Abstract
This paper is concerned with an axiomatic approach to the analysis and construction ofthe utility structure that underlies the values of “opportunity sets”. A family of subsetsof a fixed universal set of alternatives is considered. These subsets are treated as opportunitysets; their (subjective) estimates by some ordinal scale are known. Also consideredis another family of subsets, “alternative bundles;” its assumed mechanism ofgenerating opportunity set values is as follows. Each opportunity set contains some bundles ofalternatives, which have their own hyper-utility values. The value of the opportunity set is the maximum “hyper-utility” over bundles that lie inside the set.We establish necessary and sufficient conditions for opportunity set values to be representableby such a mechanism, with some hyper-utility function for bundles. Particular cases are considered, including the “limit” case where the opportunity set value equals theconventional utility value of the best alternative in the set.
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Malishevski, A. Generalized utility based on values of opportunity sets. Annals of Operations Research 80, 11–26 (1998). https://doi.org/10.1023/A:1018955612731
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DOI: https://doi.org/10.1023/A:1018955612731