Randomized collective choices based on a fractional tournament
研究了如何将描述每对方案偏好比例的分数锦标赛扩展为随机选择函数，发现线性性和无关比较独立性无法与随机理性化兼容，并识别了保证唯一扩展的序贯二元域。
An extension rule assigns to each fractional tournament x (specifying, for every pair of social alternatives a and b , the proportion x ab of voters who prefer a to b ) a random choice function y (specifying a collective choice probability distribution for each subset of alternatives), which chooses a from { a , b } with probability x ab . There exist multiple neutral and stochastically rationalizable extension rules. Both linearity (requiring that y be an affine function of x ) and independence of irrelevant comparisons (asking that the probability distribution on a subset of alternatives depend only on the restriction of the fractional tournament to that subset) are incompatible with very weak properties implied by stochastic rationalizability. We identify a class of maximal domains, which we call sequentially binary , guaranteeing that every fractional tournament arising from a population of voters with preferences in such a domain has a unique admissible stochastically rationalizable extension.