Random Preferences, Acyclicity, and the Threshold of Rationality

17 Pages Posted: 24 Feb 2020 Last revised: 15 Sep 2020

See all articles by Bassel Tarbush

Bassel Tarbush

University of Oxford - Merton College

Date Written: January 25, 2020

Abstract

Draw an agent's preferences over $n$ alternatives at random as follows: independently, for each pair of distinct alternatives, with probability $1-p$ the agent is indifferent between the alternatives in the pair, and with probability $p$ the agent is equally likely to prefer one alternative over the other. The agent's preferences are rational if they are transitive or, equivalently, if there are no preference cycles. I show that rationality exhibits a threshold behavior: if $p$ is asymptotically smaller than $n^{-2}$ then the agent's preferences are rational with high probability, and if $p$ is asymptotically larger than $n^{-2}$ then the agent's preferences are not rational with high probability.

Keywords: Random preferences, random graphs, transitivity, preference cycles

JEL Classification: D01, D85

Suggested Citation

Tarbush, Bassel, Random Preferences, Acyclicity, and the Threshold of Rationality (January 25, 2020). Available at SSRN: https://ssrn.com/abstract=3525382 or http://dx.doi.org/10.2139/ssrn.3525382

Bassel Tarbush (Contact Author)

University of Oxford - Merton College ( email )

Merton College
Oxford, OX1 4JD
United Kingdom

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