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On the Likelihood of Cyclic Comparisons

Author

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  • Ariel Rubinstein
  • Uzi Segal

Abstract

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.
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Suggested Citation

  • Ariel Rubinstein & Uzi Segal, 2011. "On the Likelihood of Cyclic Comparisons," Levine's Working Paper Archive 786969000000000096, David K. Levine.
    • Handle: RePEc:cla:levarc:786969000000000096
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    References listed on IDEAS

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    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, October.
    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

    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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