Context and decision : utility on a union of mixture spaces
O'Callaghan, Patrick H. D. (2011) Context and decision : utility on a union of mixture spaces. Working Paper. Coventry: University of Warwick. Dept. of Economics. Warwick economics research paper series (TWERPS), Vol.2011 (No.973).
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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 modeling incomplete preferences and explaining the Allais paradox.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Social Sciences > Economics
Faculty of Science > Mathematics
|Library of Congress Subject Headings (LCSH):||Decision making, Statistical decision|
|Series Name:||Warwick economics research paper series (TWERPS)|
|Publisher:||University of Warwick. Dept. of Economics|
|Place of Publication:||Coventry|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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