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In the forward direction, resolutions amalgamate simple choices to create a complex one. In the backward direction, resolutions detect when and how a primitive choice can be deconstructed into smaller choices. A choice is resolvable if it is the resolution of smaller choices. Rationalizability, rationalizability by a preorder, and path independence are all preserved (backward and forward) by resolutions, whereas rationalizability by a weak order (equivalently, ) is not. We characterize resolvable choices, and show that resolvability generalizes .<\/jats:p>","DOI":"10.1007\/s00355-020-01285-9","type":"journal-article","created":{"date-parts":[[2020,11,3]],"date-time":"2020-11-03T17:02:58Z","timestamp":1604422978000},"page":"713-753","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Choice resolutions"],"prefix":"10.1007","volume":"56","author":[{"given":"Domenico","family":"Cantone","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2109-1381","authenticated-orcid":false,"given":"Alfio","family":"Giarlotta","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Watson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,3]]},"reference":[{"issue":"5","key":"1285_CR1","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1109\/TAC.1981.1102777","volume":"26","author":"MA Aizerman","year":"1981","unstructured":"Aizerman MA, Malishevski AV (1981) General theory of best variants choice. 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