Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate

Eric Kamwa (1, 2) , Vincent Merlin (3, 4, 5) , Faty Mbaye Top (6)

1 LC2S - Laboratoire caribéen de sciences sociales
2 UA FDEM - Université des Antilles - Faculté de droit et d'économie de la Martinique
3 CREM - Centre de recherche en économie et management
4 CNRS - Centre National de la Recherche Scientifique
5 UNICAEN UFR SEGGAT - Université de Caen Normandie - UFR de Sciences Économiques, Gestion, Géographie et Aménagement des Territoires
6 INC - Institut National de la Consommation

This paper analyzes the vulnerability of scoring run-off rules to abstention and participation paradoxes when voters preferences are single-peaked. These paradoxes occur when the size of the electorate varies (grows or diminishes). In particular, the Abstention or No-show paradox occurs when a voter is better off by not casting his ballot in the election. First, we show that all the scoring run-off rules that always elect the Condorcet winner on this domain are immune to the different forms of Abstention and Participation paradoxes. Secondly, when these paradoxes are still possible, we compute their likelihood in three-candidate elections under the Impartial Anonymous Culture assumption. We conclude that considering the single-peaked domain drastically reduces, and even sometimes eliminates the impact of No-show paradoxes, for scoring run-off rules.

Mots clés: Paradoxes; Scoring Rules; Run-offs; No-show; Abstention; Participation; Impartial Anonymous Culture; Probability

Domaines: Economies et finances

Eric Kamwa, Vincent Merlin, Faty Mbaye Top. Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate. 2023. ⟨hal-03143741v2⟩