Geometry on the Utility Space
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
Cite
@article{arxiv.1511.01303,
title = {Geometry on the Utility Space},
author = {François Durand and Benoît Kloeckner and Fabien Mathieu and Ludovic Noirie},
journal= {arXiv preprint arXiv:1511.01303},
year = {2015}
}
Comments
in Fourth International Conference on Algorithmic Decision Theory, Sep 2015, Lexington, United States. pp.16, 2015, Fourth International Conference on Algorithmic Decision Theory