Quantile agent utility and implications to randomized social choice

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. This yields a purely ordinal yet informative comparison of randomized outcomes.We revisit fundamental questions in randomized social choice using the new utility definition. We study the compatibility of efficiency and strategyproofness for randomized voting rules, and of efficiency, fairness, and strategyproofness for randomized one-sided matching mechanisms. In contrast to classical impossibility results, we show that under quantile agent utilities, these properties can often be satisfied simultaneously.