Bad cycles and chaos in iterative Approval Voting - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Bad cycles and chaos in iterative Approval Voting

Résumé

We consider synchronized iterative voting in the Approval Voting system. We give examples with a Condorcet winner where voters apply simple, sincere, consistent strategies but where cycles appear that can prevent the election of the Condorcet winner, or that can even lead to the election of a "consensual loser", rejected in all circumstances by a majority of voters. We conduct numerical experiments to determine how rare such cycles are. It turns out that when voters apply Laslier's Leader Rule they are quite uncommon, and we prove that they cannot happen when voters' preferences are modeled by a one-dimensional culture. However a slight variation of the Leader Rule accounting for possible draws in voter's preferences witnesses much more bad cycle, especially in a one-dimensional culture. Then we introduce a continuous-space model in which we show that these cycles are stable under perturbation. Last, we consider models of voters behavior featuring a competition between strategic behavior and reluctance to vote for candidates that are ranked low in their preferences. We show that in some cases, this leads to chaotic behavior, with fractal attractors and positive entropy.
Fichier principal
Vignette du fichier
BadCycles.pdf (5.69 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02434670 , version 1 (10-01-2020)
hal-02434670 , version 2 (19-11-2020)
hal-02434670 , version 3 (05-01-2022)
hal-02434670 , version 4 (09-02-2022)

Identifiants

Citer

Benoît Kloeckner. Bad cycles and chaos in iterative Approval Voting. 2020. ⟨hal-02434670v2⟩
121 Consultations
178 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More