Existence of homogeneous representations of interval orders on a cone in a topological vector space
G Bosi, JC Candeal, E Induráin, M Zudaire - Social Choice and welfare, 2005 - Springer
G Bosi, JC Candeal, E Induráin, M Zudaire
Social Choice and welfare, 2005•SpringerNecessary 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 on a
real cone K in a topological vector space E (in the sense that, for every x, y∈ K, xy 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. We conclude presenting a
new approach to get such kind of representations, based on the concept of a biorder.
positively homogeneous of degree one real functions representing an interval order on a
real cone K in a topological vector space E (in the sense that, for every x, y∈ K, xy 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. We conclude presenting a
new approach to get such kind of representations, based on the concept of a biorder.
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 on a real cone K in a topological vector space E (in the sense that, for every x,y∈K, x 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 . We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder.
Springer
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