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Axioms for measuring utility on partial mixture sets

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  • O’Callaghan, Patrick H.

Abstract

A mixture set is path-connected via a suitable collection of paths, the most common example being a convex set. We introduce partial mixture sets (where certain paths may be missing or excluded) and provide a formal extension of the well-known axiomatisation of cardinal linear utility by Herstein and Milnor. In order to compensate for the weaker structure of partial mixture sets, it is necessary to strengthen the Herstein–Milnor axioms. We show that partial mixture sets feature in a variety of benchmark models in the literature and especially where utility may be cardinal nonlinear on a richer set of paths or a larger set of prospects. For instance, in the theory of ambiguity: the canonical partial mixture set consists of the full set of acts together with the set of convex paths that connect comonotonic acts.

Suggested Citation

  • O’Callaghan, Patrick H., 2018. "Axioms for measuring utility on partial mixture sets," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 76-86.
    • Handle: RePEc:eee:mateco:v:77:y:2018:i:c:p:76-86
    DOI: 10.1016/j.jmateco.2018.05.006
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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    3. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, September.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Simon Grant & Atsushi Kajii & Ben Polak & Zvi Safra, 2010. "Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem," Econometrica, Econometric Society, vol. 78(6), pages 1939-1971, November.
    6. Karni, Edi & Safra, Zvi, 2000. "An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 315-327, November.
    7. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
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