Aggregating Preferences over Lotteries in the Absence of Expected Utility

经济学中有很多例子需要综合多个代理人的偏好，比如招聘委员会对不同的求职者进行投票，议会决定如何将预算分配给不同的项目，或者市政当局根据学生的偏好将学生分配到学校。社会选择理论及其子领域匹配理论是正式研究偏好聚集，特别是聚集偏好的机制的经济学科。对于许多应用，彩票，即概率分布，在一些确定性的选择集资格作为可行的结果。除其他好处外，彩票可以保证代理人之间的公平性，例如，在分配学生到学校时。大部分关于彩票偏好的文献都假设偏好是基于预期效用的，也就是说，代理人为每个确定性的选择分配一个效用值，并偏好具有更高预期效用的彩票。然而，决策理论为系统性地违反预期效用假设和过多的替代偏好模型提供了证据。 这个项目的目的是研究对彩票的偏好的聚合，而不是基于预期的效用。主要目标是构建从规范的角度来看具有吸引力的聚合机制，即满足理想属性的机制，例如代理之间的公平性，不同决策之间的一致性，或代理对策略行为的抵抗力。所提出的方法基于形式推理，即使用数学方法证明或反驳陈述。

Economics abounds with instances that require aggregating the preferences of multiple agents, such as a hiring committee voting on different applicants for a job, a parliament deciding on how to allocate a budget to different projects, or a municipality allocating students to schools based on the preferences of the students. Social choice theory and its subfield matching theory are the economic disciplines that formally study preference aggregation and, in particular, mechanisms for aggregating preferences. For many applications, lotteries, that is, probability distributions, over some set of deterministic alternatives qualify as feasible outcomes. Among other benefits, lotteries can guarantee fairness across agents, for example, when assigning students to schools. Much of the literature on aggregating preferences over lotteries assumes that preferences are based on expected utility, that is, agents assign a utility value to every deterministic alternative and prefer lotteries with higher expected utility. However, decision theory has provided evidence for systematic violations of the expected utility hypothesis and a plethora of alternative preference models. This project aims to study the aggregation of preferences over lotteries that are not based on expected utility. The main goal is to construct aggregation mechanisms that are appealing from a normative viewpoint, that is, mechanisms that satisfy desirable properties such as fairness across agents, consistency across different decisions, or resistance to strategic behavior by agents. The proposed approach grounds on formal reasoning, that is, statements are proved or disproved using mathematical methods.