ABSTRACT

In this chapter, we focus on one of Arrow’s conditions, independence of irrelevant alternatives to obtain nondictatorial results. We give special consideration to auxiliary functions considered by Garcia-Lapresta and Llamazares [21]. It was shown in [21] that neutral aggregation rules based on quadratic arithmetic means generalize simple majority when individuals have ordinary preferences, and collective preferences are reciprocal and that a weighted average is a nondictatorial fuzzy aggregation rule. We also show that it is not the automorphic image of the ordinary average.