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

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

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 (US)
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

Keywords

Paradox of nontransitive dice
Preference formation
Transitivity

ASJC Scopus subject areas

Economics and Econometrics

Access to Document

10.1016/j.jet.2012.05.005

Cite this

@article{8c1769e4bd2045b8b66184fd6714b460,

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 . ",

year = "2012",

month = nov,

doi = "10.1016/j.jet.2012.05.005",

language = "English (US)",

volume = "147",

pages = "2483--2491",

journal = "Journal of Economic Theory",

issn = "0022-0531",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - On the likelihood of cyclic comparisons

AU - Rubinstein, Ariel

AU - Segal, Uzi

N1 - Funding Information: We thank Noga Alon, Jason Dana, Michael Richter, an associate editor and a referee for their comments and suggestions and to Inácio 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 .

PY - 2012/11

Y1 - 2012/11

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

KW - Transitivity

UR - http://www.scopus.com/inward/record.url?scp=84869098639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869098639&partnerID=8YFLogxK

U2 - 10.1016/j.jet.2012.05.005

DO - 10.1016/j.jet.2012.05.005

M3 - Article

AN - SCOPUS:84869098639

SN - 0022-0531

VL - 147

SP - 2483

EP - 2491

JO - Journal of Economic Theory

JF - Journal of Economic Theory

IS - 6

ER -

On the likelihood of cyclic comparisons

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this