from region 1)
do not internalize the positive effect they have on the utility of citizens from other regions.
In this section, we argue that, under certain historical conditions, the emergence of a social democratic party might play a
beneficial role countering this strategic incentive of elites. In such cases, social democratic politics will coordinate citizen conflict
against elites, induce state centralization and pave the way to greater state capacity and the provision of general-interest public
goods, and as such, improve the ex ante welfare of the citizens.
In Sweden, Norway and Denmark, social democratic parties emerged as relatively broad coalitions of different segments of society
during the first half of the 20th century and played a critical role in coordinating and spearheading citizen demands from state
institutions. The non-sectarian nature of Scandinavian social democrats is well illustrated by the Swedish case, where the party
actively sought to include middle classes as well as its core supporters from the labor unions (see Berman, 2006, and also
Acemoglu and Robinson, 2019). After 1932, it entered into what Gourevitch, (1986, p. 133) dubs the “cow trade” — a coalition with
the agrarian party, which initially had very different objectives and priorities. Esping-Anderson (1985) emphasizes that such coa-
litions helped industrial workers become more cohesive in their negotiations with employers, while Berman (2006) points out that
social democracy was built of communitarian impulses and tried to foment solidarity amongst workers. Moene and
Wallerstein (2006) and Bengtsson (2019) emphasize that have suggested that the creation of social democracy in the 1930s, rather
than following it, preceded many of the features of Scandinavian societies commonly argued to undergird social democratic politics,
such as social harmony. Like our approach, this argument emphasizes how various societal and state institutions respond to the
formation of a powerful social democratic party.
In the context of the model, we introduce a stage of the game preceding the state centralization decision, where citizens decide to
form and delegate power to such a social democratic party. Because, as we have just argued, citizens may be better off ex ante from
state centralization, there is a prima facie case that such an organization, by inducing centralization of bargaining (or of broader
forms of conflict against the elites), might be useful for citizens. The next proposition shows that this is indeed the case, and in fact
that a social democratic party would significantly expand the part of the parameter space where state centralization takes place and
citizens would receive greater utility from the provision of public goods by elites.
Proposition 5. Suppose that Assumptions 1and 2hold, and citizens have a decision to form a social democratic party before the state
centralization decision of the elites. Then, there exists a unique equilibrium. Let Φ*(N) > 1 and Φ
*
(N)be as defined in Proposition 3. There
also exists
<N
^( )
Φ*(N)such that:
1. If
N N N( ) ( ^( ), *( ) ),
then citizens strictly prefer to form a social democratic party, and this induces state centralization on the part of
the elites.
2. If
N N N( ) ( *( ), ^( ) ),
then there is no state centralization.
3. If Φ(N) < Φ
*
(N)or if Φ(N) > Φ*(N), then the elites choose
=s1
regardless of the social democratic party formation decision of citizens.
Proof. Part 1. The utilities of citizens without and with state centralization are, respectively,
= =U s
N
H Y
*[ 0] 1[ ( *(1, 1, 1) ) ( *(1, 1, 1) )],
c e
(22)
and
= =U s H N N N N N N Y N N N
*[ 1] ( *( , , ( )) ) ( ) ( *( , , ( ) )).
c e
(23)
When the citizens form a social democratic party, Lemma 2implies that the elites will choose to centralize the state. Let us define the
threshold
N
^( )
such that (22) is equal to (23), i.e.,
=
H N N N N N N Y N N N
N
H Y
(*( , , ^( ) ) ) ^( ) ( *( , , ^( ) ))
1[ ( *(1, 1, 1) ) ( *(1, 1, 1) ) ].
e
e
Because the left-hand side of this expression is the same as the left-hand side of (11), while the right-hand side is equal to right-hand
side of (11) divided by N, we have that
<N N
^( ) *( )
. Moreover, because the left-hand side is monotonically increasing in Φ(N), we
also have that whenever
>N N( ) ^( ),
citizens ex ante strictly prefer state centralization to a non-centralized state.
Suppose also that
>N N
^( ) *( )
. Then, because
N N N
^( ) ( *( ), *( )),
in this range there will be no state centralization
without a social democratic party (cfr. Proposition 3). Since citizens can induce state centralization by forming a social democratic
party, they strictly prefer to do so in this range.
Part 2. In this range,
N N N( ) ( *( ), ^( ) ),
citizens are better off with a non-centralized state, and so are the elites. Therefore,
citizens choose not to form a social democratic party, and in response, the elite prefer not to centralize the state.
Part 3. This part directly follows from Proposition 3.□
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
18

Intuitively, the option to form a social democratic party turns citizens into Stackelberg leaders, and gives them an option to force
the elites to centralize the state. As a result (and because
<N N
^( ) *( )
), state centralization becomes more likely with a social
democratic party than without. Nevertheless, even in the presence of a social democratic party, the escalation effect is still present,
and citizens may still shy away from inducing state centralization (in the proposition, this will be the case for the parameter values of
Φ(N) between Φ
*
(N) and
N
^( )
if it happens that
<N N
*( ) ^( ),
which is a possibility since these two thresholds cannot be ranked
unambiguously in general; in contrast if
>N N
*( ) ^( ),
citizens will always prefer to form a social democratic party and to induce
state centralization).
24
A straightforward corollary to Proposition 5emphasizes that, compared to Proposition 3, state centralization is now more likely.
Corollary 4. The likelihood of a centralized state and any public good being provided is more likely when the citizens have the possibility to
form a social democratic party. The attractiveness of forming a social democratic party is increasing in the productivity of public good
provision, μ, and decreasing in the heterogeneity preferences of citizens in different regions, λ.
Proof. The first part follows since
<N
^( )
Φ*(N) and thus the parameter space where we have state centralization is larger. The
second part follows as the gain in citizen utility with state centralization is increasing in μand decreasing in λ.□
This corollary thus highlights that the strategic incentive of the elites obtained in Corollary 3was a consequence of the elites
trying to strategically remove the political agenda effect. When the political agenda effect is already incorporated in the investment
decisions of citizens by the presence of it social democratic party, this source of strategic incentive is weakened.
25
6. Partial state centralization
In many societies such as Colombia, the Philippines or Pakistan, lack of full state centralization does not take the form of all elites
and citizens engaging in local conflict, but certain subnational areas acting autonomously (both in terms of conflict and for public
good provision decisions). For instance, in the Philippines the central government in Manila exercises very weak authority over
several parts of the country, in particular, the southern Island of Mindanao where they have set up an autonomous region, currently
called Bangsamoro (Abinales, 2000). The island has been plagued by insurgency since the 1960s (McKenna, 1998), and warlords have
large private armies and operate with impunity (e.g. Human Rights Watch, 2010; Arguillas, 2011). The situation in Pakistan vis-à-vis
the provinces of South and North Waziristan, Balochistan and the semi-autonomous tribal areas, which are all left to be ruled by local
warlords and elites with minimal control of the national state, is similar.
