On the Likelihood of Cyclic Comparisons
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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- Osborne, M-J & Rubinstein, A, 1997.
"Games with Procedurally Rational Players,"
4-97, Tel Aviv.
- 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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