More on independent decisiveness and Arrow's theorem

Denicolò 2, Theorem 1] strengthens Arrow's 1, p. 97] theorem by replacing the independence of irrelevant alternatives (IIA) condition by a strictly weaker one, relational independent decisiveness (RID). It is shown here that RID can be still substantially weakened. Yet, the new condition is equivalent to RID under the weak Pareto principle P and unrestricted domain U. In fact, any condition that can be put in place of IIA in Arrow's theorem must imply RID in the presence of P and U. Incidentally, it is argued that Denicolò's proof of his Theorem 1 contains an imprecision. Received: 7 March 2000/Accepted: 11 December 2000