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..

Necessary and possible indifferences

GIARLOTTA, Alfio
;
2017-01-01

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..
2017
Preference modeling; NaP-preference; NaP-indifference; Resolution; Equivalence relation; Similarity relation; Revealed preference; Primitive similarity; Comparability graph.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/313099
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