# Special Seminar in CMS and HSS

*,*Economics

*,*Stanford University

*,*

Florian is a postdoctoral fellow at the Department of Economics at Stanford University. He obtained a PhD degree in mathematics from Technical University of Munich in 2018. Florianâ€™s research focuses on social choice, game theory, and decision theory, with a particular interest in decision-making under risk and uncertainty.

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.