Symmetric reduced form voting

TL;DR

This paper characterizes the implementation of symmetric voting rules in a two-alternative setting, showing they can be expressed as convex combinations of qualified majority and anti-majority rules, with applications to Rawlsian rules.

Contribution

It provides a complete characterization of symmetric voting rules via convex combinations of deterministic rules, extending to monotone and unanimous voting rules.

Findings

Interim allocation probabilities are convex combinations of qualified majority and anti-majority rules.

Symmetric monotone and unanimous rules have analogous implementation characterizations.

Ex-ante Rawlsian rule is a convex combination of qualified majority rules.

Abstract

We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probabilities can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti-majority. We also provide analogous results by requiring implementation by a symmetric monotone (strategy-proof) voting rule and by a symmetric unanimous voting rule. We apply our results to show that an ex-ante Rawlsian rule is a convex combination of a pair of qualified majority rules.