2020/07/17 by Cerreia-Vioglio, Simone, Lindberg, Per Olov, Maccheroni, Fabio +2
#FOS: Economics and business #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2007.11386
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."