A Genesis of Interval Orders and Semiorders: Transitive NaP-preferences

被引:15
|
作者
Giarlotta, Alfio [1 ]
机构
[1] Univ Catania, Dept Econ & Business, Catania, Italy
关键词
NaP-preference; NaP-preorder; Interval order; Semiorder; Strong interval order; Strong semiorder; Mixed transitivity; Preference resolution; Social choice problem; UTILITY REPRESENTATION; INTRANSITIVE INDIFFERENCE; NUMERICAL REPRESENTATIONS; FAMILIES; BIORDER;
D O I
10.1007/s11083-013-9298-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A NaP-preference (necessary and possible preference) on a set A is a pair of binary relations on A such that its necessary component is a partial preorder, its possible component is a completion of , and the two components jointly satisfy natural forms of mixed completeness and mixed transitivity. We study additional mixed transitivity properties of a NaP-preference , which culminate in the full transitivity of its possible component . Interval orders and semiorders are strictly related to these properties, since they are the possible components of suitably transitive NaP-preferences. Further, we introduce strong versions of interval orders and semiorders, which are characterized by enhanced forms of mixed transitivity, and use a geometric approach to compare them to other well known preference relations.
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页码:239 / 258
页数:20
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