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A Rationalization of the Weak Axiom of Revealed Preference

Author

Listed:
  • Victor H. Aguiar
  • Per Hjertstrand
  • Roberto Serrano
  • Ozgur Evren

Abstract

Given a finite collection of choices over budgets, rational consumer behavior is identified with the generalized axiom of revealed preference (GARP). As an alternative, the weak generalized axiom of revealed preference--WGARP--only rules out strict choice cycles of size two. While GARP failures are routinely found in both the field and the lab, the same is not true for WGARP. We study how WGARP-consistent choices can be rationalized as a form of optimal behavior. Our main result is an analogue of the celebrated Afriat's theorem, but for WGARP. We show that choices are consistent with WGARP if and only if they can be rationalized by an asymmetric and strictly monotonic preference function. Equivalently, they can be rationalized by a preference function that admits a coalitional multi-utility (CMU) representation with a coherence restriction. A coherent CMU representation aggregates multiple utility functions --selves-- within the individual, so that binary preference reversals do not occur, while longer preference cycles remain possible. As a result, the class of incomplete, intransitive, and nonconvex preferences compatible with WGARP is studied.

Suggested Citation

  • Victor H. Aguiar & Per Hjertstrand & Roberto Serrano & Ozgur Evren, 2019. "A Rationalization of the Weak Axiom of Revealed Preference," Papers 1906.00296, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:1906.00296
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    Cited by:

    1. Madhav Chandrasekher & Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2022. "Dual‐Self Representations of Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(3), pages 1029-1061, May.
    2. Schlee, Edward E. & Ali Khan, M., 2023. "Money-metrics in local welfare analysis: Pareto improvements and equity considerations," Journal of Economic Theory, Elsevier, vol. 213(C).
    3. Roy Allen & John Rehbeck, 2020. "Counterfactual and Welfare Analysis with an Approximate Model," Papers 2009.03379, arXiv.org.
    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.
    5. Marcos Demetry & Per Hjertstrand & Matthew Polisson, 2022. "Testing axioms of revealed preference in Stata," Stata Journal, StataCorp LLC, vol. 22(2), pages 319-343, June.
    6. Alvaro Sandroni & Leo Katz, 2024. "The leveling axiom," Theory and Decision, Springer, vol. 96(1), pages 135-152, February.
    7. Per Hjertstrand, 2025. "Nonparametric analysis of the mixed-demand model," Empirical Economics, Springer, vol. 69(4), pages 2109-2140, October.
    8. Wilfried Youmbi, 2024. "Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences," Papers 2406.13969, arXiv.org.
    9. Marcos Demetry & Per Hjertstrand, 2023. "Consistent subsets: Computing the Houtman–Maks index in Stata," Stata Journal, StataCorp LLC, vol. 23(2), pages 578-588, June.

    More about this item

    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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