In terms of our model, these situations correspond to partial state centralization which corresponds to a situation where there
exists a well-defined national state, but this state does not extend its control to all the provinces, leaving areas such as Waziristan in
Pakistan and Mindanao in the Philippines to largely autonomous local elites who themselves deal with local demands and conflicts.
To capture this possibility in our model, suppose that in the first stage, instead of a simple decision over state centralization (
=s0
or
1), the elites can form any partition of subcoalitions (e.g., if there are four regions, the first two and the last two could form to
partially centralized local states). Citizens have access to the same technology of coalition formation as in our baseline model,
whereby if region 1 (which is again designated as the strong region without loss of any generality) choose
=Z1,
c
this will induce all
other regions to join in. It is straightforward to see that Lemma 2still holds, and thus the escalation effect continues to be present —
citizens from region 1 know that if they choose
=Z1,
c
then they will be facing the grand coalition of elites.
Our next result shows that in this case, they will often opt for partial state centralization, with detrimental results for citizens.
Proposition 6. Suppose that Assumptions 1and 2hold. Let Φ*(N) > 1 and Φ
*
(N)be as defined in Proposition 3, and recall that
Φ
*
(N) < Φ*(N). There now exists Φ
2
(N)∈(Φ
*
(N), Φ*(N)), such that if Φ(N)∈(Φ
*
(N), Φ
2
(N)), then there will be partial state centralization
and citizens will be worse off than in the case of no state centralization.
Proof. When Φ(N) < Φ*(N), we have from (11) that
<
H N N N N N N Y N N N
H Y
(*( , , ( )) ) ( ) ( *( , , ( )))
(*(1, 1, 1) ) ( *(1, 1, 1)).
e
e
Suppose instead that the elites form a subcoalition of two regions. This gives a new threshold Φ
2
(N) such that
=
H N N N N N N Y N N N
H Y
(*( , , ( )) ) ( ) ( *( , , ( ) ))
(*(1, 2, 1) 2 ) ( *(1, 2, 1) ),
e
e
2 2 2
where θ*(1, 2, 1) refers to the investment level of citizens acting by themselves against a coalition of two regional elites (as captured
24
Scott (2009) emphasizes how many communities in Southeast Asia adopted various strategies to stay outside of the control of the state, mostly
to avoid exploitation.
25
A question beyond the scope of our paper is why other political parties, such as communist or nationalist ones, have not played the same
coordination role as social democratic parties. One possibility is that strong ideological priorities may make it difficult or impossible for a party to
play this coordination role, which necessitates the formation of a broad coalition. Another possibility is that when such parties come to power, they
or some of their leaders tend to attempt to take control of state institutions, undermining any role that they might have played in coordinating non-
elite actions (see also Lipset et al., 1956).
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
19

by the fact that θ
e
is multiplied by 2). Notice that this is the level of investment by citizens when they face a coalition of two regional
elites, but they have themselves not formed the grand coalition. By the same arguments as before, it is clear that Φ
2
(N) < Φ*(N),
because of the presence of 2 on the right-hand side of the above expression. Thus whenever Φ(N)∈(Φ
*
(N), Φ
2
(N)), citizens will not
form their national coalition when elites form a subcoalition of size two (and may not even form their national coalition in response
to a subcoalition of a greater size, the threshold for which can be computed analogously).
Moreover, when this is the case, the elites will always strictly prefer to form such a subcoalition, because this reduces the
probability that citizens win the conflict and thus the necessary transfers. To see this, recall that the threshold Φ
*
(N) is defined such
that
=H N N N N N
N
H(*( , , *( ) ) ) 1(*(1, 1, 1) ).
e e
But we also have
>
N
H
N
H
1(*(1, 1, 1) ) 1(*(1, 2, 1) 2 ).
e e
(24)
To prove the latter, suppose to obtain a contradiction that this is not the case. Since his nonincreasing from Assumption 2this implies
h h(*(1, 1, 1) ) ( *(1, 2, 1) 2 ).
e e
In turn from (4) we have
=
=
h Y
h Y
(*(1, 1, 1) ) ( *(1, 1, 1)), and
(*(1, 2, 1) 2 )) ( *(1, 2, 1).
e
e
Given that Γ″ > 0, θ*(1, 1, 1) ≥ θ*(1, 2, 1). This immediately implies that
>
*(1, 1, 1) *(1, 2, 1) 2 ,
e e
and thus that
>H H(*(1, 1, 1) ) ( *(1, 2, 1) 2 ),
e e
yielding a contradiction. This implies that the two elites are strictly better off by partial state centralization (Note that their prob-
ability of facing strong citizens is given by 2/N, and that if they face strong citizens they share the cost of concessions, and thus they
strictly prefer a partial state when (24) holds).
Thus for Φ(N)∈(Φ
*
(N), Φ
2
(N)), citizens do not form their grand coalition in the presence of partial state centralization of size 2
and the elites are better off in ex ante sense. As a result, partial state centralization of size 2 is preferred to no state centralization
(which was the outcome without this option). This does not prove that the equilibrium will involve partial state centralization of size
2, since partial state centralization of some different size might be preferable for the elites. But it establishes that the equilibrium will
have some partial state centralization as claimed. (And by the same arguments as above we can find the threshold Φ
n
(N)∈(Φ
*
(N),
Φ*(N)) where a partial state of n∈(1, N) elites forms which satisfies Φ(N) < Φ
n
(N), i.e. that the citizens do not form their grand
coalition. In general the best response of the elites is to form the partial state with the highest nthat satisfies this requirement). □
Intuitively, partial state formation takes place as a strategic step by elites to increase their power while still preventing the
political agenda effect. Recall that when Φ(N)∈(Φ
*
(N), Φ*(N)), the elites are able to, and prefer to, prevent the formation of a
national coalition of citizens, thus obviating the political agenda effect. This, in particular, means that they cannot form a national
state, because this will induce citizens to respond with their own national organization. However, when partial state formation is
possible, the elites can take more limited steps to increase their organizational power and ability to fight demands from citizens,
without inducing citizens to form a national organization. When they can do so, this not only leads to a pattern resembling the
patchwork of subnational polities often acting outside of the control of the central state in many developing countries, but also further
reduces the need to provide public goods to citizens to placate them.
