No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach
Abstract
We consider the performance and incentive compatibility of voting rules in a Bayesian environment: agents have independent private values, there are at least three alternatives, and monetary transfers are prohibited. First, we show that in a neutral environment, meaning alternatives are symmetric ex-ante, essentially any ex-post Pareto efficient ordinal rule is incentive compatible. Importantly, however, we can improve upon ordinal rules. We show that we can design an incentive compatible cardinal rule which achieves higher utilitarian social welfare than any ordinal rule. Finally, we provide numerical findings about incentive compatible cardinal rules that maximize utilitarian social welfare.
... The results on approval voting in Sect. 4 of this paper can be seen as complementary to the findings of Giles and Postl (2014), but extended to an arbitrary number of alternatives and a large number of voters. Kim (2014) pushes this investigation further. In a setting with three or more alternatives, and voters with independent (but not identically distributed) random utilities, he characterizes the rules which are ex ante Pareto efficient in the class of ordinal voting rules: they are "non-anonymous" rank scoring rules (where each voter has perhaps a different score vector). ...
... Thus, virtual implementation is also well-suited to the probabilistic approach of the present paper. Another partial solution to strategic voting is suggested by Kim (2014), who shows that, with stochastically independent voters, the rank scoring rules considered in Sect. 5 are truth-revealing in Bayesian Nash equilibrium. ...
... For example, the scoring rules ofKim (2014; §5) and the weighted majority rules ofBordley (1985b;1986),Fleurbaey (2009) andAzrieli and Kim (2014; §4) have this feature. ...
Given a large enough population of voters whose utility functions satisfy certain statistical regularities, we show that voting rules such as the Borda rule, approval voting, and evaluative voting have a very high probability of selecting the social alternative which maximizes the utilitarian social welfare function. We also characterize the speed with which this probability approaches one as the population grows.
... Indeed, Ehlers et al. (2020) shows that if a social choice rule satisfies some continuity condition in addition to Bayesian incentive compatibility, then it must be vNM-ordinal in expectation, meaning that the rule responds to a change in an agent's type only if his expected-utility ranking of alternatives changes. Kim (2017) shows that there is a Bayesian incentive compatible vNM-ordinal rule that achieves a higher utilitarian welfare than any ordinal rule. ...
This paper studies a general class of social choice problems in which agents’ payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions which may respond to agents’ preference intensities as well as preference rankings. We show that a social choice function is ex ante Pareto efficient and Bayesian incentive compatible if and only if it is dictatorial. The result holds for arbitrary numbers of agents and alternatives, and under a fairly weak assumption on the joint distribution of types, which allows for arbitrary correlations and asymmetries.
... Since utilitarian welfare is additive, our results underline the importance of the compromise option for their results. Kim (2017) considers a related setting with at least three ex-ante symmetric alternatives and several agents with iid private values whose interests are not necessarily opposed. Feng and Wu (2019) ask in a setting without transfer with a perfect conflict of interests not between the agents but between the agents and the principal if the later can do better than choosing her ex-ante preferred option. ...
A principal must decide between two options. Which one she prefers depends on the private information of two agents. One agent always prefers the first option; the other always prefers the second. Transfers are infeasible. One application of this setting is the efficient division of a fixed budget between two competing departments. We first characterize all implementable mechanisms under arbitrary correlation. Second, we study when there exists a mechanism that yields the principal a higher payoff than she could receive by choosing the ex-ante optimal decision without consulting the agents. In the budget example, such a profitable mechanism exists if and only if the information of one department is also relevant for the expected returns of the other department. We generalize this insight to derive necessary and sufficient conditions for the existence of a profitable mechanism in the n-agent allocation problem with independent types.
... d 'Aspremont and Peleg (1988) and Bogomolnaia and Moulin (2001) are papers that use ordinality in this way. It is well-known that, in general, a planner who elicits cardinal information can typically do better than one that uses only ordinal information; for example, see Carroll (2018) and Kim (2017). A question, therefore, is why the planner would restrict himself to ordinal mechanisms. ...
