Randomized collective choices based on a fractional tournament

Yves Sprumont ()
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Yves Sprumont: Department of Economics, Deakin University

Theoretical Economics, 2025, vol. 20, issue 1

Abstract: 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.

Keywords: Fractional tournament; voting; random choice; stochastic rationalizability (search for similar items in EconPapers)
JEL-codes: D70 (search for similar items in EconPapers)
Date: 2025-01-28
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