Interdependent preferences on finite sets

Abstract The degree of interdependence of a preference relation ≻ on a finite subset X of a product set X 1 × X 2 × … × X n is defined in terms of the highest order of preference interaction among the X i that must be taken into account in a real-valued, interdependent additive representation for ≻. The degree is zero when indifference holds throughout X , and zero or one in the additive conjoint measurement case. A degree of n signifies complete preference interdependence among the X i . Following an axiomatic characterization of degree of interdependence, it is shown that two special instances of this characterization are equivalent to the original. This is caused by the combinatorial aspects of the situation. The final section discusses the case where each X i has two elements.