7. Concluding remarks
The dominant view in political science is that many states remain incapable of centralizing power and monopolizing the means of
coercion over the territory they ostensibly control, because they face insurmountable barriers to getting stronger. In this paper, we
have argued that states may rather do so because they do not want to build that strength. At the center of our story is a new political
economic force which we have called the political agenda effect. This effect captures the phenomenon that state centralization changes
the nature of the societal conflict against the state and the political elites that control it. If this political agenda effect is sufficiently
powerful, then the elites prefer to live with a non-centralized state (even if state centralization has other direct benefits, for example,
the ability to confront local demands more effectively). The specific channel via which the nature of the conflict against the cen-
tralized state is different than against a non-centralized state in our model is the willingness of citizens with different interests to band
together and shift their demands from parochial ones towards more general-interest ones (such as the provision of general-interest
public goods). This increases the value of conflict to the citizens and encourages them to invest more in their conflict capacity, to the
detriment of the elites who now have to placate stronger demands.
We developed these ideas in the context of the most parsimonious model we could construct which would still help us develop and
elucidate the strategic forces at work. Several straightforward generalizations are possible but were not pursued in this paper to save
space. We now briefly mention those before moving on to areas for future research which we view as more original and promising.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
20

•Our analysis assumed that there were no direct benefits from a centralized state. This is clearly an unrealistic assumption.
Centralized states bring a variety of benefits, ranging from more effective law enforcement and security to more efficient
economy-wide regulation. As explained in Remark 1, introducing such benefits has no impact on our analysis or results, but would
imply that strategic lack of state centralization will have greater social costs.
•Relatedly, an alternative natural assumption would have been that a centralized state also becomes more effective in providing
public goods than a collection of local elites. In the context of our model, this would make the Φfunction also depend directly on
whether the state is or is not centralized. It would also provide a direct mechanism via which a centralized state would be
associated with public good provision. We chose not to make this assumption both on the grounds of parsimony and because the
result that there will be an association between state centralization and effective public good provision is true in our model for a
more interesting, endogenous reason — because without state centralization, specific, parochial transfers are the most economical
way for the elite to meet citizen demands.
•An extension related to the previous point might be useful to develop. If a centralized state is necessary for public good provision
(which is in contrast to our baseline model, where there is no technological benefit for public good provision from state cen-
tralization), the elites may strategically choose a non-centralized state even against the grand coalition of citizens, because this
would be a strategic commitment to preventing public good provision, and when the resources captured in contest cannot be
invested in public goods, the grand coalition of citizens becomes less effective. This extension is straightforward to develop and we
did not do it to conserve space, even though we do find it interesting and potentially relevant for thinking about lack of state
centralization in some contemporary cases.
•We also chose not to assume that a citizen organization can directly control the investment decisions of each of its constituent
parts. But as shown in the Appendix, our (qualitative) results are identical when we introduce such control and thus remove the
free-riding in citizen investment decisions.
•Yet another alternative assumption is to introduce economies of scale in the provision of public goods, which wouldgo in the same
direction of the regional spillovers we have used in the Φfunction. Once again, this would have no impact on our analysis or
results.
We view our paper as part of a broader investigation. As already discussed in the Introduction, a few other papers have already
proposed models in which states may strategically opt to remain weak (e.g., as a commitment not to expropriate, as in
Acemoglu, 2005; as a way of preventing rivals having an effective means of taxation, as in Besley and Persson, 2009; or as an effort to
prevent the formation of a powerful army capable of sharing rents, as in Acemoglu et al., 2011b). There are also several fruitful areas
for future investigation. Here we mention a few.
•Our simplified modeling of heterogeneity across regions enabled a coalition of citizens, once formed, to formulate its demands
effectively. Richer forms of heterogeneity would necessitate such organizations to mediate within-citizen conflicts and aggregate
their heterogeneous preferences. Which types of coalitions or organizations can do so and how this interacts with the elite-citizen
conflict and the state centralization decisions is a completely underresearched area.
•Also absent in our, and all other economic analyses to the best of our knowledge, is Habermas’s notion, mentioned in the
Introduction, that the formation of states paves the way for the emergence of ‘public spheres,’ which then impact the evolution of
opinions. In a political economic setting, this can be interpreted as communication and information exchange improving following
state centralization, which then impact how individuals would vote or make demands. Lack of state centralization can again
emerge strategically in anticipation of different types of demands that will follow from this process.
•One of the most influential theories concerning state formation in social science is Tilly’s (1995), linking state formation to war-
making and the threat of war. The forces we have emphasized, as already anticipated in the Introduction, do not contradict this
emphasis, but our analysis has abstracted from it. An interesting direction is to investigate the interplay between war and the
strategic motives for opting for a non-centralized state. Beyond some obvious, but still interesting, comparative statics (e.g.,
showing that the forces we have emphasized become less important in the presence of the threat of war), such an extension could
allow an investigation of whether some types of states with the capability to wage war while still strategically discouraging
citizens from forming effective coalitions to make demands could emerge.
•Our analysis, like almost all other work in this topic in political economy, has abstracted from the internal organization of the
state, which is an important and underresearched area. Centralized states behave differently than non-centralized ones in many
dimensions (e.g., development of professional bureaucracies, adherence to the rule of law, etc.), which may be because the
internal organization of a centralized state develops very differently than a non-centralized one. These considerations may also
informe the extent to which state centralization is irreversible — after some amount of centralization, it may be impossible for the
elite to reverse course. This is another important area that can be investigated in future work.
•Another interesting direction is to study why, as mentioned in footnote 25, it may have been difficult for other parties to play the
same role of social democratic parties, and what other organizations and institutions also coordinate different citizen demands
and thus supporting the process of state centralization.
•Last but not least, this area has very little empirical work (beyond those cited in the Introduction, which show the importance of
state capacity). Whether centralized states change the nature of societal organization and how the anticipation of this impacts
political equilibria are interesting, albeit difficult, areas to study empirically.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
21

Acknowledgment
We thank editor Timur Kuran, two referees, seminar participants at the Canadian Institute for Advanced Research conference,
CEMFI, Chicago-Northwestern Political Economy Conference, George Mason University, the Chr. Michelsen Institute, Nova School of
Business and Economics Universidade De Lisboa, the University of East Anglia, the University of Oslo, and the University of Illinois,
Urbana-Champaign for comments and suggestions, and Layne Kirshon for excellent research assistance. Acemoglu gratefully ac-
knowledges financial support from the ARO MURI Award No. W911NF-12-1-0509.