We consider two-person bargaining problems in which (only) the players' disagreement payoffs are private information and it is common knowledge that disagreement is inefficient. We show that if the Pareto frontier is linear, or the utility functions are quasi-linear, the outcome of an ex post efficient mechanism must be independent of the players' disagreement values. Hence, in this case, a bargaining solution must be ordinal: the players' interim expected utilities cannot depend on the intensity of their preferences. For a non-linear frontier, the result continues to hold if disagreement payoffs are independent or if one of the players only has a few types. We discuss implications of these results for axiomatic bargaining theory and for full surplus extraction in mechanism design.
... Since utilitarian welfare is additive, our results underline the importance of the compromise option for their results. Kim (2017) considers a related setting with at least three ex-ante symmetric alternatives and several agents with iid private values whose interests are not necessarily opposed. Feng and Wu (2019) ask in a setting without transfer with a perfect conflict of interests not between the agents but between the agents and the principal if the later can do better than choosing her ex-ante preferred option. ...
A principal must decide between two options. Which one she prefers depends on the private information of two agents. One agent always prefers the first option; the other always prefers the second. Transfers are infeasible. One application of this setting is the efficient division of a fixed budget between two competing departments. We first characterize all implementable mechanisms under arbitrary correlation. Second, we study when there exists a mechanism that yields the principal a higher payoff than she could receive by choosing the ex-ante optimal decision without consulting the agents. In the budget example, such a profitable mechanism exists if and only if the information of one department is also relevant for the expected returns of the other department. We generalize this insight to derive necessary and sufficient conditions for the existence of a profitable mechanism in the n-agent allocation problem with independent types.
... This observation is in line with papers such asKim [2017] andEhlers et al. [2020] that show how discontinuous mechanisms can help expand the space of implementable rules in some environments. ...
In the single-peaked domain, the median rule is strategy-proof but not implementable in (Bayes-)Nash equilibrium by its associated direct mechanism. We define the value-based median mechanism that implements the median rule in (Bayes-)Nash equilibrium in the single-peaked domain under complete and incomplete information. Such a mechanism selects the median of the profile of different values announced by the agents (i.e., ignoring redundant announcements). The value-based median does not depend on agents' beliefs (in line with robust mechanism design). In the case of incomplete information, it induces truthful revelation of preferences (in line with strategy-proofness) for almost all peaks. We present extensions of our results to generalized median rules and finite policy spaces and their limitations.
... A significant array of papers (Hylland and Zeckhauser 1979;Miralles 2008;Abdulkadiroglu et al. 2011 andAbdulkadiroglu et al. 2015;Pycia 2014;Ashlagi and Shi 2016;Featherstone and Niederle 2016;Kim 2017 for voting schemes; He et al. 2018;Miralles and Pycia 2020) has stressed the importance of taking cardinal utilities into account. Empirically, and particularly the school choice case, the seminal paper by Black (1999) evidences that parents have cardinal preferences for the schools that can be expressed in monetary terms as willingness to pay through the residential market. ...
Most environments where assignment mechanisms (possibly random) are
used are such that participants have outside options. For instance private schools and private housing are options that participants in a public choice or public housing assignment problems may have. We postulate that, in cardinal mechanisms, chances inside the assignment process could favor agents with better outside options. By imposing a robustness to outside options condition, we conclude that, on the universal domain of cardinal preferences, any mechanism must be (interim) ordinal.
... Miralles (2012) considers a model of allocating two objects to agents without monetary transfers and Bayesian incentive compatibility. A recent paper by Kim (2017) considers the vNM domain with Bayesian incentive compatibility. He shows that every ordinal mechanism is dominated (in terms of utilitarian social welfare) by a suitable cardinal mechanism in the vNM domain. ...
We show that every cardinal incentive compatible voting mechanism satisfying a continuity condition, can only take ordinal, but not cardinal information into account. Our results apply to many standard models in mechanism design without transfers, including the standard voting models with any domain restrictions.
... Although there is work involving both ordinal and cardinal games [18]; [19]; [20]; [21] but there is still no generally accepted method for the transformation of both cardinal and ordinal games. In spite of the fact that both cardinal and ordinal payoffs are integral part of game theory, most of the available literature in game theory mainly focuses on ordinal transformations alone. ...
