On the likelihood of cyclic comparisons

Ariel Rubinstein, Uzi Segal*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2483-2491
Number of pages9
JournalJournal of Economic Theory
Issue number6
StatePublished - Nov 2012


  • Paradox of nontransitive dice
  • Preference formation
  • Transitivity


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