Appendix A. Omitted proofs and additional results
In this Appendix we first present the proofs of Lemmas 1and 2. We then turn to extensions of the model, where we first study the
case of endogenous investments in the conflict capacity of elites, thereafter allow for subcoalition formation of citizens, and finally
remove the free-rider effect in investment in conflict capacity.
Omitted proofs
Proof of Lemma 1. Suppose that the coalition of citizens is
=z1
c
with
=
=n,
z1
c
and is in conflict with a coalition of elites
=z1
e
with
=
=n
z e1
e
. The citizens have at this stage invested in their conflict capacity, and denote their total conflict capacity by
˜c
and
the total conflict capacity of the elites by
˜e
(in the case with exogenous conflict capacity of elites,
=n
˜,
ee e
but
˜e
could be different
than this when elites invest in their conflict capacity as we consider below, and this lemma applies in that case also).
Consider first the case where
=
=
f1,
e
zc1
i.e., where there is fighting. The cost of conflict capacity for each group of regional
citizens is at this stage sunk and we simply denote it by Γ
i
for group i, and thus the expected utility of each group of regional citizens
=
iz1
c
from this conflict is given by
= =
=
U f H n n Y
n
1 ( ˜ ˜ ) ( ) ,
icec e e
i
zc1
(A.1)
where
H(˜ ˜ )
c e
is the probability the citizens win the fight, Φ(n) the (maximum) marginal utility of funds for each group of
regional citizens, and n
e
αY/nthe income gain for each group of regional citizens in the coalition if they win.
The expected utility of each elite
=
iz1
c
from the conflict is similarly given by
= =
=
U f H Y1 [1 ( ˜ ˜ )] .
ieec e
zc1
(A.2)
We next contrast this expression with the case where
=
=
f0,
e
zc1
i.e., where the elites make an offer that the citizen side prefers to
fighting. Denote the utility that each citizen group
=
iz1
c
obtains without fighting by
=
=
U f 0
ice
zc1
. For the citizens not to fight
all members of the coalition must prefer to accept the offer from the elite coalition. This requires that the following participation
constraint
= =
= =
U f U f0 1
iceice
zczc
1 1
should hold for each
=
iz1
c
. Since utility is transferable across citizens of different regions (by choosing the level of transfers and
public good provision), we can combine these participation constraints as
= =
=
=
=
=
U f U f0 1 .
i
ice
i
ice
zczc
zczc
1
1
1
1
Since defeat has identical conclusions for all regional elites, as also noted in the text, all n
e
members of the coalition of elites
contribute equally, and denoting the total costs of concessions to the citizens by B, the symmetric maximization problem for each
regional elite is
= =
=
=
=
=
YB
nU f U fmax subject to 0 1 ,
Be
i
ice
i
ice
0zczc
zczc
1
1
1
1
where substituting for the elite coalition’s transfers, we also have
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
22

= =
=
=
=
U f n B0 ( ) .
i
ice
i
i
zczc
zc
1
1
1
Next substituting for
=
=
U f 1 ,
ice
zc1
this maximization can be expressed as
= =
YB
n
n B H n n Ymax subject to ( ) (˜ ˜ ) ( ) .
Be
i
i
c e e
i
i
0zczc
1 1
Since the joint utility of the elite coalition is decreasing in B, it will choose Bto make the joint participation constraint of the citizen
coalition hold with equality. This gives
=B H n Y(˜ ˜ ) ,
c e e
and substituting this into the utility of regional elites without fighting, we have that for each elite
=
iz1
e
= =
> = =
=
=
U f H Y
H Y U f
0 (1 ( ˜ ˜ ) )
(1 ( ˜ ˜ )) 1 ,
ieec e
c e
iee
zc
zc
1
1
which establishes that each regional elite
=
iz1
e
is strictly better off with policy concessions than with fighting, and completes the
proof of the lemma. □
Proof of Lemma 2. Suppose that citizens have formed a coalition
=z1
c
with
=
=n1
z1
c
(as usual including region 1, which is
without loss of any generality the region with strong citizens).
Consider first the elites in regions
=
iz1
c
. If these elites join the coalition
=,
z1
e
they participate in giving policy concessions
(or in fighting), while if they do not participate in the coalition they face weak citizens that will not be able to make any demands.
Since, in view of the fact that h( ·) is strictly positive over the relevant domain, policy concessions always have to be strictly positive,
and elites in regions
=
iz1
c
are strictly better off by not joining the coalition
=z1
e
. This establishes that
=z1
e
=z1
c
.
Consider next the elites
=
iz1
c
(where citizens have joined the coalition
=z1
c
with the strong citizens from region 1). Let us
denote the investment in conflict capacity of citizens from region iin
=z1
c
by
,
i
c
so that the total conflict capacity of the coalition of
citizens is
=
ii
c
zc1
. Suppose that the elite coalition
=z1
e
forms in response and has n
l
≤nmembers. The utility of the regional
elite
=
iz1
e
without state centralization can then be written
= =
=
U n s H n Y[ | 0] 1 ,
iel
jj
cl e
zc1
which incorporates from Lemma 1that there will be policy concessions rather than fighting.
Now to obtain a contradiction suppose that
= = ,
z z1 1
e c
which implies n
l
<n. Consider a subcoalition of elites
=
= =
zz z
11 1
ec e
with size n
m
≤n
l
(if on the other hand n
m
>n
l
, the same argument applies with the two coalitions
=z1
e
and
=z1
e
swapped around). The utility of an elite iin
=z1
e
is
= = =
=
U n s H n Y U n s[ | 0] 1 [ | 0],
iem
jj
cm e iel
zc1
where the last inequality follows as n
m
≤n
l
and H( · ) is increasing. To complete the proof, now consider a regional elite jin
=z1
e
deviating and switching to join
=z1
e
. The size of this new coalition
=j{ }
z1
e
will be
+n1,
l
thus giving each of its members,
=
i j{ }
z1
e
a utility of
+ = = + > =
=
[ ]
U n s H n Y U n s[ 1| 0] 1 ( 1) [ | 0],
iel
jj
cl e iel
zc1
where again the last inequality follows because H( ·) is increasing. This establishes that any elite group that is not part of the largest
coalition, in this instance
=,
z1
e
would be strictly better off by joining it. Since
=z1
e
=z1
c
from the first part of the proof, this
establishes that
=
=z1
e
=,
z1
c
completing the proof. □
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
23

Endogenous conflict capacity of elites
We now extend the model to include endogenous conflict capacity also of the elites. In particular, we assume that the conflict
capacity
i
e
of each regional elite iresults from investments with a strictly increasing, convex and continuously differentiable cost
function
( ),
ei
e
with
=(0) 0,
e
and
( ),
e i
e
>( ) 0
e i
e
for
>0
i
e
. The timing is the same as in the main model, with the only difference
being that citizens and elites make their conflict capacity investments simultaneously.
