Robust Voting under Uncertainty

TL;DR

This paper introduces a normative framework for voting rules under preference uncertainty, emphasizing responsiveness, and characterizes $P$-robust rules through weighted averages of individual responsiveness across convex sets of distributions.

Contribution

It provides a characterization of $P$-robust voting rules using weighted averages, linking responsiveness to convex preference distributions.

Findings

A voting rule is $P$-robust iff a weighted average of responsiveness exceeds one-half at all extreme points of $P$.

Weighted majority rules without ties are $P$-robust when $P$ includes all degenerate distributions.

The framework emphasizes responsiveness as a key criterion under preference uncertainty.

Abstract

This paper proposes normative criteria for voting rules under uncertainty about individual preferences. The criteria emphasize the importance of responsiveness, i.e., the probability that the social outcome coincides with the realized individual preferences. Given a convex set of probability distributions of preferences, denoted by $P$, a voting rule is said to be $P$-robust if, for each probability distribution in $P$, at least one individual's responsiveness exceeds one-half. Our main result establishes that a voting rule is $P$-robust if and only if there exists a nonnegative weight vector such that the weighted average of individual responsiveness is strictly greater than one-half under every extreme point of $P$. In particular, if the set $P$ includes all degenerate distributions, a $P$-robust rule is a weighted majority rule without ties.