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
U2 - 10.1016/j.jet.2012.05.005
DO - 10.1016/j.jet.2012.05.005
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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 -