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).

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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 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
Date:	2011
Volume:	Vol.2011
Number:	No.973
Status:	Not Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/41118

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