An Axiomatic and Computational Study of Probabilistic Social Choice

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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.