Lexicographic quasilinear utility
The author derives necessary and sufficient conditions for the existence of a finite-dimensional quasilinear utility function whose lexicographically ordered utility vectors preserve a decision maker's preference order on a mixture space. The main theorem of the paper gives four axioms for this equivalence: weak order, betweeness and two further axioms A3 and A4\((n)\). A3 says that if either the upper or lower Archimedean axiom holds for a triple \((x, y, z)\) then a weak requirement of the independence axiom (with \(\lambda= 1/2\)) holds. A4\((n)\) is a relaxation of the Archimedean axiom. A further theorem characterizes \(n\)-dimensional lexicographic linear representations using independence axioms.
scientific article; zbMATH DE number 1839105