Quantile agent utility and implications to randomized social choice
Ioannis Caragiannis, Sanjukta Roy
TL;DR
The paper introduces quantile utility for randomized outcomes, formalizing the $h$-quantile representative $ ext{rep}(x, ext{succ},h)$ and showing that agent comparisons reduce to comparing representatives. It then develops and analyzes mechanisms across three domains—voting, one-sided matching, and two-sided matching—identifying conditions under which efficiency, strategyproofness, and fairness relations can be achieved, sometimes simultaneously (e.g., two-alternative voting via $R$-plurality; SD in one-sided matching; half-DA in two-sided matching for $h\ge 1/2$) and outlining open problems for more general settings. The framework connects to stochastic dominance while enabling tractable, representative-based comparisons and LP-based algorithmic constructions, yielding new positive results where classical impossibilities would suggest none. Overall, the quantile utility model offers a versatile tool to balance efficiency, incentive-compatibility, and fairness in randomized social choice and matching, with concrete mechanisms and clear directions for future work. $h$-quantile representations and corresponding LP formulations underpin the methodological core, suggesting practical pathways for designing equitable randomized mechanisms in diverse domains.
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.