On the likelihood of cyclic comparisons

Ariel Rubinstein; Uzi Segal

doi:10.1016/j.jet.2012.05.005

On the likelihood of cyclic comparisons

Ariel Rubinstein, Uzi Segal^*

^*Corresponding author for this work

School of Economics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	2483-2491
Number of pages	9
Journal	Journal of Economic Theory
Volume	147
Issue number	6
DOIs	https://doi.org/10.1016/j.jet.2012.05.005
State	Published - Nov 2012

Funding

Funders	Funder number
Israel Science Foundation	259/08
Foerder Institute for Economic Research

Keywords

Paradox of nontransitive dice
Preference formation
Transitivity

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10.1016/j.jet.2012.05.005

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title = "On the likelihood of cyclic comparisons",

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.",

keywords = "Paradox of nontransitive dice, Preference formation, Transitivity",

author = "Ariel Rubinstein and Uzi Segal",

note = "Funding Information: We thank Noga Alon, Jason Dana, Michael Richter, an associate editor and a referee for their comments and suggestions and to In{\'a}cio Guerberoff and Irina Manea for their assistance. We acknowledge financial support from the Israeli Science Foundation (grant No. 259/08 ) and the Foerder Institute for Economic Research . ",

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AU - Segal, Uzi

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N2 - 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.

AB - 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.

KW - Paradox of nontransitive dice

KW - Preference formation

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On the likelihood of cyclic comparisons

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