Game theory literature largely lacks a generally accepted method, capable of transforming both cardinal and ordinal games or games where one player is cardinal and the other one is ordinal. We devised a new method to overcome this problem. We used propositional logic to represent our general argument. Afterwards developed basic inferences, conclusion is derived according to modus ponens, based on these inferences we derived bicondotional statement and truth table. By adding and subtracting same figure to/from opposite expected outcomes (according to change in preference of one or both players) games having ordinal and/or cardinal payoffs can be transformed. We used the Notorious “Prisoners Dilemma” as an example and transformed it under our new method. Our method will not only expand the available knowledge in game theory by including both ordinal and cardinal transformations but it can also be helpful for the potential development of new taxonomies and topologies.
Mechanism design, a subset of game theory focusing on developing institutions and rules to drive strategic behavior toward specified goals, has emerged as a valuable tool for analyzing and managing international political difficulties. Mechanism design enables scholars and policymakers to construct cooperative solutions to complex problems ranging from conflict resolution and climate change to trade and international governance by studying the incentives and constraints many participants face in the global arena. This chapter explores the applications, contributions, and challenges of mechanism design in the context of politics.KeywordsMechanism designAuctionsVotingMarket mechanismsMatching mechanismsGame theory
Nous proposons un cadre général pour l’étude et l’évaluation des règles de vote derrière le « voile d’ignorance ». Nous montrerons comment de nombreuses contributions recensées dans notre revue de la littérature sur le vote peuvent être considérées comme des cas particuliers de ce modèle général. L’analyse se concentre ensuite sur l’optimisation utilitariste dans le cas d’élections à trois candidats et une spécification bayésienne où les préférences cardinales des électeurs entre trois options sont de l’information privée. Dans ce contexte spécifique, nous étudions les règles de vote qui sont des règles de score à deux paramètres, telles qu’introduites par Myerson (2002). Nous montrons que tous les équilibres bayésiens symétriques induits par ces règles de vote sont des équilibres sincères et ont une forme particulière. Ces équilibres sont uniques pour une vaste gamme de paramètres, ce qui nous permet de comparer la performance à l’équilibre de différentes règles de vote. Les résultats de nos calculs relatifs à l’efficacité des diverses règles de score (où l’efficacité est évaluée à l’aide d’une variation de la mesure proposée par Weber, 1978) permettent de conclure que les règles qui représentent le plus efficacement les préférences des électeurs permettent l’expression de l’intensité de ces préférences, contrairement aux règles plus couramment utilisées telles que la règle de pluralité et celle de Borda. Alors que la règle de vote par assentiment permet l’expression de l’intensité des préférences, elle ne maximise pas l’efficacité, car elle ne parvient pas à rendre sans ambiguïté les préférences ordinales des électeurs.
We consider the design of decision rules in an environment with two alternatives, independent private values and no monetary transfers. The utilitarian rule subject to incentive compatibility constraints is a weighted majority rule, where agents' weights correspond to expected gains given that their favorite alternative is chosen. It is shown that a rule is interim incentive efficient if and only if it is a weighted majority rule, and we characterize those weighted majority rules that are ex ante incentive efficient. We also discuss efficiency in the class of anonymous mechanisms and the stability of weighted majority rules.
Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model.
Can we devise mechanisms that allow voters to express the intensity of their preferences when monetary transfers are forbidden? Would we then be able to take account of how much voters wish the approval or dismissal of any particular issue? In such cases, would some minorities be able to decide over those issues they feel very strongly about? As opposed to the classical voting system (one person - one decision - one vote), we propose a new voting system where each agent is endowed with a fixed number of votes that can be distributed freely between a predetermined number of issues that must be approved or dismissed. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. This voting system is optimal in a well-defined sense: in a setting with two voters, two issues and preference intensities uniformly and independently distributed across possible values, Qualitative Voting Pareto dominates Majority Rule and, moreover, achieves the only ex-ante optimal (incentive compatible) allocation. The result also holds true with three voters as long as the voters preferences towards the issue differ sufficiently.
