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 then random choice occurs according to a tie-breaking mechanism 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." (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

A canon of probabilistic rationality

Cerreia-Vioglio, Simone;Maccheroni, Fabio
;
Marinacci, Massimo;Rustichini, Aldo
2021-01-01

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 then random choice occurs according to a tie-breaking mechanism 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." (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
2021
Cerreia-Vioglio, Simone; Lindberg, Per Olov; Maccheroni, Fabio; Marinacci, Massimo; Rustichini, Aldo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4052168
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