Aggregating Preferences over Lotteries in the Absence of Expected Utility

经济学中有很多需要汇总多个主体偏好的例子，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合，特别是偏好聚合机制的经济学学科。对于许多应用来说，彩票，也就是概率分布，在一组确定的备选方案上可以作为可行的结果。在其他好处中，彩票可以保证代理人之间的公平，例如，在分配学生到学校时。许多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，代理为每个确定性选择分配一个效用值，并且更喜欢期望效用更高的彩票。然而，决策理论已经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。这个项目旨在研究不基于预期效用的彩票偏好的集合。主要目标是构建从规范观点来看具有吸引力的聚合机制，即满足理想属性的机制，例如跨代理的公平性，跨不同决策的一致性，或代理对战略行为的抵抗力。提出的方法以形式推理为基础，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.