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Geometry on the Utility Space

  • François DurandEmail author
  • Benoît Kloeckner
  • Fabien Mathieu
  • Ludovic Noirie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9346)

Abstract

We study the geometrical properties of the utility space (the space of expected utilities over a finite set of options), which is commonly used to model the preferences of an agent in a situation of uncertainty. We focus on the case where the model is neutral with respect to the available options, i.e. treats them, a priori, as being symmetrical from one another. Specifically, we prove that the only Riemannian metric that respects the geometrical properties and the natural symmetries of the utility space is the round metric. This canonical metric allows to define a uniform probability over the utility space and to naturally generalize the Impartial Culture to a model with expected utilities.

Keywords

Utility theory Geometry Impartial culture Voting 

Notes

Acknowledgments

The work presented in this paper has been partially carried out at LINCS (http://www.lincs.fr).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • François Durand
    • 1
    Email author
  • Benoît Kloeckner
    • 2
  • Fabien Mathieu
    • 3
  • Ludovic Noirie
    • 3
  1. 1.InriaParisFrance
  2. 2.Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), UPEM, UPEC, CNRSCréteilFrance
  3. 3.Alcatel-Lucent Bell Labs FranceNozayFrance

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