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

Gianni Bosi, Juan Carlos Candeal (), Esteban Induráin () and Margarita Zudaire ()

Social Choice and Welfare, 2005, vol. 24, issue 1, 45-61

Abstract: 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

Date: 2005
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DOI: 10.1007/s00355-003-0290-2

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