Numerical representation of choice functions

  1. Josep Enric Peris Ferrando 1
  2. Mª Carmen Sánchez Antón 2
  3. Begoña Subiza Martínez 1
  1. 1 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

  2. 2 Cergy-Pontoise University
    info

    Cergy-Pontoise University

    Cergy-Pontoise, Francia

Journal:
Working papers = Documentos de trabajo: Serie AD

Year of publication: 1998

Issue: 1

Pages: 1-23

Type: Working paper

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Abstract

Numerical representations of choice functions allow the expression of a problem of choice as a problem of finding maxima of real valued functions, which requires less information to be defined and which is easier to work with. In this paper, the existence of numerical representations of choice functions by imposing assumptions directly on the choice function, is obtained. In particular, it is proved that (IIA) is a necessary and sufficient condition for a choice function to be representable, if the set of alternatives is countable, while the conjunction of (IIA) and a continuity condition is sufficient to ensure it in separable topological spaces.

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