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• W2765134581 abstract "Abstract A NaP-preference (necessary and possible preference) is a pair of nested reflexive relations on a set such that the smaller is transitive, the larger is complete, and the two relations jointly satisfy properties of transitive coherence and mixed completeness. It is known that a NaP-preference is characterized by the existence of a set of total preorders whose intersection and union give its two components. We introduce the symmetric counterpart of a NaP-preference, called a NaP-indifference: this is a pair of nested symmetric relations on a set such the smaller is an equivalence relation, and the larger is a transitively coherent extension of the first. A NaP-indifference can be characterized by the existence of a set of equivalence relations whose intersection and union give its two components. NaP-indifferences naturally arise in applications: for instance, in the field of individual choice theory, suitable pairs of similarity relations revealed by a choice correspondence yield a NaP-indifference. We classify NaP-indifferences in two categories, according to their genesis: (i) derived, which are canonically obtained by taking the symmetric part of a NaP-preference; (ii) primitive, which arise independently of the existence of an underlying NaP-preference. This partition into two classes turns out to be related to the notion of incomparability graph." @default.
• W2765134581 created "2017-11-10" @default.
• W2765134581 creator A5034075314 @default.
• W2765134581 creator A5075887933 @default.
• W2765134581 date "2017-12-01" @default.
• W2765134581 modified "2023-09-24" @default.
• W2765134581 title "Necessary and possible indifferences" @default.
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• W2765134581 doi "https://doi.org/10.1016/j.jmp.2017.09.006" @default.
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