Self-Equivalent Voting Rules

TL;DR

This paper introduces a new stability axiom called self-equivalence for stochastic voting rules and shows that under certain principles, the uniform random dictatorship is the unique rule satisfying these conditions.

Contribution

It establishes the self-equivalence axiom and proves that the uniform random dictatorship uniquely satisfies this along with other democratic principles.

Findings

Self-equivalence is a stability criterion for voting rules.

Under certain principles, the uniform random dictatorship is uniquely characterized.

Societies seeking stability and democratic principles must use or consider rules other than self-application.

Abstract

In this paper, I introduce a novel stability axiom for stochastic voting rules, called self-equivalence, by which a society considering whether to replace its voting rule using itself will choose not to do so. I then show that under the unrestricted strict preference domain, the unique voting rule satisfying the democratic principles of anonymity, optimality, monotonicity, and neutrality as well as the stability principle of self-equivalence must assign to every voter equal probability of being a dictator (i.e., uniform random dictatorship). Thus, any society that desires stability and adheres to the aforementioned democratic principles is bound to either employ the uniform random dictatorship or decide whether to change its voting rule using a voting rule other than itself.