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Non-Archimedean preferences over countable lotteries

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  • Russell, Jeffrey Sanford

Abstract

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

Suggested Citation

  • Russell, Jeffrey Sanford, 2020. "Non-Archimedean preferences over countable lotteries," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 180-186.
    • Handle: RePEc:eee:mateco:v:88:y:2020:i:c:p:180-186
    DOI: 10.1016/j.jmateco.2020.03.011
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    References listed on IDEAS

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    1. Peter C. Fishburn, 1971. "A Study of Lexicographic Expected Utility," Management Science, INFORMS, vol. 17(11), pages 672-678, July.
    2. D. Borie, 2016. "Lexicographic expected utility without completeness," Theory and Decision, Springer, vol. 81(2), pages 167-176, August.
    3. Seidenfeld, Teddy & Schervish, Mark J. & Kadane, Joseph B., 2009. "Preference for equivalent random variables: A price for unbounded utilities," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 329-340, May.
    4. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
    Full references (including those not matched with items on IDEAS)

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