English

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}
}
R2 v1 2026-06-22T06:30:19.009Z