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Transitivity of preferences: when does it matter?

Author

Listed:
  • Cherchye, Laurens

    (Department of Economics, KULeuven)

  • Demuynck, Thomas

    (Ecares, Université Libre de Bruxelles)

  • De Rock, Bram

    (Ecares, Université Libre de Bruxelles)

Abstract
We define necessary and sufficient conditions on prices and incomes under which quantity choices can violate SARP (Strong Axiom of Revealed Preference) but not WARP (Weak Axiom of Revealed Preference). As SARP extends WARP by additionally imposing transitivity on the revealed preference relation, this effectively defines the conditions under which transitivity adds bite to the empirical analysis. For finite datasets, our characterization takes the form of a triangular condition that must hold for all three-element subsets of normalized prices, and which is easy to verify in practice. For infinite datasets, we formally establish an intuitive connection between our characterization and the concept of Hicksian aggregation. We demonstrate the practical use of our conditions through two empirical illustrations.

Suggested Citation

  • Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    • Handle: RePEc:the:publsh:2733
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Khushboo Surana, 2022. "How different are we? Identifying the degree of revealed preference heterogeneity," Discussion Papers 22/09, Department of Economics, University of York.
    2. Takashi Kunimoto & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-15, Brown University, Department of Economics.
    3. Victor H. Aguiar & Roberto Serrano, 2018. "Cardinal Revealed Preference, Price-Dependent Utility, and Consistent Binary Choice," Working Papers 2018-3, Brown University, Department of Economics.
    4. Alvaro Sandroni & Leo Katz, 2024. "The leveling axiom," Theory and Decision, Springer, vol. 96(1), pages 135-152, February.
    5. Sam Cosaert, 2019. "What Types are There?," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 533-554, February.
    6. Laurens Cherchye & Dieter Saelens & Reha Tuncer, 2024. "From unobserved to observed preference heterogeneity: a revealed preference methodology," Economica, London School of Economics and Political Science, vol. 91(363), pages 996-1022, July.
    7. Cherchye, Laurens & Demuynck, Thomas & Rock, Bram De, 2019. "Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures," Journal of Econometrics, Elsevier, vol. 211(2), pages 483-506.
    8. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.
    9. Christopher P. Chambers & John Rehbeck, 2022. "Nonparametric market supply with variable participants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 899-921, October.
    10. Wilfried Youmbi, 2024. "Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences," Papers 2406.13969, arXiv.org.
    11. Zhibin Wu & Rong Yuan & Jiancheng Tu, 2021. "Group Decision Making with Transitive Preferences Under Ordinal and Cardinal Consistencies: An Optimization Approach," Group Decision and Negotiation, Springer, vol. 30(1), pages 221-250, February.

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    More about this item

    Keywords

    Revealed preferences; warp; sarp; transitive preferences; testable implications; Hicksian aggregation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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