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On the likelihood of cyclic comparisons


  • Rubinstein, Ariel
  • Segal, Uzi


One problem caused by cycles of choice functions is indecisiveness—decision makers will be paralyzed when they face choice sets with more than two options. We investigate the procedure of “random sampling” where the alternatives are random variables. When comparing any two alternatives, the decision maker samples each of the alternatives once and ranks them according to the comparison between the two realizations. We show that while this procedure may lead to violations of transitivity, the probability of such cycles is bounded from above by 827. Even lower bounds are obtained for some other related procedures.

Suggested Citation

  • Rubinstein, Ariel & Segal, Uzi, 2012. "On the likelihood of cyclic comparisons," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2483-2491.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:6:p:2483-2491 DOI: 10.1016/j.jet.2012.05.005

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    References listed on IDEAS

    1. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    2. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
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    More about this item


    Transitivity; Preference formation; Paradox of nontransitive dice;

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty


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