Party objectives in the "Divide a dollar" electoral competition

Cet article se place dans le cadre d'un modèle de pure politique redistributive entre trois groupes d'électeurs. Il compare deux variantes de la compétition électorale entre deux partis, l'objectif d'un parti étant soit la probabilité de victoire ("jeu du tournoi majoritaire"), soit le nombre de voix obtenues ("jeu de la pluralité"). On exhibe des équilibres en stratégies mixtes pour ces deux variantes. En moyenne tous les individus sont traités de la même manière dans le jeu de la pluralité, alors que le jeu du tournoi majoritaire favorise les individus appartenant aux petits groupes.Compétition électorale;Stratégies mixtes;Blotto;Objectif des partis

In Silico Voting Experiments

This paper presents computer simulations of voting rules: Plurality rule, Approval voting and the Copeland and Borda rules, with voters voting sincerly or strategically. Different ways of generating random preference profiles are introduced: Rousseauist cultures are suitable for common interest project assessment; Impartial cultures are standard in Social Choice Theory; Distributive cultures and Spatial Euclidean ones are standard in Political Science.Social Choice. Voting Rules. Impartial Culture. Condorcet. Borda

A note on choosing the alternative with the best median evaluation

The voting rule proposed by Basset and Persky (Public Choice 99: 299-310) picks the alternative with best median evaluation. The present note shows that this MaxMed principle is equivalent to ask the social planner to apply the MaxMin principle allowing him to discard half of the population. In one-dimensional, single-peaked domains, the paper compares this rule with majority rule and the utilitarian criterion. The MaxMed outcome is rejected by a majority of voters in favor of outcomes which are also utilitarian improvements.

Ambiguity in electoral competition.

L'article propose une théorie de la compétition électorale ambigüe. Une plate-forme est ambigüe si les votants peuvent l'interpréter de différentes manières. Une telle plate-forme met plus ou moins de poids sur sur les différentes options possibles de sorte qu'elle est plus ou moins facilement interprétée comme une politique ou une autre. On fait l'hypothèse que les partis politiques peuvent contrôler exactement leurs plate-formes mais ne peuvent pas cibler celles-ci vers les votants individuellement. Chaque électeur vote d'après son interprétation des plate-formes des partis mais est averse à l'ambiguité. On montre que ce jeu de compétition électorale n'a pas d'équilibre de Nash. Cependant ses stratégies max-min sont les stratégies optimales du jeu Downsien en stratégies mixtes. De plus, si les partis se comportent de manière suffisament prudente par rapport à l'aversion pour l'ambiguité des électeurs, ces mêmes stratégies forment un équilibre.Compétition électorale;Ambigüité;Comportement prudent;Jeux à somme nulle

Hydrodynamic limit equation for a lozenge tiling Glauber dynamics

We study a reversible continuous-time Markov dynamics on lozenge tilings of the plane, introduced by Luby et al. Single updates consist in concatenations of $n$ elementary lozenge rotations at adjacent vertices. The dynamics can also be seen as a reversible stochastic interface evolution. When the update rate is chosen proportional to $1/n$, the dynamics is known to enjoy especially nice features: a certain Hamming distance between configurations contracts with time on average and the relaxation time of the Markov chain is diffusive, growing like the square of the diameter of the system. Here, we present another remarkable feature of this dynamics, namely we derive, in the diffusive time scale, a fully explicit hydrodynamic limit equation for the height function (in the form of a non-linear parabolic PDE). While this equation cannot be written as a gradient flow w.r.t. a surface energy functional, it has nice analytic properties, for instance it contracts the $\mathbb L^2$ distance between solutions. The mobility coefficient $\mu$ in the equation has non-trivial but explicit dependence on the interface slope and, interestingly, is directly related to the system's surface free energy. The derivation of the hydrodynamic limit is not fully rigorous, in that it relies on an unproven assumption of local equilibrium.Comment: 31 pages, 8 figures. v2: typos corrected, some proofs clarified. To appear on Annales Henri Poincar

How quickly can we sample a uniform domino tiling of the 2L x 2L square via Glauber dynamics?

TThe prototypical problem we study here is the following. Given a $2L\times 2L$ square, there are approximately $\exp(4KL^2/\pi )$ ways to tile it with dominos, i.e. with horizontal or vertical $2\times 1$ rectangles, where $K\approx 0.916$ is Catalan's constant [Kasteleyn '61, Temperley-Fisher '61]. A conceptually simple (even if computationally not the most efficient) way of sampling uniformly one among so many tilings is to introduce a Markov Chain algorithm (Glauber dynamics) where, with rate $1$, two adjacent horizontal dominos are flipped to vertical dominos, or vice-versa. The unique invariant measure is the uniform one and a classical question [Wilson 2004,Luby-Randall-Sinclair 2001] is to estimate the time $T_{mix}$ it takes to approach equilibrium (i.e. the running time of the algorithm). In [Luby-Randall-Sinclair 2001, Randall-Tetali 2000], fast mixin was proven: $T_{mix}=O(L^C)$ for some finite $C$. Here, we go much beyond and show that $c L^2\le T_{mix}\le L^{2+o(1)}$. Our result applies to rather general domain shapes (not just the $2L\times 2L$ square), provided that the typical height function associated to the tiling is macroscopically planar in the large $L$ limit, under the uniform measure (this is the case for instance for the Temperley-type boundary conditions considered in [Kenyon 2000]). Also, our method extends to some other types of tilings of the plane, for instance the tilings associated to dimer coverings of the hexagon or square-hexagon lattices.Comment: to appear on PTRF; 42 pages, 9 figures; v2: typos corrected, references adde

Why not proportional?

This paper reviews the arguments that justify the principles of proportional and degressively proportional representation.Proportional representation, Degressive proportionality

Strategic Approval Voting in a large electorate

L'article est consacré au vote par assentiment pour une grande population de votants. On montre que, partant d'une information statistique sur les scores des candidats, les électeurs rationels votent sincèrement. On montre alors que, si un candidat est vainqueur de Condorcet, ce candidat est élu.Vote par assentiment;Vote stratégique;vote probabiliste;Elections