Randomized collective choices based on a fractional tournament

• 成果类型: Article
• 署名作者: Sprumont, Yves
• 署名单位: Deakin University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5589
• 发表日期: 2025
• 关键词: Preference aggregation; probabilities; POWER

摘要

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.