# Conditional preference orders and their numerical representations

*Samuel Drapeau* and
*Asgar Jamneshan*

*Journal of Mathematical Economics*, 2016, vol. 63, issue C, pages 106-118

**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.

**Keywords:** Conditional preferences; Utility theory; Gap Lemma; von Neumann and Morgenstern (search for similar items in EconPapers)

**Date:** 2016

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**Persistent link:** http://EconPapers.repec.org/RePEc:eee:mateco:v:63:y:2016:i:c:p:106-118

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