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On the Preference Relations with Negatively Transitive Asymmetric Part. I

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  • Maria Viktorovna Droganova
  • Valentin Vankov Iliev

Abstract

Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an equivalence relation), lifting the linear order on A, and "agglutinating" this structure with the balloons. Every ballooning A of a structure of linearly ordered set I is a set of preferences whose preference relation (not necessarily complete) is negatively transitive and every such structure on a given set A can be obtained by ballooning of certain structure of a linearly ordered set I, intrinsically encoded in A. In other words, the difference between linearity and negative transitivity is constituted of balloons. As a consequence of this characterization, under certain natural topological conditions on the set of preferences A furnished with its interval topology, the existence of a continuous generalized utility function on A is proved.

Suggested Citation

  • Maria Viktorovna Droganova & Valentin Vankov Iliev, 2013. "On the Preference Relations with Negatively Transitive Asymmetric Part. I," Papers 1302.7238, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1302.7238
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    References listed on IDEAS

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    1. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    2. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    3. Rechenauer, Martin, 2008. "On the non-equivalence of weak and strict preference," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 386-388, November.
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