Geometry on the Utility Space

Abstract : We examine the geometrical properties of the space of expected utilities over a finite set of options, which is commonly used to model the preferences of an agent. We focus on the case where options are assumed to be symmetrical a priori. 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.
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https://hal.archives-ouvertes.fr/hal-01096018
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Submitted on : Tuesday, December 16, 2014 - 4:16:44 PM
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François Durand, Benoît Kloeckner, Fabien Mathieu, Ludovic Noirie. Geometry on the Utility Space. The 12th Meeting of the Society for Social Choice and Welfare (SSCW 2014), Jun 2014, Boston, United States. ⟨hal-01096018⟩

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