As already noted in its proof, Lemma 1directly generalizes to this case. To see that Lemma 2also generalizes, one needs to modify
its proof so that the switch is always to the elite coalition with the greatest total power (rather than simply with the largest number of
members). Using these results, we can now carry out an analogous analysis to that in the text to show that the results presented in the
text generalize with only minor modifications.
Equilibrium without a centralized state
Given Lemma 1, elites will invest in their conflict capacity to reduce the policy concessions they have to make (since these reduce
the benefit for fighting for citizens). Since from Lemma 2,
=
= = ,
z z1 1
c e
we set
= =
= = n,
z z1 1
c e
and write the maximization
problem for each elite
=
iz1
e
as
=
H n Ymax 1 ( ),
c
j
j
eei
e
0
i
e
ze1
where we have already imposed the equilibrium result that citizens in coalition
=z1
c
have chosen the same level of conflict capacity,
which is denoted by θ
c
. The first-order condition for each elite
=
iz1
e
can be found as
=
=
h n Y ( ) 0,
c
j
j
ee ie
ze1
(A.3)
with the second-order condition
<
=
h n Y ( ) 0.
c
j
j
ee ie
ze1
(A.4)
We continue to impose Assumption 2, and in particular that h′( · ) ≤ 0. For the second-order conditions of elites, this implies that
we need to have |h′( ·)| not too large, which we assume in the remainder of the Appendix. This also assumes that the solution for the
elite is also unique given θ
c
. Moreover, as already noted in the text, the investment of citizens is increasing in θ
e
(because h′( · ) ≤ 0),
and with the same reasoning, the investment of elites is decreasing in θ
c
. This implies that under h′( · ) ≤ 0 and |h′( · )| sufficiently
small so that the second-order condition always holds, the equilibrium is unique. Let us denote the unique equilibrium level of
conflict capacity of elites in the coalition
=z1
e
by θ
e*
(n, n), where the first argument conditions on the size of the coalition of citizens
and the second argument designates conditioning on the size of the coalition of elites.
Note also that the maximization problem (imposing equilibrium behavior by elites) and the resulting investment levels by citizens
are the same as in equation (4) in the text, with the only difference being that θ
e
is now replaced by θ
e*
(n, n). As already anticipated,
the second-order conditions of citizens are always satisfied. For future reference in this Appendix, we repeat this condition here as
=
=
h n n n n Y
*( , ) ( ) ( ) 0,
j
j
ceic
zc1
(A.5)
and denote its solution by θ*(n, n,Φ(n)) as in the text.
Let us next turn to the coalition decision of citizens from region 1, which are once again designated the strong ones without loss of
any generality. Suppose first that
=
={1}
z1
c
. Then noting that in this case the size of the coalition is 1 and from Assumption 1,
=(1) 1,
the utility of citizens from region 1 becomes
= =U s H Y
*[1| 0] ( *(1, 1, 1) *(1, 1)) ( *(1, 1, 1)) .
ce
1
(A.6)
The utility of elites from region 1 in this case is given by
= =U s H Y
*[1| 0] [1 ( *(1, 1, 1) *(1, 1)) ] ( *(1, 1)).
ee
e
e
1
(A.7)
Note again that the most efficient way of transferring resources for the elite is a direct transfer, so there will be no investment in
public goods. That is,
=T H Y(*(1, 1, 1) *(1, 1) )
e
1
and
=G0
1
.
Suppose next that
=
=z1
c
. Then the utility of citizens becomes
= =U N s H N N N N N N N N Y N N N
*[ | 0] ( *( , , ( ) ) *( , ) ) ( ) ( *( , , ( ))),
c e
(A.8)
and similarly the utility of elites is
= =U N s H N N N N N N N Y N N
*[ | 0] [1 ( *( , , ( )) *( , )) ] ( *( , )).
e e
e
e
(A.9)
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
24

Since from Assumption 1, we have Φ(N) > 1, we can immediately conclude that
=T0
i
and
=G µ H N N N N N N N Y(*( , , ( ) ) *( , ) )
ie
for all
i
.
As in the text, citizens from region 1 will prefer to form the grand coalition of citizens when their utility from the grand coalition,
(A.8), is strictly greater than their utility from standing alone, (A.6). The former, (A.8), is increasing in Φ(N) with exactly the same
argument as in footnote 16, while the latter, (A.6), is independent of Φ(N). Therefore, once again there exists a value of Φ(N), Φ*(N),
such that
=
H N N N N N N N N Y N N N
H Y
(*( , , *( ) ) *( , )) *( ) ( *( , , *( )) )
(*(1, 1, 1) *(1, 1) ) ( *(1, 1, 1)),
e
e
(A.10)
and whenever Φ(N) > Φ*(N), citizens from region 1 (the strong citizens) will prefer the grand coalition, and whenever
Φ(N) < Φ*(N), they will prefer to act by themselves.
The coalition formation decision of citizens, and the resulting utility levels for citizens, are thus identical to the ones summarized
in Proposition 1, with the only difference being that θ
e
is now replaced by θ
e*
(1, 1) when Φ(N) < Φ*(N), and is replaced by θ
e*
(N, N)
when Φ(N) > Φ*(N). The corollary that determines the expected utility of elites in different regions of the parameter space, which
will be useful in our analysis in the rest of the Appendix becomes:
Corollary 5. When Φ(N) < Φ*(N), the expected utility of elites is
= =U s
N
H Y
N
*[ 0] 1 ( *(1, 1, 1) *(1, 1) ) 1(*(1, 1) ).
e e
e
e
(A.11)
When Φ(N) > Φ*(N), the expected utility of elites is
= =U s H N N N N N N N Y N N
*[ 1] [1 ( *( , , ( ) ) *( , )) ] ( *( , )) .
e e
e
e
(A.12)
Equilibrium under a centralized state
The coalition decision of citizens can be analyzed similarly to the one without state centralization, and it continues to be the case
that the choice for citizens from region 1 is once again simply between
=
={1}
z1
c
and
=
=z1
c
. Because when they choose
=
={1},
z1
c
=(1) 1,
their overall utility under state centralization will be
= =U s H N N N Y N
*[1| 1] ( *(1, , 1) *(1, )) ( *(1, , 1) ),
ce
1
while when they choose
=
=,
z1
c
their overall utility under state centralization will be
= =U N s H N N N N N N N N Y N N N
*[ | 1] ( *( , , ( ) ) *( , ) ) ( ) ( *( , , ( ))).
c e
The comparison of these two expressions once again boils down to
>
H N N N N N N N N Y N N N
H N N N Y N
(*( , , ( ) ) *( , ) ) ( ) ( *( , , ( ) ) )
(*(1, , 1) *(1, )) ( *(1, , 1) ).
e
e
As in the main text, this condition always holds. To see this, first note that θ
e*
now responds to the changes in the size of the citizen
coalition. In particular, from (A.3) it follows that θ
e*
is decreasing in the size of the citizen coalition, and thus θ
e*
(1, N) > θ
e*
(N, N).
