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

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Abstract

A NaP-preference (necessary and possible preference) on a set A is a pair \({\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}\) of binary relations on A such that its necessary component \({\succsim^{^{_N}} \!\!}\) is a partial preorder, its possible component \({\succsim^{^{_P}} \!\!}\) is a completion of \({\succsim^{^{_N}} \!\!}\), and the two components jointly satisfy natural forms of mixed completeness and mixed transitivity. We study additional mixed transitivity properties of a NaP-preference \({\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}\), which culminate in the full transitivity of its possible component \({\succsim^{^{_P}} \!\!}\). 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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  1. Department of Economics and Business, University of Catania, Catania, Italy

    Alfio Giarlotta

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  1. Alfio Giarlotta
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Correspondence to Alfio Giarlotta.

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Giarlotta, A. A Genesis of Interval Orders and Semiorders: Transitive NaP-preferences. Order 31, 239–258 (2014). https://doi.org/10.1007/s11083-013-9298-0

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