Robust Voting under Uncertainty

2025-07-30

AI Summary

This paper addresses the design of voting rules under uncertainty about individual preferences. To ensure that social outcomes align with true preferences with probability at least 1/2 (i.e., responsiveness), it introduces “P-robustness” as a new normative criterion. Method: It establishes, for the first time, a robustness framework based on a set *P* of preference probability distributions, integrating convex analysis and weighted majority rules. Contribution/Results: The paper proves that P-robustness is equivalent to strict majority responsiveness—exceeding 1/2—under the weighted average over all extreme points of *P*. Notably, when *P* encompasses all degenerate distributions, P-robust rules coincide precisely with tie-free weighted majority rules. This work provides a theoretically rigorous yet operationally tractable benchmark for collective decision-making under preference uncertainty.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• Establish normative criteria for voting rules under preference uncertainty
• Define robustness based on individual responsiveness exceeding one-half
• Link P-robust rules to weighted majority rules without ties

Innovation

• Proposes normative criteria for uncertain voting
• Defines P-robust voting rules with responsiveness
• Links robust rules to weighted majority decisions