Arrovian Aggregation of Convex Preferences
研究了当结果空间是有限备选方案的凸包时，满足阿罗独立性和帕累托最优的社会福利函数，在连续凸偏好下刻画了允许匿名加总的偏好域和函数，将阿罗不可能转化为唯一社会福利函数的完整刻画。
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.