Conditional Preference Orders and their Numerical Representations
Economics
2016-01-19 v4
Abstract
We provide an axiomatic system modeling conditional preference orders which is based on conditional set theory. Conditional numerical representations are introduced, and a conditional version of the theorems of Debreu on the existence of numerical representations is proved. The conditionally continuous representations follow from a conditional version of Debreu's Gap Lemma the proof of which relies on a conditional version of the axiom of choice, free of any measurable selection argument. We give a conditional version of the von Neumann and Morgenstern representation as well as automatic conditional continuity results, and illustrate them by examples.
Cite
@article{arxiv.1410.5466,
title = {Conditional Preference Orders and their Numerical Representations},
author = {Samuel Drapeau and Asgar Jamneshan},
journal= {arXiv preprint arXiv:1410.5466},
year = {2016}
}