On the likelihood of cyclic comparisons
AbstractOne 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 147 (2012)
Issue (Month): 6 ()
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Web page: http://www.elsevier.com/locate/inca/622869
Transitivity; Preference formation; Paradox of nontransitive dice;
Other versions of this item:
- Ariel Rubinstein & Uzi Segal, 2011. "On the Likelihood of Cyclic Comparisons," Levine's Working Paper Archive 786969000000000096, David K. Levine.
- 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.
- 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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- Osborne, Martin J & Rubinstein, Ariel, 1998.
"Games with Procedurally Rational Players,"
American Economic Review,
American Economic Association, vol. 88(4), pages 834-47, September.
- 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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