A Geometric Examination of Majorities Based on Difference in Support

25 Pages Posted: 21 May 2014

See all articles by Richard Baron

Richard Baron

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Mostapha Diss

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Eric Rémila

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Philippe Solal

University of Saint Etienne

Date Written: May 19, 2014

Abstract

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 transitivity.

Keywords: Geometric voting, Reciprocal preferences, Difference in support, Stochastic transitivity

JEL Classification: D72

Suggested Citation

Baron, Richard and Diss, Mostapha and Rémila, Eric and Solal, Philippe, A Geometric Examination of Majorities Based on Difference in Support (May 19, 2014). Available at SSRN: https://ssrn.com/abstract=2438683 or http://dx.doi.org/10.2139/ssrn.2438683

Richard Baron (Contact Author)

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Mostapha Diss

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Eric Rémila

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France

Philippe Solal

University of Saint Etienne ( email )

6, rue basse des rives
Saint Etienne, 42023
France

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