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Stochastic Rationality and Möbius Inverse

Author

Listed:
  • Antoine Billot

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, UP2 - Université Panthéon-Assas, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

  • Jacques-François Thisse

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

Abstract

Discrete choice theory is very much dominated by the paradigm of the maximization of a random utility, thus implying that the probability of choosing an alternative in a given set is equal to the sum of the probabilities of all the rankings for which this alternative comes first. This property is called stochastic rationality. In turn, the choice probability system is said to be stochastically rationalizable if and only if the Block-Marschak polynomials are all nonnegative. In the present paper, we show that each particular Block-Marschak polynomial can be defined as the probability that the decision-maker faces the loss in flexibility generated by the fact that a particular alternative has been deleted from the choice set.

Suggested Citation

  • Antoine Billot & Jacques-François Thisse, 2005. "Stochastic Rationality and Möbius Inverse," Post-Print halshs-00754062, HAL.
    • Handle: RePEc:hal:journl:halshs-00754062
    DOI: 10.1111/j.1742-7363.2005.00013.x
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    Keywords

    Stochastic rationality; Möbius inverse; Choice context;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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