Binary Self-Selective Voting Rules

TL;DR

This paper explores a new stability property for voting rules called binary self-selectivity, analyzing its implications for different classes of voting rules and conditions, including neutrality, unanimity, and the presence of a Condorcet winner.

Contribution

It establishes the equivalence between binary self-selectivity and universal self-selectivity for neutral voting rules, and characterizes voting rules that are binary self-selective under various conditions.

Findings

Neutral voting rules are binary self-selective iff they are universally self-selective.

Unanimous, neutral, and anonymous voting rules are binary self-selective iff they are the Condorcet rule.

Under certain conditions, dictatorial and Condorcet rules are characterized as binary self-selective.

Abstract

This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In Theorem 1, we show that a neutral voting rule is binary self-selective if and only if it is universally self-selective. We then use this equivalence to show, in Corollary 1, that under the unrestricted strict preference domain, a unanimous and neutral voting rule is binary self-selective if and only if it is dictatorial. In Theorem 2 and Corollary 2, we show that whenever there is a strong Condorcet winner; a unanimous, neutral and anonymous voting rule is binary self-selective (or universally self-selective) if and only if it is the Condorcet voting rule.