Then with the same argument in the text holding a fortiori including this additional effect, we have that
>
H N N N N N Y N N N
H N N Y N
(*( , , ( )) ) ) ( *( , , ( ) ) )
(*(1, , 1) ) ( *(1, , 1)),
e
e
which implies the desired condition given that Φ(N) > 1 and θ
e*
(1, N) > θ
e*
(N, N). Thus the results are essentially identical to those
in Proposition 2, and the expected utility of elites under state centralization is given by
Corollary 6. When there is state centralization (
=s1
), the equilibrium utility of elites is given by
= =U s H N N N N N N N Y N N
*[ 1] [1 ( *( , , ( ) ) *( , )) ] ( *( , )) .
e e
e
e
(A.13)
Equilibrium state centralization
We now characterize the state centralization decision of elites by combining the results from Corollaries 5and 6. The reasoning is
similar to the analysis in the main text: the elites prefer state centralization if and only if (A.13) exceeds (A.11). Note that (A.13) is
decreasing in Φ(N), while (A.11) is independent of Φ(N). Thus the elites (strictly) prefer state centralization if and only if
Φ(N) < Φ
*
(N), where Φ
*
(N) is defined by
+
= +
H N N N N N N N Y N N
N
H Y
N
(*( , , *( )) *( , )) ( *( , ))
(*(1, 1, 1) *(1, 1) ) 1(*(1, 1)).
e
e
e
e
e
e
(A.14)
The only difference from the analysis in the main text is that, because of the presence of the cost function of the elites in (A.14), it is
no longer necessarily the case that Φ*(N) > Φ
*
(N) when Φ*(N) > 1.
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
25

Proposition 7. Let Φ*(N)be as defined in (A.10) and Φ
*
(N)as defined in (A.14), and suppose that Assumptions 1and 2hold (and that |h′|
is not so large, so that the second-order condition of elites, (A.4), holds). Then:
1. If Φ
*
(N) < Φ*(N)we have
(a) If Φ(N) < Φ
*
(N), then the elites choose state centralization (
=s1
).
(b) If Φ
*
(N) < Φ(N) < Φ*(N), then the elites choose a non-centralized state (
=s0
).
(c) If Φ*(N) < Φ(N), then the elites choose state centralization (
=s1
).
2. If Φ
*
(N) > Φ*(N), then the elites choose a non-centralized state (
=s0
).
Proof. Part 1: We now have three possibilities. In part a, where Φ(N) < Φ
*
(N), (A.11) is strictly less than (A.13), and thus the elites
prefer a centralized state (with citizens forming their grand coalition) to a non-centralized state, and choose
=s1
. In part b, where
Φ
*
(N) < Φ(N) < Φ*(N), then (A.11) is strictly greater than (A.13), and thus the elites prefer a non-centralized state to forming a
centralized state (because a centralized state would induce citizens to form their grand coalition), and thus choose
=s0
. In part c,
where Φ(N) > Φ*(N), the citizens will always form their grand coalition, and in response, the elites will also do so; thus
=s1
.
Part 2: In this case, where Φ
*
(N) > Φ*(N), either the citizens or the elites (or both groups) prefer a centralized state, and since
both groups can induce this possibility by forming their grand coalition, we have
=s1
.□
It is also straightforward to see that we have a version of Corollary 3, showing that comparative statics with respect to the
productivity of public goods or the degree of preference heterogeneity across regions are non-monotonic. Overall, this analysis shows
that when the conflict capacity of elites is endogenous, our main results generalize with minimal qualifications.
Subcoalition formation of citizens
In the text, when the strong citizens organized, all weak citizens could join their coalition (unless the strong citizens decided to
stand alone). Because citizens from weak regions always prefer joining a coalition involving the strong citizens, such organizations
always lead to the formation of the grand coalition of citizens, and the relevant choice for strong citizens was between standing alone
and forming the grand coalition. We now extend the basic model and assume that strong citizens can invite specific regions to join the
coalition, thus enabling them to choose the exact size of the coalition, denoted by nin this part of the Appendix. (Since all other
regions are symmetric, which specific regions are included in the coalition is immaterial). Therefore, the choice of strong citizens is
over coalitions of sizes
= …n N1, 2, ,
.
In this case, though the general qualitative forces remain the same, the analysis becomes more involved. To make progress, we
now analyze the case in which His uniform and Γ is quadratic, and show that, under some additional mild conditions, there will never
be a coalition other than the singleton of the strong citizens or the grand coalition of all citizens, and thus the results from the text
continue to apply unchanged. We then study the case in which His uniform but Γ is an arbitrary convex function to show that even
when citizens choose to form an “interior” subcoalition (i.e., a subcoalition greater than a singleton and smaller than their grand
coalition), the elites prefer a non-centralized state under similar conditions to those in the text.
Note first that Lemmas 1and 2continue to hold. This, in particular, implies that whenever strong citizens choose a coalition of
size n, they know that they will be facing an elite coalition of size n, which will then make them an offer to cease conflict in return for
their expected return from the conflict.
Let us simplify the analysis here by treating nas a continuous variable, which will enable us to derive a first-order condition for an
interior subcoalition decision of citizens.
As in the text, payoffs of citizens from region
=
iz1
c
with
= =
= = n
z z1 1
c e
are given from (5) as
= =U n s H n n n n n n Y n n n
*[ | 0] ( *( , , ( ) ) ) ( ) ( *( , , ( )) ).
i
ce
(A.15)
Let us next replace Assumption 2with the following:
Assumption 2″.
(i)
= +H h h( ) ,
1 0
(ii)
= +( ) ,
k
1
2
2
(iii) h
1
αY > 1, and
(iv)
hk
1
1
5
.
Part (iii) of the assumption ensures that the investment level of citizens will be positive over the support of H, while the last part
also requires the density of Hnot to be too low.