We compare six concepts of efficiency for economies with incomplete information, depending on the stage at which individuals' welfare is evaluated and on whether incentive constraints are recognized. An example is shown in which an incentive-efficient decision rule may be unanimously rejected by the individuals in the economy. We define durable decision rules, which can resist such unanimous rejection, and show that efficient durable decision rules exist.
We derive the incentive compatible and ex-ante welfare maximizing (i.e., utilitarian) mechanism for settings with an arbitrary number of agents and alternatives where the privately informed agents have single-crossing and single-peaked preferences. The optimal outcome can be implemented by modifying a sequential voting scheme, due to Bowen (1943), and used in many legislatures and committees. The modification uses a flexible majority threshold for each of several alternatives, and allows us to replicate, via a single sequential procedure, the entire class of anonymous, unanimous and dominant strategy incentive compatible mechanisms. Our analysis relies on the elegant characterization of this class of mechanisms for single-peaked preferences by Moulin (1980) and, subsequently, for single-crossing preferences by Saporiti (2009).
We consider the design of decision rules in an environment with two alternatives, independent private values and no monetary transfers. The utilitarian rule subject to incentive compatibility constraints is a weighted majority rule, where agents' weights correspond to expected gains given that their favorite alternative is chosen. It is shown that a rule is interim incentive efficient if and only if it is a weighted majority rule, and we characterize those weighted majority rules that are ex ante incentive efficient. We also discuss efficiency in the class of anonymous mechanisms and the stability of weighted majority rules.
We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978 ) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.
Motivated by the need for more flexible decision-making mechanisms in the European Union, the paper proposes a simple but novel voting scheme for binary decisions taken by committees that meet regularly over time. At each meeting, committee members are allowed to store their vote for future use; the decision is then taken according to the majority of votes cast. The possibility of shifting votes intertemporally allows agents to concentrate their votes when preferences are more intense, and although the scheme will not achieve full efficiency, storable votes typically lead to ex ante welfare gains over non-storable votes. Welfare gains can be proven rigorously in the case of 2 voters. With more voters, counterexamples can be found, but the analysis suggests that the welfare improvements should continue to hold if one of the following conditions is satisfied: (i) the number of voters is above a minimum threshold; (ii) preferences are not too polarized; (iii) the horizon is long enough.
We consider a setting in which two players must take a single action. The analysis is done within a private values model in which (i) the players’ preferences over actions are private information, (ii) utility is quadratic (non-transferable), (iii) implementation is bayesian and (iv) the welfare criterion is utilitarian. We characterize an optimal monotonic allocation rule. Instead of asking the agents to directly report their types, this allocation can be implemented dynamically. The agents are asked if they are to the left or to the right of the midpoint of the interval of possible types (eg.1/2 for the initial interval [0, 1]). If both reports agree, the section of the interval which none preferred is discarded and the remaining interval is divided in two parts and the process continued until one agent chooses left and the other right. In that case, the midpoint of this remaining interval is implemented. This implementation can be carried out by a Principal who lacks commitment, implying this process is an optimal communication protocol. When players interact repeatedly, the first best can be arbitrarily approximated (but never attained) as the agents become patient. We also show that the optimal provision of intertemporal incentives eventually leads to a dictatorial mechanism.
Nontransfer allocation mechanisms are used in many contexts, from collusion to children-to-school assignment. This paper works on cardinal mechanisms, which elicit and use information on preference intensities, instead of the widely analyzed ordinal al-location mechanisms, where only ordinal preferences are used. I study the allocation of two objects under Bayesian incentive compatibility (BIC), symmetric agents and inde-pendent private valuations. I obtain two main results. One is the solution to the optimal (ex ante utilitarian welfare maximizing) cardinal mechanism problem, for a wide family of prior valuation distributions. The second one is a simple cardinal mechanism that improves over ordinal mechanisms and does not require an exact knowledge of priors, in two-agent cases. Additionally, if the problem is constrained to ensure exactly one object per agent, then BIC implies ordinality, and the optimal ordinal mechanism is optimal among cardinal mechanisms.
