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Arguments for a Better World: Essays in Honor of Amartya SenVolume I: Ethics, Welfare, and Measurement$
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Kaushik Basu and Ravi Kanbur

Print publication date: 2008

Print ISBN-13: 9780199239115

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199239115.001.0001

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Convexity and Separability in Representing Consensus

Convexity and Separability in Representing Consensus

Chapter:
(p.193) Chapter 11 Convexity and Separability in Representing Consensus
Source:
Arguments for a Better World: Essays in Honor of Amartya Sen
Author(s):

Isaac Levi (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239115.003.0012

This chapter discusses some issues concerning the representation of the valuation of options when decision makers have different probability judgments, different value commitments or both, and must engage in a joint deliberation based on some kind of consensus. The representation of consensus in such a setting is assumed to exhibit a structure similar to that appropriate to a single decision maker conflicted between competing commitments who makes decisions while in doubt. A case is made for representing doubt concerning probability judgment by sets of permissible probabilities, evaluations of consequences by sets of permissible utilities, and assessments of the available options by expectations derived from permissible probability-utility pairs. Sen has considered cognate problems where the evaluations of options are incomplete. He advocates restricting choice to options that are maximal among the available ones. The merits of this proposal are compared with restricting choice to options that are E-admissible in the sense that they are optimal according to at least one permissible probability-utility pair. Two variants of this view are considered. The chapter expresses a preference for requiring sets of permissible probabilities and permissible assessments of utilities for consequences to be convex, and taking the permissible probability-utility pairs to be the cross products of such sets. Seidenfeld, Schervish, and Kadane impose no general constraint on the convexity of sets of permissible probabilities or sets of utilities.

Keywords:   consensus and doubt, maximality, E-admissibility, seperability of probable and utility, cross product rule, permissible probability, permissible utility, convexity

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