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.

翻译：我们在随机社会选择中开创了一个新方向，提出了一种针对随机结果的主体效用新定义。每个主体对所有结果存在偏好，并拥有一个{\em 分位数}参数。给定一个结果上的{\em 彩票}，主体从某个特定的{\em 代表结果}中获得效用，该代表结果被定义为：在满足任意更差排序结果得以实现的概率不超过主体分位数值的条件下，能够实现的最不受偏好结果。与随机社会选择中考虑的其他效用模型（例如随机占优、期望效用）相比，我们的{\em 分位数主体效用}在比较两个彩票对某个主体的效用时，仅需比较其代表结果，这与确定性结果的比较方式相同。这为随机结果提供了一种纯粹序数式且信息丰富的比较方法。我们利用这一新的效用定义重新审视了随机社会选择中的基本问题。我们研究了随机投票规则中效率与策略证明性的兼容性，以及随机单边匹配机制中效率、公平性与策略证明性的兼容性。与经典的不可能性结果相反，我们证明在分位数主体效用下，这些性质通常可以同时得到满足。