An Axiomatic and Computational Study of Probabilistic Social Choice

这个项目的目标是研究概率社会选择函数的公理化性质，即，将个体主体的偏好聚合到社会可接受的概率结果的函数。概率社会选择在经济学和计算机科学中受到越来越多的关注，并在随机分配和匹配市场等特殊领域中有许多应用。我们将通过使用经典的数学分析工具以及计算机辅助技术，包括SAT求解、混合整数规划和计算机实验来实现这一目标。主要的方法创新是计算机辅助定理证明技术和复杂的几何和拓扑分析工具。主要的概念创新涉及不同程度的效率、策略证明性和基于偏好扩展的参与的定义，以及渐近公理，研究某些公理是否“几乎总是”或“几乎从不”被满足。

The goal of this project is to investigate the axiomatic properties of probabilistic social choice functions, i.e., functions that aggregate the preferences of individual agents to socially acceptable probabilistic outcomes. Probabilistic social choice is gaining increasing attention in economics and computer science and has many applications in special domains of interest such as random assignment and matching markets. We will pursue this goal by using classical analytical tools from mathematics as well as computer-aided techniques including SAT solving, mixed integer programming, and computer experiments. The main methodological novelties are computer-aided theorem proving techniques and sophisticated analytical tools from geometry and topology. The main conceptual novelties concern the definition of varying degrees of efficiency, strategyproofness, and participation based on preference extensions, and asymptotic axiomatics, the study of whether certain axioms are ``almost always'' or ``almost never'' satisfied.