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Conditional preference orders and their numerical representations

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  • Drapeau, Samuel
  • Jamneshan, Asgar

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.

Suggested Citation

  • Drapeau, Samuel & Jamneshan, Asgar, 2016. "Conditional preference orders and their numerical representations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 106-118.
    • Handle: RePEc:eee:mateco:v:63:y:2016:i:c:p:106-118
    DOI: 10.1016/j.jmateco.2015.12.004
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    Cited by:

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    2. Marco Maggis & Andrea Maran, 2018. "Stochastic Dynamic Utilities and Inter-Temporal Preferences," Papers 1803.05244, arXiv.org, revised Feb 2020.
    3. Wei-zhi Qin & Hendrik Rommeswinkel, 2024. "Quasi-separable preferences," Theory and Decision, Springer, vol. 96(4), pages 555-595, June.

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