A Canon of Probabilistic Rationality
Theoretical Economics
2021-05-11 v2
Abstract
We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice then occurs according to a tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom. Our result shows that the Choice Axiom is, in a precise formal sense, a probabilistic version of the Weak Axiom. It thus supports Luce's view of his own axiom as a "canon of probabilistic rationality."
Cite
@article{arxiv.2007.11386,
title = {A Canon of Probabilistic Rationality},
author = {Simone Cerreia-Vioglio and Per Olov Lindberg and Fabio Maccheroni and Massimo Marinacci and Aldo Rustichini},
journal= {arXiv preprint arXiv:2007.11386},
year = {2021}
}