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On the Likelihood of Cyclic Comparisons

Author

Listed:
  • Ariel Rubinstein

    (University of Tel Aviv)

  • Uzi Segal

    (Boston College)

Abstract

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. Our main result is that when applied to three alternatives, the procedure yields a cycle with a probability bounded above by 8/27. Bounds are also obtained for other related procedures.

Suggested Citation

  • Ariel Rubinstein & Uzi Segal, 2011. "On the Likelihood of Cyclic Comparisons," Boston College Working Papers in Economics 773, Boston College Department of Economics, revised 12 Feb 2012.
    • Handle: RePEc:boc:bocoec:773
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    References listed on IDEAS

    as
    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. Jacobs,Donald P. & Kalai,Ehud & Kamien,Morton I. & Schwartz,Nancy L. (ed.), 1998. "Frontiers of Research in Economic Theory," Cambridge Books, Cambridge University Press, number 9780521635387, September.
    3. 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.
    4. Ilia Tsetlin & Michel Regenwetter & Bernard Grofman, 2003. "The impartial culture maximizes the probability of majority cycles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 387-398, December.
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    Cited by:

    1. repec:cup:judgdm:v:13:y:2018:i:3:p:217-236 is not listed on IDEAS
    2. Charles-Cadogan, G., 2021. "Incoherent Preferences," CRETA Online Discussion Paper Series 69, Centre for Research in Economic Theory and its Applications CRETA.
    3. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    4. David J. Butler & Ganna Pogrebna, 2018. "Predictably intransitive preferences," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(3), pages 217-236, May.

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    More about this item

    Keywords

    Transitivity; preference formation; the paradox of nontransitive dice;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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