A geometric examination of majorities based on difference in support

Reciprocal preferences have been introduced in the literature of social choice theory in order to deal with preference intensities. They allow individuals to show preference intensities in the unit interval among each pair of options. In this framework, majority based on difference in support can be used as a method of aggregation of individual preferences into a collective preference: option a is preferred to option b if the sum of the intensities for a exceeds the aggregated intensity of b in a threshold given by a real number located between 0 and the total number of voters. Based on a three dimensional geometric approach, we provide a geometric analysis of the non transitivity of the collective preference relations obtained by majority rule based on difference in support. This aspect is studied by assuming that each individual reciprocal preference satisfies a g-stochastic transitivity property, which is stronger than the usual notion of transitivit

Mayorías basadas en diferencias: análisis de la consistencia y extensiones

En esta tesis se estudian las mayorías por diferencia de votos y por diferencia de apoyo. Los capítulos 1 y 2 se centran en el análisis de la transitividad y de la triple-aciclicidad de la relación de preferencia fuerte generada por las mayorías por diferencia de apoyo, al agregar relaciones de preferencia recíprocas individuales. En el capítulo 3 se estiman las probabilidades con las que se producen resultados colectivos consistentes, tanto en las mayorías por diferencia de apoyo como en las mayorías por diferencia de votos. En el capítulo 4 se extienden las mayorías por diferencia de votos al contexto de las preferencias lingüísticas, a través de conjuntos difusos y del modelo de las 2-tuplas; se justifica la equivalencia entre ambas modelizaciones bajo determinadas condiciones de regularidad y se estudian las propiedades que cumplen estas mayorías lingüísticasDepartamento de Economía Aplicad

Triple-acyclicity in majorities based on difference in support

In this paper we study to what extent majorities based on difference in support leads to triple-acyclic collective decisions. These majorities, which take into account voters' intensities of preference between pairs of alternatives through reciprocal preference relations, require to the winner alternative to exceed the support for the other alternative in a difference fixed before the election. Depending on that difference, i.e., on the threshold of support, and on some requirements on the individual rationality of the voters, we provide necessary and sufficient conditions for avoiding cycles of three alternatives on the collective decision

Lost in Translation: Social Choice Theory is Misapplied Against Legislative Intent

Several prominent scholars use results from social choice theory to conclude that legislative intent is meaningless. We disagree. We support our argument by showing that the conclusions in question are based on misapplications of the theory. Some of the conclusions in question are based on Arrow\u27s famous General Possibility Theorem. We identify a substantial chasm between what Arrow proves and what others claim in his name. Other conclusions come from a failure to realize that applying social choice theory to questions of legislative intent entails accepting assumptions such as legislators are omniscient and legislators have infinite resources for changing law and policy. We demonstrate that adding more realistic assumptions to models of social choice theory yields very different theoretical results-including ones that allow for meaningful inferences about legislative intent. In all of the cases we describe, important aspects of social choice theory were lost in the translation from abstract formalisms to real political and legal domains. When properly understood, social choice theory is insufficient to negate legislative intent

Preference fusion and Condorcet's Paradox under uncertainty

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.Comment: International Conference on Information Fusion, Jul 2017, Xi'an, Chin

Chronicle of a Failure Foretold: 2017 Rector Election at Ghent University

Producción CientíficaAfter more than half a year of elections (yielding three voting stages and nine voting rounds), the 2017 Rector election at Ghent University (Belgium) resulted in a victory for the duo leading all nine voting rounds, and in a resounding defeat for the electoral system. Significant regulation changes were needed in order to break the institutional deadlock in which Ghent University found itself. In this paper, we follow the timeline of the election and dissect what went wrong in the election planningMinisterio de Economía, Industria y Competitividad (Project ECO2016-77900-P)European Regional Development Fund (ERDF)Research Foundation of Flanders (FWO17/PDO/160

La voluntad general de Rousseau como un límite al voto estratégico autointeresado

Condorcet’s voting method, as its extension known as the Kemeny-Young rule, is often seen as the incarnation of Rousseau’s general will. But the Kemeny-Young rule has problems when cycles in the social ranking arise. In particular, it can lead to choose a “covered” alternative, i.e. one for which there are candidates with better performances in pairwise comparisons. On the other hand, the uncovered set, the set of all the alternatives that are not covered, puts limits to insincere votes of sophisticated voters under certain conditions. Basically, voting insincerelly for a non-preferred alternative in order to favor the actually preferred candidate would lead to the choice of an uncovered alternative. We argue that Rousseau’s general will could be embodied in a different kind of rule than Kemeny-Young’s, with both epistemic credentials and whose outcomes are within the uncovered set altogether. In this work we begin to explore that possibility.Fil: Bodanza, Gustavo Adrian. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Linares, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

Arithmetic vs. Morality: Liberalism in Collective Choice

The author argues that collective choice theory relies on a number of background concepts that are not recognized in the formal delineations of the theory. Some of these background concepts describe a liberal community. These liberal premises conflict with the more explicit arithmetical languages of collective choice, and this conflict explains some of the rational breakdowns between one and all demonstrated in collective choice