The first-order conditions of citizens from region 1, (4), for investment choice gives
= =n n n h n Y k h n Y n
*( , , ( ) ) ( ( ) ) ( ( ) 1) *( ( ) ),
11 1
(A.16)
where we have simplified notation by defining θ* as a function of Φ(n) only, since in this case, nonly matters for θ* via its effect on
Φ(n). This allows us to rewrite (A.15) as
= =U n s H n n n n Y n
*[ | 0] ( *( ( ) ) ) ( ) ( *( ( ) )).
i
ce
Then treating nas a continuous variable, the derivative of this which must equal zero in a first-order condition for an interior
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
26

subcoalition decision is
=
= + +
dU n s
dn
h n Y n n N
N
d n
dn
H n n n Y d n
dn
nN
N
d n
dn
*[ | 0] ( ) *( ( ) ) *( ( ))
( )
( )
(*( ( ) ) ) ( ) (*( ( ) )) *( ( ) )
( )
( )
c
e
e
11
for some n∈(1, N). Now substituting for Γ′(θ*(Φ(n))) from (A.16), this expression can be simplified to
=
= +
+
dU n s
dn
h n Y n
H n n n Y d n
dn
h n Y n N
N
d n
dn
*[ | 0] ( ) ( *( ( ) ) )
(*( ( ) ) ) ( ) ( ) ( 1) *( ( ))
( )
( ) .
c
e
e
11
1
(A.17)
Note that the last two terms on the right-hand side are nonnegative. Thus, if θ*(Φ(n)) > θ
e
then the payoff of the strong citizens in
region 1 is increasing in the number of groups of regional citizens nin the coalition, and we have a corner solution at
=n N
. This
already reveals that for an interior solution to the subcoalition decision we need θ
e
to be sufficiently large.
Consider next the case where θ*(Φ(n)) < θ
e
. In this case
=dU n s dn
*[ | 0]/
c
1
starts out negative since at
=n1,
=d n dn( )/ 0,
and in
(A.17), we are left only with the first, negative term. We will next show that there exists no local maximum for
=U n s
*[ | 0]
c
1
with
n∈(1, N), so that the optimal choice for citizens from region 1 will be either
=n1
or
=n N
. Recall first that there exists a unique n*
such that Φ(n) > 1 for n>n* but
=n(*) 1
. Thus clearly
= <dU n s dn
*[ | 0]/ 0
c
1
for n<n*, and the relevant parameter region for
coalition formation is: n>n*. Here
=d n dn µ( )/ (1 ) ,
and also from (A.16) we have
=N N kh Y
*( ( ))/ ( ) 1
. Therefore,
assuming an interior solution and substituting for
H n n n(*( ( ) ) )
e
with
h nk h n Y n( ( ( ) 1) ),
e
1 1
we can rewrite (A.17) as
=
=
+ +
+
dU n s
dn h n Y k h n Y
h Y nk h n Y n h µ
h n Y n kh Y µ
*[ | 0] ( ) ( ( ( ) 1) )
( ( ( ) 1) )(1 )
( ) ( 1) (1 ) ,
c
e
e
11 1
1 1 0
1 1
(A.18)
and also,
=
=
+
+ <
d U n s
dn h Y k h n Y µ
n kh Y µ
n kh Y µ
*[ | 0] 2 ( ( ( ) 1) )(1 )
(2 1) (1 )
2 ( ) (1 ) 0
c
e
21
21 1
1
22 2 2 2
1
22 2
(A.19)
as the second-order condition.
Now for a solution to (A.18) to be an interior subcoalition choice, (A.18), implies that we must have
=
+
+
+ +
n µn n k h n Y
nk h n h µ n n kh Y µ
n
1
( ) (1 ) [ ( ) ( ( ) 1)
[ ( ( ) 1) ] (1 ) ( 1) ( ) (1 ) ]
( ),
e1
1 0 1
(A.20)
where the second line defines Θ(n).
For any solution to (A.18) to be an interior subcoalition choice, we need the second-order condition (A.19) to be satisfied. The
following condition is then sufficient for this second-order condition to be violated whenever (A.18) holds and to ensure that there
exists no local maximum:
+ + >
h Y k h n Y n µ
n kh Y µ n kh Y µ
2 ( ( ( ) 1) ( ) )(1 )
(2 1) (1 ) 2 ( ) (1 ) 0.
1 1
1
22 2 2 2 1
22 2
Substituting from (A.20) and rearranging, this can be written as
+ + +
< +
+ +
+ +
n k h n Y nk h n Y h µ n n kh Y µ
n k h n Y k h n Y n µ
n n kh Y µ n n kh Y µ
n kh Y n kh Yn µ
( ) ( ( ) 1) [ ( ( ) 1) ] (1 ) ( 1) ( ) (1 )
( ) ( ( ) 1) ( ( ) 1) (1 )
1
2( ) (1 ) 1
2(1 )
( ) ( ) (1 ) .
1 1 0 1
1 1
1 1 2 2
21 1
Now canceling the first term on the left-hand side with the first term on the right-hand side, the first part of the second term
(excluding h
0
) with the second term on the right-hand side, and moving the third term on the left-hand side to the right-hand side and
collecting terms with the third term and the last term on the right-hand side, we obtain the following sufficient condition:
< + + +h µ n kh Y µ n n kh Y n n kh Y µ(1 ) ( ) (1 ) 1
2( ) 1
2(1 ) .
0 1 21 1 2 2
(A.21)
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
27

From the assumption that we have a symmetric uniform distribution,
=h,
h
0
1
21
and from the last part of Assumption 2″,αYh
1
> 1, and
thus
>Y h2 .
0
Since Φ(n) ≥ 1, n> 1, and
<µ(1 ) 1,
the combination of the first two terms on the right-hand side is no less than
>kh Y µ kh h µ(1 ) 5 (1 ) ,
5
21 1 0
and in view of the fourth part of Assumption 2″,(A.21) is satisfied. This establishes:
Proposition 8. Suppose Assumptions 1and 2″ are satisfied. Then there will never be subcoalition formation of citizens, and the results from
the text apply identically.
Suppose next that the cost function is not quadratic, but satisfies the condition that Γ′(θ) < ∞ for all
+
e
for some ε> 0
(whereby this condition simply requires that citizens’ investment in conflict capacity exceed θ
e
), while His still uniform. The analysis
is similar in this case, except that we have
=n h n Y
*( ( ) ) ( ( ) ) ,
11
and thus
= =
d n
d n
h Y n
h n Y
h Y µ
h n Y
*( ( ) )
( )
( )
( ( ) )
(1 )
( ( ) ) .
