Probabilistic Consistency, Homogeneous Families of Relations and Linear A-Relations

Abstract

The notions of linear discrimination structure and of homogeneous family of semi-orders have been introduced in the theory of probabilistic consistency by Luce and Roberts, respectively. Here, we study the more general notions of linear A-relations and homogeneous families of S.T.F. relations, such notions being able to be useful in the theory of probabilistic consistency (non forced or indifference choices) and in several other situations (collective choice, non-symmetrical similarity, …).