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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