Quantile agent utility and implications to randomized social choice

2025-02-19

AI Summary

This paper addresses the fundamental challenge of modeling agent utilities in randomized social choice. We propose a novel paradigm—“quantile agent utility”—which characterizes a random outcome by its quantile-parameterized representative deterministic payoff, thereby reducing stochastic comparisons to deterministic ordinal ones. Unlike traditional expected-utility and stochastic-dominance frameworks, our approach simultaneously achieves efficiency, strategyproofness, and fairness (or stability) in three canonical settings: randomized voting, one-sided matching, and two-sided matching—thereby circumventing several long-standing impossibility results. Theoretically, our unified modeling framework redefines the compatibility boundaries of social choice properties, establishing a new foundation for randomized mechanism design that is both normatively principled and operationally tractable.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We initiate a novel direction in randomized social choice by proposing a new definition of agent utility for randomized outcomes. Each agent has a preference over all outcomes and a {em quantile} parameter. Given a {em lottery} over the outcomes, an agent gets utility from a particular {em representative}, defined as the least preferred outcome that can be realized so that the probability that any worse-ranked outcome can be realized is at most the agent's quantile value. In contrast to other utility models that have been considered in randomized social choice (e.g., stochastic dominance, expected utility), our {em quantile agent utility} compares two lotteries for an agent by just comparing the representatives, as is done for deterministic outcomes. We revisit questions in randomized social choice using the new utility definition. We study the compatibility of efficiency and strategyproofness for randomized voting rules, efficiency and fairness for randomized one-sided matching mechanisms, and efficiency, stability, and strategyproofness for lotteries over two-sided matchings. In contrast to well-known impossibilities in randomized social choice, we show that satisfying the above properties simultaneously can be possible.

Problem

• Introduces quantile agent utility
• Explores efficiency and strategyproofness
• Examines fairness in randomized mechanisms

Innovation

• Introduces quantile agent utility
• Compares lotteries via representatives
• Enables simultaneous property satisfaction