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Context and decision : utility on a union of mixture spaces
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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)).

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Abstract
Suppose a decisionmaker 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 decisionmakers 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 statedependence 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Status:  Not Peer Reviewed 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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