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Conditional preference orders and their numerical representations

Samuel Drapeau and Asgar Jamneshan

Journal of Mathematical Economics, 2016, vol. 63, issue C, 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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Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:106-118