On the likelihood of cyclic comparisons

• 成果类型: Article
• 署名作者: Rubinstein, Ariel; Segal, Uzi
• 署名单位: Tel Aviv University; New York University; Boston College
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.05.005
• 发表日期: 2012
• 页码: 2483-2491
• 关键词: Transitivity; preference formation; Paradox of nontransitive dice

摘要

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 8/27. Even lower bounds are obtained for some other related procedures. (C) 2012 Elsevier Inc. All rights reserved.