We consider collective choice from two alternatives. Ex ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmet-ric across agents and neutral across alternatives. In many environ-ments, the majority voting rule maximizes agents' ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents' utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim-viewpoint.
Which decision rules are the most efficient? Which are the best in terms of maximin or maximax? We study these questions for the case of a group of individuals faced with a collective choice from a set of alternatives. A key message from our results is that the set of optimal decision rules is well defined, particularly simple, and well known: the class of scoring rules. We provide the optimal scoring rules for the three different ideals of justice under consideration: utilitarianism (efficiency), maximin, and maximax. The optimal utilitarian scoring rule depends crucially on the probability distribution of the utilities. The optimal maximin (respectively maximax) scoring rule takes the optimal utilitarian scoring rule and applies a factor that shifts it towards negative voting (respectively plurality voting). Copyright 2011, Oxford University Press.
This paper investigates one of the possible weakening of the (too demanding) assumptions of the Gibbard-Satterthwaite theorem. Namely we deal with a class of voting schemes where at the same time the domain of possible preference preordering of any agent is limited to single-peaked preferences, and the message that this agent sends to the central authority is simply its peak — his best preferred alternative. In this context we have shown that strategic considerations justify the central role given to the Condorcet procedure which amounts to elect the median peak: namely all strategy-proof anonymous and efficient voting schemes can be derived from the Condorcet procedure by simply adding some fixed ballots to the agent's ballots (with the only restriction that the number of fixed ballots is strictly less than the number of agents).Therefore, as long as the alternatives can be ordered along the real line with the preferences of the agents being single-peaked, it makes little sense to object against the Condorcet procedure, or one of its variants that we display in our characterization theorem.An obvious topic for further research would be to investigate reasonable restrictions of the domain of admissible preferences such that a characterization of strategy-proof voting schemes can be found. The single-peaked context is obviously the simplest one, allowing very complete characterizations. When we go on on to the two-dimensional state of alternatives the concept of single peakedness itself is not directly extended and a generalization of our one-dimensional results seems to us to be a difficult but motivating goal.
In every probabilistic mechanism, society selects an alternative, through a random device, out of a subset of indifferent alternatives. Consequently, in this context individuals face uncertainty and value the different lotteries on alternatives by their expected utility, so that they make use of a Von Neumann-Morgenstern cardinal utility function. Surprisingly, the social choice approach to probabilistic mechanisms assumes the use of ballots which preclude the complete expression of behaviour towards risk: individuals can only announce their ordinal preferences, or an approximation of their cardinal preferences, since in any case only a finite number of representations of preferences is available. This paper attempts to study voting systems in which individuals can express the cardinality of their preferences by assigning weights to the alternatives. It is shown that by voting with ballots which reflect weighting a new class of straightforward probabilistic mechanisms is defined, and that this class strictly contains the class of probabilistic straightforward mechanism designed by Gibbard.
Scoring rules are compared by their equilibria in simple voting games with Poisson population uncertainty, using new techniques for computing pivot probabilities. Best-rewarding rules like plurality voting can generate discriminatory equilibria where the voters disregard some candidate as not a serious contender, although he may be universally liked, or may be symmetric to other candidates as in the Condorcet cycle. Such discriminatory equilibria are eliminated by worst-punishing rules like negative voting, but then even a universally disliked candidate may have to be taken seriously. In simple bipolar elections, equilibria are always majoritarian and efficient under approval voting, but not other scoring rules. Journal of Economic Literature Classification: D72.
Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.
Two agents must select one of three alternatives. Their ordinal rankings are commonly known and diametrically opposed. Efficiency requires choosing the alternative the agents rank second whenever the weighted sum of their von Neumann Morgenstern utilities is higher than under either agent's favorite alternative. The agents' utilities of the middle-ranked alternative are i.i.d., privately observed random variables. In our setup, which is closely related to a public goods problem where agents face liquidity constraints but no participation constraints, decision rules that truthfully elicit utilities and implement efficient decisions do not exist. We provide analytical and numerical results on second-best rules.
