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Context and Decision: Utility on a Union of Mixture Spaces

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  • O'Callaghan, Patrick
Abstract
Suppose a decision-maker is willing to make statements of the form: “I prefer to choose alternative a when in context p, than to choose alternative b when in context q”. Contexts p and q may refer to given probability distributions over a set of states, and b and c to alternatives such as: “turn left” or “turn right” at a junction. In such decision problems, the set of alternatives is discrete and there is a continuum of possible contexts. I assume there is a is a mixture operation on the space of contexts (eg. convex combinations of lotteries), and propose a model that defines preferences over a collection of mixture spaces indexed by a discrete set. The model yields a spectrum of possibilities: some decision-makers are well represented by a standard von Neumann–Morgenstern type of utility function; whilst for others, utility across some or all the mixture spaces is only ordinally comparable. An application to the decision problem of Karni and Safra (2000) leads to a generalization, and shows that state-dependence and comparability are distinct concepts. A final application provides a novel way of modeling incomplete preferences and explaining the Allais paradox.

Suggested Citation

  • O'Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," Economic Research Papers 270751, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:270751
    DOI: 10.22004/ag.econ.270751
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    References listed on IDEAS

    as
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