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A Simple Test of Richter-Rationality


  • Marc-Arthur Diaye

    () (Centre d’Etude de l’Emploi and University of Evry (EPEE))

  • Michal Wong-Urdanivia

    () (Centre de Recherche en Mathématiques, Statistique, et Economie Mathématique (CERMSEM), University Paris 1 Panthéon-Sorbonne)


We propose in this note a simple non-parametric test of Richterrationality which is the basic definition of rationality used in choice functions theory. Loosely speaking, the data set is rationalizable in the Richter’ sense if there exists a complete-acyclic binary relation that rationalizes the data set. Hence a data set is rationalizable in the Richter’ sense if there exists a variable intervals function which rationalizes this data set. Since an acyclic binary relation is not necessary transitive then the proposed Richter-rationality test is weaker than GARP. Finally the test is performed over Mattei’s1 data sets.

Suggested Citation

  • Marc-Arthur Diaye & Michal Wong-Urdanivia, 2006. "A Simple Test of Richter-Rationality," Documents de recherche 06-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  • Handle: RePEc:eve:wpaper:06-01

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    References listed on IDEAS

    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
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    4. Agaev, Rafig & Aleskerov, Fuad, 1993. "Interval choice: classic and general cases," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 249-272, November.
    5. Fishburn, P. C., 1984. "SSB utility theory and decision-making under uncertainty," Mathematical Social Sciences, Elsevier, vol. 8(3), pages 253-285, December.
    6. Timothy Berry & William Harbaugh & Kate Krause, 2001. "Garp for kids: On the development of rational choice behavior," Artefactual Field Experiments 00056, The Field Experiments Website.
    7. Mattei, Aurelio, 2000. "Full-scale real tests of consumer behavior using experimental data," Journal of Economic Behavior & Organization, Elsevier, vol. 43(4), pages 487-497, December.
    8. William T. Harbaugh & Kate Krause & Timothy R. Berry, 2001. "GARP for Kids: On the Development of Rational Choice Behavior," American Economic Review, American Economic Association, vol. 91(5), pages 1539-1545, December.
    9. Jamison, Dean T & Lau, Lawrence J, 1973. "Semiorders and the Theory of Choice," Econometrica, Econometric Society, vol. 41(5), pages 901-912, September.
    10. Famulari, Melissa, 1995. "A Household-Based, Nonparametric Test of Demand Theory," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 372-382, May.
    11. Begoña Subiza Martínez, 1993. "Numerical Representation Of Acyclic Preferences," Working Papers. Serie AD 1993-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    12. Dombi, Jozsef & Vincze, Nandor J., 1994. "Universal characterization of non-transitive preferences," Mathematical Social Sciences, Elsevier, vol. 27(1), pages 91-104, February.
    13. Anand, Paul, 1995. "Foundations of Rational Choice Under Risk," OUP Catalogue, Oxford University Press, number 9780198774426.
    14. Sippel, Reinhard, 1997. "An Experiment on the Pure Theory of Consumer's Behaviour," Economic Journal, Royal Economic Society, vol. 107(444), pages 1431-1444, September.
    15. Rodriguez-Palmero, Carlos, 1997. "A representation of acyclic preferences," Economics Letters, Elsevier, vol. 54(2), pages 143-146, February.
    16. Diaye, Marc-Arthur, 1999. "Variable intervals model," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 21-33, July.
    17. James Andreoni & John Miller, 2002. "Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism," Econometrica, Econometric Society, vol. 70(2), pages 737-753, March.
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    More about this item


    GARP; Choice Functions; Richter-Rationality; Variable Intervals Functions;

    JEL classification:

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


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