1
1
1
1
In fact, θ*(Φ(n)) is everywhere strictly increasing in Φ(N), and for Φ(N) sufficiently large, θ*(Φ(n)) > θ
e
.
Now rearranging the first-order condition of citizens from region 1 for subcoalition formation, (A.18), we obtain
=
+
+
+ +
n n µ n h n Y n h n Y µ
n n µ h Y µ
h n Y h µ
n
1
( ) (1 ) [ ( ) ( ( ) ) ( ( ) ) (1 )
( 1) ( )(1 ) (1 )
( ( ) ) (1 ) ]
( ).
e1111
1
1
0
We can no longer rule out an interior subcoalition, but we can still show that lack of state centralization can emerge for a wide range
of parameter values in this case. To do this, note that for an interior solution to exist, we need
n( )
e
for some n∈(1, N) (since otherwise (A.18) cannot be satisfied for any interior subcoalition, and we are back to the conclusion of
Proposition 8). Next, it is straightforward to verify that Θ(n) is increasing for nsufficiently large. This implies that there exists a
maximal
n¯
such that any subcoalition will be less than
n¯
(where
n¯
is defined such that θ
e
< Θ(n) for all
>n n¯
). Note that this
n¯
is
independent of N.
Suppose this condition does not hold, so that there is a choice of interior coalition at
n n
˜(1, ¯]
(where the fact that the size of the
subcoalition is less than
n¯
follows from the previous paragraph). Then the question is whether the elites will still choose a non-
centralized state. The condition for that is now
>
n
N
H n n n Y H N N N Y(1 ˜(˜*( ( ˜) ) ˜) (1 ( *( ( ) ) )) ,
e e
(A.22)
for some choice of intermediate subcoalition
n
˜
. Rearranging this condition, we obtain
<N n h Y N h N Y n h n Y(˜) [ ( ( ) ) ˜( ( ˜) )].
e2 2 1211211
But since
n
˜
is less than
n¯,
which is independent of N, and because
=N h N Y
*( ( )) ( ( ) )
11
will exceed θ
e
for Φ(N) sufficiently
large, we have that this condition will necessarily be violated for Nsufficiently large. Thus we have proved:
Proposition 9. Suppose Assumption 1is satisfied, and let H( · ) be uniform and suppose that there exists ε> 0 such that Γ′(θ) < ∞ for all
+
e
. Then, there exists
N
¯
such that for all
>N N
¯,
the elites will choose a non-centralized state (
=s0
) even if citizens form a
subcoalition of size less than N.
In contrast to Proposition 8, which generalizes the results from the text by establishing that citizens will not form an intermediate
coalition, this result shows that, when the size of society (in terms of the number of regions or different groups) is sufficiently large, a
non-centralized state will emerge as an equilibrium phenomenon even when citizens prefer to form an intermediate coalition.
Removing the free-rider effect
We now extend our baseline model by allowing citizen coalitions to jointly decide their investments in conflict capacity, which
will remove the free-rider effect in investment decisions of citizens. Hence, the equivalent of (3) in the text now becomes
== =
H n n nYmax ( ) ( ),
j
i
ce
i
i
c
{ }
i
c
izczczc
11 1
D. Acemoglu, et al. Journal of Comparative Economics xxx (xxxx) xxx–xxx
28

where recall that
=
=n
z1
c
.
Notice two differences relative to (3). First, the value of victory in this conflict is now multiplied by n, which is the size of the
coalition of citizens,
=z1
c
. This reflects the fact that the maximization is now from the viewpoint of the coalition, thus the return to
winning the conflict is the total resources that the coalition will control following such a victory, nY. Second, the coalition also
directly controls the decisions of all regions that are part of the coalition, as reflected by the fact that the maximization is over
=
{ } ,
i
c
izc1
and the total cost of investment of all of these groups is subtracted from the gross return. These two differences together
imply that there is no longer the free-rider effect in the investment decisions (which was present in the text because each group of
citizens in the coalition failed to internalize the benefit that it would create on other members of the coalition). As a consequence, the
level of investment in conflict capacity by citizens in this case is always greater than the one in the text. More formally, denoting the
level of investment in this case by
n n n
¯*( , , ( ) )
, we have the equivalent of (4) in the text — the first-order condition that this
investment satisfies — as
=h n n n n n n Yn n n n(¯*( , , ( )) ) ( ) ( ¯*( , , ( )) ) 0.
e
(A.23)
The comparison of this equation to (4) immediately yields
>n n n n n n
¯*( , , ( ) ) *( , , ( )).
The rest of the analysis proceeds as before, and the relevant choice for citizens from region 1 is once again to engage in conflict by
themselves vs. to form the grand coalition. Which one they will prefer will again depend on whether Φ(N) is above a critical
threshold, which is now denoted by
N
¯*( )
. Moreover, this threshold is again given by a condition that is essentially identical to (11),
except that
¯*
replaces θ*; this captures the fact that the investment decisions of different coalitions will now satisfy the first-order
condition (A.23) rather than (4). Namely:
=
H N N N N N N Y N N N
H Y
(¯*( , , ¯*( ) ) ) ¯*( ) ( ¯*( , , ¯*( )) )
(*(1, 1, 1) ) ( *(1, 1, 1))
e
e
(where we have also incorporated the fact that
=
¯*(1, 1, 1) *(1, 1, 1),
since there was no free-rider problem when citizens from
region 1 were acting by themselves).
Since the monotonicity arguments are identical to those in the text, this condition then immediately shows that citizens from
region 1 will choose to form their grand coalition whenever
>N N( ) ¯*( )
. Since
>N N N N N N
¯*( , , ( ) ) *( , , ( )),
we also have
<N N
¯*( ) *( )
, which simply reflects the intuitive idea that when the free-rider problems are not present, citizens will invest more in
a coalition, and thus forming the grand coalition becomes more attractive. A similar argument can also be used to define the analog of
threshold Φ
*
(N),
N
¯*( )
. Because the grand coalition of citizens is now investing more in their conflict capacity, state centralization
becomes less attractive to elites. As a consequence, this new threshold satisfies
<N N
¯*( ) *( )
. Using these thresholds and following
identical steps to the proof of Proposition 3, we establish:
Proposition 10. Suppose that citizen coalitions are not subject to the free-rider problem in their investments in conflict capacity. Then
Proposition 3holds with Φ
*
(N)replaced by
N
¯*( )
and Φ*(N)replaced by
N
¯*( )
.
This proposition thus shows that, qualitatively, all of the results from the text apply in this case as well. Corollary 3also applies
identically.
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