Lancasterian logic of taste and preference
Abstract
The aim of this paper is to reconcile the natural meaning of a taste defined as a subset of attributes and the theoretical modeling of a preference defined as a binary relation over alternatives. For that purpose, in a Lancasterian framework we first introduce attributes, addresses, alternatives and subjective associations between attributes. Second, we define tastes as subsets of attributes resulting from a specific mapping T over the powerset of attributes and we establish the two conditions, monotonicity and normalization of the mapping T, under which tastes can be said to be well-formed; that is, formally relevant as a representation of the subjective associations between attributes (Theorem 1). Third, we exhibit the formal properties, reflexivity and transitivity of the subjective associations that structure the attributes set if tastes are well-formed (Theorem 2). Finally, we prove that whenever tastes are consistently represented by preferences, tastes are well-formed iff preferences are totally weak-ordered (Theorem 3).