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An Advised Indirect-Utility Ranking of Opportunity Sets

BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain
Author to whom correspondence should be addressed.
Current address: Facultad de Economía y Empresa, Universidad de Salamanca, Campus Unamuno, E37007 Salamanca, Spain.
Academic Editors: Francisco Javier Garcia-Pacheco and Marina Murillo Arcila
Symmetry 2021, 13(8), 1404;
Received: 4 May 2021 / Revised: 16 June 2021 / Accepted: 4 July 2021 / Published: 2 August 2021
There is a substantial strand of literature about ranking the subsets of a set of alternatives, usually referred to as opportunity sets. We investigate a model that is dependent on the preference of a grand set of alternatives. In this framework, the indirect-utility criterion ranks the opportunity sets by the following rule: a subset A is weakly preferred to another subset B if and only if A contains at least one preference maximizing element from AB. This criterion leads to the indifference of each subset of alternatives to a singleton; symmetry appears at this stage, as the property holds true for any one of the maximizers in A. Conversely, suppose that a ranking of opportunity sets satisfies the property that each opportunity set is indifferent to a singleton contained within it. Then, we prove that such a ranking must use a generalized form of the indirect-utility criterion, where maximization is applied to a selection of the alternatives. Altogether, these results produce a characterization of the advised indirect-utility criterion for ranking opportunity sets. View Full-Text
Keywords: sequential preference; ranking subsets; indirect-utility criterion; choice correspondence sequential preference; ranking subsets; indirect-utility criterion; choice correspondence
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MDPI and ACS Style

García-Sanz, M.D.; Alcantud, J.C.R. An Advised Indirect-Utility Ranking of Opportunity Sets. Symmetry 2021, 13, 1404.

AMA Style

García-Sanz MD, Alcantud JCR. An Advised Indirect-Utility Ranking of Opportunity Sets. Symmetry. 2021; 13(8):1404.

Chicago/Turabian Style

García-Sanz, María Dolores, and José Carlos R. Alcantud. 2021. "An Advised Indirect-Utility Ranking of Opportunity Sets" Symmetry 13, no. 8: 1404.

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