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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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