Preferential Polarization Measures

Given opinions of members of a society on a set of policies, as ordinal preferences; an approach to polarization is introduced. The concept here is considering polarization in a society as an aggregation of pairwise antagonisms, which depend on identi fication within groups as well as alienation among groups. Among measures which comply to this sort of conceptualization, a class of functions which satisfi es certain plausible properties is introduced for the case of three alternatives. This class coincides with the class characterized for unidimensional spaces in Esteban and Ray (1994)

Measuring Public Preferential Polarization

We adapt an axiomatically derived measure of polarization due to Esteban and Ray (1994) to measure polarization of political preferences. Previous work used different measures such as variance, kurtosis, Cronbach's alpha, median distance to median and the mean distance between groups. Yet, none of these measures are theoretically connected to a notion of polarization. Although the initiation of the current one is in the lieu of income inequality measurement, it is conceptually suitable for preferential polarization as well. This paper offers a methodology for that purpose. The second contribution of the paper is that we use the Aldrich-McKelvey Scaling to correct for differential-item functioning in estimating ideal points of the individuals. We use the American National Election Survey Data for years between 1984-2008 to implement the theory offered in the paper. Our findings suggest that there is not a statistically significant increasing trend in polarization in this time period in many issue dimensions but there is an upward trend in the latent ideology dimension which is significant during the 1990s

Hyper-Stable Social Welfare Functions

We introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function a selects a complete weak order from a profile PN of linear orders over any finite set of alternatives, given N individuals. Each linear order P in PN generates a linear order over orders of alternatives,called hyper-preference, by means of a preference extension. Hence each profile PN generates a hyper-profile ˙PN. We assume that all preference extensions are separable: the hyper-preference of some order P ranks order Q above order Q0 if the set of alternative pairs P and Q agree on contains the one P and Q0 agree on. A special sub-class of separable extensions contains all Kemeny extensions, which build hyper-preferences by using the Kemeny distance criterion. A social welfare function a is hyper-stable (resp. Kemeny-stable) if at any profile PN, at least one linearization of a(PN) is ranked first by a( ˙PN), where ˙PN is any separable (resp. Kemeny) hyper-profile induced from PN. We show that no scoring rule is hyper-stable, and that no unanimous scoring rule is Kemeny-stable, while there exists a hyper-stable Condorcet social welfare function

Measuring Polarization in Preferences

In this paper, we study the measurement of polarization in collective decision making problems with ordinal preferences over alternatives. We argue that polarization can be measured as an aggregation of antagonisms over pairs of alternatives in the society. We propose a measure of this sort and show that it is the only measure satisfying some normatively appealing conditions

Essais sur les hyper-preferences, la polarisation et l'aggrégation des informations

