Figure 4 - available via license: Creative Commons Attribution 4.0 International
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(a) Schematic illustration of the application of ELO rating system in chess compared with models of dating apps. (b) Distribution of ranks for the product Kernel K(c, c ) = c(c + 1). (c) Average Elo for non-unitary transition between ranks based on a ELO-like ranking system. In the inset the parameter α was distributed randomly from a Caucht distribution with parameters (0, 1). Even with this choice of a scale-free distribution, the condensation threshold is unaltered. (d) Average likes (rescaled by the maximum) for non-unitary transition between ranks based on a Elo-like ranking system. (e) Distribution of ranks for v(c) = c, K(c, c ) = 1/(1 + (c − c ) 2 ), βγ = 16, β = 0.02. This choice is in accordance with the standard chess Elo rating system. (Inset) Magnification of the higher mode of the distribution with logarithmic scale for Elo ratings.
Source publication
Over the last ten years, a sharp rise in the number of dating apps has broadened the spectrum of how one can get in contact with new acquaintances. A common feature of such apps is a swipe, enabling a user to decide whether to like or dislike another user. As is the case in real life, a user may be more or less popular, which implies that the distr...
Contexts in source publication
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... general feature of the Elo rating system is that a user, who receives a like from another user in a higher rank, will climb ranks directly proportional to the difference between the rank of the users. The opposite holds true in case of a dislike ( figure 4(a)). We define n(c, x, t) as the density of users in the rank c who are attractive x, whose dynamics are given by , (14) where P(y) is the distribution of attractiveness and w, j, c). ...
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... gelating system, the first order moment diverges in our system, as the total mass is not a conserved quantity. In figure 4(b), we confirm this theoretical prediction by showing how the Elo distribution evolves in time. We notice that the distribution flattens over time with a high peak around zero and a broad tail that moves dynamically to higher Elo values, as expected in a gelating system [19]. ...
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... last constraint is encoded in the interaction kernel K(w, j, c). In figure 4(a), we outline the difference between chess-based Elo and the Elo in a model for dating apps. Equation (14) with the Elo chess-based representation for the dynamics of ranks becomes ...
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... figure 4(c), we show that the condensate has not disappeared. There is a smoother transition at the condensation threshold for the steady state average probability with respect to the attractiveness. ...
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... is a smoother transition at the condensation threshold for the steady state average probability with respect to the attractiveness. Moreover, the number of likes received is more evenly distributed among users ( figure 4(d)), similar to the 'push' algorithm. In figure 4(e), we show the distribution of Elo independent of attractiveness. ...
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... the number of likes received is more evenly distributed among users ( figure 4(d)), similar to the 'push' algorithm. In figure 4(e), we show the distribution of Elo independent of attractiveness. We consider another possible scenario, in which users constantly change their acceptance probability, thus including noise effect and misjudgments. ...
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... is included in the model by choosing α at every time step according to a Cauchy distribution with parameters (0, 1). The condensation threshold and the average Elo are not affected by noise ( figure 4(a), inset), suggesting that the condensation mechanism is quite strong against intrinsic noise. Interestingly, the distribution flattens initially, and becomes bimodal in the long-term limit. ...
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... the distribution flattens initially, and becomes bimodal in the long-term limit. The higher mode is broad, figure 4(e) (inset), signalling what we expected from studying the average rank: the Elo ratings are more proportionally distributed among the users with x > x C . At the same time, Elo ratings are not evenly distributed when we consider that the totality of users as the condensate is still present. ...
