{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:36Z","timestamp":1760240016074,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A preference defined on a set of alternatives can be extended to a preference on the subsets of alternatives (named opportunity sets) in different ways. We specifically consider the application of the indirect-utility (IU) criterion in various stages, when both the alternatives and the preferences can change over time. In other words, we maintain the symmetry over time as far as criteria are concerned, but neither in the preferences, nor in the alternatives. We characterize this criterion by three testable axioms. Our study bears comparison with Krause (Economic Theory, 2008) for the two-period model.<\/jats:p>","DOI":"10.3390\/sym11020241","type":"journal-article","created":{"date-parts":[[2019,2,17]],"date-time":"2019-02-17T22:11:50Z","timestamp":1550441510000},"page":"241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Indirect-Utility Criterion for Ranking Opportunity Sets over Time"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1430-3603","authenticated-orcid":false,"given":"Mar\u00eda Dolores","family":"Garc\u00eda-Sanz","sequence":"first","affiliation":[{"name":"BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-9281","authenticated-orcid":false,"given":"Jos\u00e9 Carlos Rodr\u00edguez","family":"Alcantud","sequence":"additional","affiliation":[{"name":"BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"565","DOI":"10.2307\/1910406","article-title":"A representation theorem for preference for flexibility","volume":"47","author":"Kreps","year":"1979","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.mathsocsci.2014.12.006","article-title":"Sequential rationalization of multivalued choice","volume":"74","author":"Alcantud","year":"2015","journal-title":"Math. 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