Two agents have to choose one of three alternatives. Their ordinal rankings
of these alternatives are commonly known among them. The rankings are diametrically
opposed to each other. Ex-ante efficiency requires that they reach
a compromise, that is choose the alternative which they both rank second,
if and only if the sum of their von Neumann Morgenstern utilities from this
alternative exceeds the sum of utilities when either agent's most preferred alternative is chosen. We assume that the von Neumann Morgenstern utilities
of the middle ranked alternative are independent and identically distributed,
privately observed random variables, and ask whether there are incentive
compatible decision rules which elicit utilities and implement efficient decisions.
We show that no such decision rules exist if the distribution of agents'
types has a density with full support. We also study the problem of finding
second-best decision rules in our set-up , and explain how this problem differs
from more familiar second-best problems. Finally, we give some numerical
insights into the nature of second-best rules. For a variety of distributions of
types, second-best rules involve every little inefficiency.
The naïve concept of social welfare as a sum of intuitively measurable and comparable individual cardinal utilities has been found unable to withstand the methodological criticism of the Pareto school. Professor Bergson2 has therefore recommended its replacement by the more general concept of. a social welfare function, defined as an arbitrary mathematical function of economic (and other social) variables, of a form freely chosen according to one’s personal ethical (or political) value judgments. Of course, in this terminology everybody will have a social welfare function of his own, different from that of everybody else except to the extent to which different individuals’ value judgments happen to coincide with one another. Actually, owing to the prevalence of individualistic value judgments in our society, it has been generally agreed that a social welfare function should be an increasing function of the utilities of individuals: if a certain situation, X, is preferred by an individual to another situation, y, and if none of the other individuals prefers Y to X, then X should be regarded as socially preferable to y. But no other restriction is to be imposed on the mathematical form of a social welfare function.
Consider a Bayesian collective decision problem in which the preferences of agents are private information. We provide a general demonstration that the utility costs associated with incentive constraints become negligible when the decision problem is linked with a large number of independent copies of itself. This is established by defining a mechanism in which agents must budget their representations of preferences so that the frequency of preferences across problems mirrors the underlying distribution of preferences, and then arguing that agents' incentives are to satisfy their budget by being as truthful as possible. We also show that all equilibria of the linking mechanisms converge to the target utility levels. The mechanisms do not require transferable utility or interpersonal comparisons of utility, and are immune to manipulations by coalitions. Copyright The Econometric Society 2007.
We study strategic voting after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truth-telling is required to maximize the expected utility of every voter, expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors, i.e., the uniform priors, there exists a large class of social choice functions that are OBIC. However, for priors that are generic in the set of independent beliefs, a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard-Satterthwaite Theorem. Copyright The Econometric Society 2004.
This paper explorers rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (JET, 1999). Is is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. Stochastic choices are rationalizable in terms of stochastic orderings on the normalized price space if and only if there exits a solution to a linear feasibility problem. Together with the weak axiom of stochastic revealed preference the existence of a solution implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here.
Where alternatives, players, and strategies for each player are finitely many, a game form assigns a lottery over alternatives to each configuration of players' strategies. It is straightforward iff it guarantees that each player, whatever his utilities, will have a dominant strategy. It is unilateral iff only one player can influence the outcome, and duple if it restricts the final outcome to a fixed pair of alternatives. Any straightforward game form, it is shown, is, on a domain which gives each player a dominant strategy for each utility scale, a probability mixture of game forms, each unilateral or duple.
It has been conjectured that no system of voting can preclude strategic voting--the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of voting in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a game form is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy.
Continuity and Incentive Compatibility in Cardinal Voting Mechanisms. Working paper. Freixas, X., 1984. A cardinal approach to straightforward probabilistic mechanisms
- L Ehlers
- D Majumdar
- D Mishra
- A Sen
Ehlers, L., Majumdar, D., Mishra, D., Sen, A., 2016. Continuity and Incentive Compatibility in Cardinal Voting Mechanisms. Working paper.
Freixas, X., 1984. A cardinal approach to straightforward probabilistic mechanisms. J. Econ. Theory 34, 227-251.