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Stochastic Rationality and Möbius Inverse

Listed author(s):
  • Antoine Billot

    (PSE - Paris-Jourdan Sciences Economiques - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - ENS Paris - École normale supérieure - Paris - École des Ponts ParisTech (ENPC), UP2 - Université Panthéon-Assas - M.E.N.E.S.R. - Ministère de l'Éducation nationale, de l’Enseignement supérieur et de la Recherche, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain)

  • Jacques-François Thisse

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

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.

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Paper provided by HAL in its series Post-Print with number halshs-00754062.

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Date of creation: Sep 2005
Publication status: Published in International Journal of Economic Theory, Wiley, 2005, 1 (3), pp.211-217. <10.1111/j.1742-7363.2005.00013.x>
Handle: RePEc:hal:journl:halshs-00754062
DOI: 10.1111/j.1742-7363.2005.00013.x
Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754062
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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