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Existence of homogeneous representations of interval orders on a cone in a topological vector space


  • Gianni Bosi


  • Juan Carlos Candeal


  • Esteban Induráin


  • Margarita Zudaire



Necessary and sufficient conditions are presented for the existence of a pair >u,v> of positively homogeneous of degree one real functions representing an interval order [InlineMediaObject not available: see fulltext.] on a real cone K in a topological vector space E (in the sense that, for every x,y∈K, x[InlineMediaObject not available: see fulltext.]y if and only if u(x)≤v(y)), with u lower semicontinuous, v upper semicontinuous, and u and v utility functions for two complete preorders intimately connected with [InlineMediaObject not available: see fulltext.]. We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder. Copyright Springer-Verlag 2005

Suggested Citation

  • Gianni Bosi & Juan Carlos Candeal & Esteban Induráin & Margarita Zudaire, 2005. "Existence of homogeneous representations of interval orders on a cone in a topological vector space," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 45-61, July.
  • Handle: RePEc:spr:sochwe:v:24:y:2005:i:1:p:45-61
    DOI: 10.1007/s00355-003-0290-2

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