Anonymous voting in a heterogeneous society

2025-08-11

AI Summary

This paper studies anonymous voting mechanism design for binary social choice under agents’ cardinal utilities that are independent but non-identically distributed, aiming to maximize expected social welfare. Using tools from mechanism design and game theory, augmented by probabilistic modeling, it rigorously compares the performance bounds of ordinal mechanisms—which rely solely on preference rankings—with cardinal mechanisms—which leverage intensity of preferences. The main contributions are two-fold: First, for two agents, the ordinal majority rule is proven universally optimal; no cardinal mechanism can improve expected welfare. Second, for three or more agents, the paper constructs explicit counterexamples demonstrating the existence of anonymous cardinal mechanisms that strictly dominate all ordinal ones. This establishes the critical agent threshold at which ordinality fails to be optimal—namely, three agents—and identifies the minimal scale at which cardinal information yields strictly positive social value under heterogeneous preferences.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the design of voting mechanisms in a binary social choice environment where agents' cardinal valuations are independent but not necessarily identically distributed. The mechanism must be anonymous -- the outcome is invariant to permutations of the reported values. We show that if there are two agents then expected welfare is always maximized by an ordinal majority rule, but with three or more agents there are environments in which cardinal mechanisms that take into account preference intensities outperform any ordinal mechanism.

Problem

• Designing anonymous voting mechanisms for heterogeneous agents
• Comparing cardinal versus ordinal mechanisms for welfare maximization
• Determining when cardinal mechanisms outperform ordinal ones

Innovation

• Anonymous voting mechanism design
• Binary social choice environment
• Cardinal mechanisms outperform ordinal