Generalized utility based on values of opportunity sets

This paper is concerned with an axiomatic approach to the analysis and construction of the utility structure that underlies the values of ‘opportunity sets’. A family of subsets of a fixed universal set of alternatives is considered. These subsets are treated as opportunity sets; their (subjective) estimates by some ordinal scale are known. Also considered is another family of subsets, ‘alternative bundles’; its assumed mechanism of generating opportunity set values is as follows. Each opportunity set contains some bundles of alternatives, 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 representable by such a mechanism, with some hyperutility function for bundles. Particular cases are considered, including the ‘limit’ case where the opportunity set value equals the conventional utility value of the best alternative in the set.