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A Rationalization of the Weak Axiom of Revealed Preference
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A Rationalization of the Weak Axiom of Revealed Preference

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Abstract

Samuelson’s (1938) weak (generalized) axiom of revealed preference– WGARP–is a minimal and appealing consistency condition of choice. We offer a rationalization of WGARP in general settings. Our main result is an exact analog of the celebrated Afriat’s theorem, but for WGARP. Its ordinal rationalization is in terms of an asymmetric and locally nonsatiated preference function. Its cardinal rationalization uses a coalitional multi-utility (CMU) maxmin representation with a coherency restriction on the coalition structure. Effectively, the CMU representation aggregates piecemeal preferences within the decision maker (multiple rationales without preference reversals that allow for transitivity violations). Basic consumer theory and welfare analysis are also developed. Extensions to the weak axiom of revealed preference–WARP–and choices obeying the law of demand are included.

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  • Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2022. "A Rationalization of the Weak Axiom of Revealed Preference," University of Western Ontario, Departmental Research Report Series 20229, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20229
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    Cited by:

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    2. Alvaro Sandroni & Leo Katz, 2024. "The leveling axiom," Theory and Decision, Springer, vol. 96(1), pages 135-152, February.
    3. Marcos Demetry & Per Hjertstrand, 2023. "Consistent subsets: Computing the Houtman–Maks index in Stata," Stata Journal, StataCorp LP, vol. 23(2), pages 578-588, June.
    4. Pawel Dziewulski, 2021. "A comprehensive revealed preference approach to approximate utility maximisation," Working Paper Series 0621, Department of Economics, University of Sussex Business School.
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    6. Roy Allen & John Rehbeck, 2020. "Counterfactual and Welfare Analysis with an Approximate Model," Papers 2009.03379, arXiv.org.
    7. Marcos Demetry & Per Hjertstrand & Matthew Polisson, 2022. "Testing axioms of revealed preference in Stata," Stata Journal, StataCorp LP, vol. 22(2), pages 319-343, June.
    8. Wilfried Youmbi, 2024. "Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences," Papers 2406.13969, arXiv.org.

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    Keywords

    abstract consumer choice; weak axiom of revealed preference; Afriat’s theorem; asymmetric preference function; coalitional multi-utility rationalization; welfare analysis;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D10 - Microeconomics - - Household Behavior - - - General

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