In this thesis, some important problems and properties of collective decision-making are studied. In particular, first, a stability property of preference aggregation rules is introduced and some well-known classes of rules are tested in this regard. Second, measuring preferential polarization is studied, both theoretically and empirically. Finally, strategic behavior in information aggregation situations is investigated in light of a sort of bounded rationality model, both theoretically and experimentally. The stability notion studied in the first part of the thesis is imposed particularly on social welfare functions and requires that the outcome of these functions should be robust to reduction in preference submission that are argued to take place when individuals submit a ranking of alternatives when the outcomes are also restricted to be rankings. Given the preference profile of a society, that is a collection of rankings of alternatives, a compatible collection of rankings of rankings are extracted and the outcome of social welfare functions in these two levels are compared. It turns out that no scoring rule gives consistent results, although there might exist Condorcet-type rules. Polarization measures studied in second part are in form of aggregation of pairwise antagonisms in a society. The public opinion polarization in the United States for the last three decades is analyzed in light of this view, by using a well-acclaimed measure of polarization introduced in the literature of income inequality. The conclusion is that no significant trend in public opinion polarization can be claimed to exist over the last several decades. Also, an adaptation of the same measure is shown to satisfy desirable properties in lieu of ordinal preference profiles when three alternatives are considered. Furthermore, a measure that is the aggregation of pairwise differences among individuals' preferences is characterized by a set of axioms. In the final part of the thesis, information aggregation situations described as in Condorcet jury model is studied in light of cognitive hierarchy approach to bounded rationality. Specifically, a laboratory experiment is run to test the theoretical predictions of the symmetric Bayesian Nash equilibrium concept. It is observed that behavior in lab is not correctly captured by this concept that assumes a strong notion of rationality and homogeneity among individuals' behaviors. To better describe the findings in the experiment, a novel model of cognitive hierarchy is developed and shown to perform better than both strong rationality approach and previous cognitive hierarchy models. This endogenous cognitive hierarchy model is compared theoretically to previous models of cognitive hierarchy and shown to improve in certain classes of games.Dans cette thèse, certains problèmes importants et des propriétés de prise de décision collective sont étudiés. En particulier, d'abord, une propriété de stabilité des règles d'agrégation de préférences est introduite et certaines classes bien connues de règles sont testées à cet égard. Deuxièmement, le mesurage de la polarisation préférentielle est étudié, à la fois théorique et empirique. Enfin, le comportement stratégique dans des situations d'agrégation de l'information est étudié à la lumière d'une sorte de modèle de la rationalité limitée, à la fois théoriquement et expérimentalement. La notion de stabilité étudié dans la première partie de la thèse est imposée en particulier sur les fonctions de bien-être sociale et exige que le résultat de ces fonctions doit être robuste à la réduction de la transmission de préférences qui sont soutenu avoir lieu lorsque les individus présentent un ordre des alternatives lorsque les résultats sont également limités à être ordres. Pour tous profils sociétaux de préférences donné, qui est une collection d'ordres des alternatives, une collection compatible d'ordre des classements est extraite et les résultats des fonctions de bien-être social dans ces deux niveaux sont comparés. Il s'avère qu'aucune règle de notation donne des résultats cohérents, bien qu'il puisse y exister des règles Condorcetien. Mesures de polarisation qui sont étudiées en deuxième partie sont en forme d'agrégation des antagonismes par paires dans une société. La polarisation de l'opinion publique aux États-Unis pour les trois dernières décennies est analysé à la lumière de ce point de vue, en utilisant une mesure de polarisation bien acclamé qui est introduit dans la littérature de l'inégalité des revenus. La conclusion est qu'aucune tendance significative dans l'opinion publique polarisation peut être réclamé à exister au cours des dernières décennies. En outre, une adaptation de la même mesure est montrée à satisfaire des propriétés souhaitables à la place de profils de préférences ordinales lorsque trois alternatives sont considérées. En outre, une mesure qui est en effet l'agrégation des différences par paires entre les préférences des individus est caractérisée axiomatiquement. Dans la dernière partie de la thèse, situations de l'agrégation de l'information telles que décrites comme dans le modèle du jury de Condorcet sont étudiées à la lumière d'une approche de rationalité limitée qui est connue hiérarchie cognitive. Plus précisément, une expérience de laboratoire est exécutée pour tester les prédictions théoriques de la notion d'équilibre symétrique de Nash bayésien. On constate que le comportement en laboratoire n'est pas correctement capturé par ce concept qui suppose une forte notion de la rationalité et de l'homogénéité entre les comportements des individus. Pour mieux décrire les résultats à l'expérience, un nouveau modèle de hiérarchie cognitive est développé et montré à faire mieux que la fois l'approche de la rationalité forte et des modèles précédentes de hiérarchie cognitive. Ce modèle de hiérarchie cognitive endogène est comparé en théorie aux modèles précédents de la hiérarchie cognitive et montré pour améliorer dans certaines catégories de jeux

Absolute Qualified Majoritarianism: How Does the Threshold Matter?

We study absolute qualified majority rules in a setting with more than two alternatives. We show that given two qualified majority rules, if transitivity is desired for the societal outcome and if the thresholds of one of these rules are at least as high as the other's for any pair of alternatives, then at each preference profile the rule with higher thresholds results in a coarser social ranking. Hence all absolute qualified majority rules can be expressed as specific coarsenings of the simple majority rule

Hyper-stable social welfare functions

International audienceWe define a new consistency condition for neutral social welfare functions, called hyper-stability. A social welfare function (SWF) selects a weak order from a profile of linear orders over any finite set of alternatives. Each profile induces a profile of hyper-preferences, defined as linear orders over linear orders, in accordance with the betweenness criterion: the hyper-preference of some order P ranks order Q above order Q’ if the set of alternative pairs P and Q agree on contains the one P and Q’ agree on. A special sub-class of hyper-preferences satisfying betweenness is defined by using the Kemeny distance criterion. A neutral SWF is hyper-stable (resp. Kemeny-stable) if given any profile leading to the weak order R, at least one linear extension of R is ranked first when the SWF is applied to any hyper-preference profile induced by means of the betweenness (resp. Kemeny) criterion. We show that no scoring rule is hyper-stable, unless we restrict attention to the case of three alternatives. Moreover, no unanimous scoring rule is Kemeny-stable, while the transitive closure of the majority relation is hyper-stable. Copyright Springer-Verlag Berlin Heidelberg 201