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