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Randomized collective choices based on a fractional tournament

Author

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  • Sprumont, Yves

    (Department of Economics, Deakin University)

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.

Suggested Citation

  • Sprumont, Yves, 2025. "Randomized collective choices based on a fractional tournament," Theoretical Economics, Econometric Society, vol. 20(1), January.
    • Handle: RePEc:the:publsh:5589
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Fractional tournament; voting; random choice; stochastic rationalizability;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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