The set of alternatives is infinite. If social welfare function f satisfies the Pareto criterion and there is a positive number β such that each pair of alternatives can be socially ordered without having to consult individual preference over a set with more than β alternatives then there are...

For four alternatives and an even number of individuals, we prove a conjecture in a companion paper: It is impossible for a social choice rule to satisfy all of (1) Pareto, (2) anonymity, (3) full domain, and (4) independence of some alternative, a relaxation of ArrowÕs IIA.

For a finite number of alternatives, in the presence of Pareto, non-dictatorship, full domain, and transitivity, an extremely weak independence condition is incompatible with each of anonymity and neutrality (Campbell and Kelly [2006]). This paper explores how those results are affected when...

For social choice rules that can select either one or two alternatives, strategy-proofness is incompatible with a weak Condorcet principle.

We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an...

Given a set of outcomes that affect the welfare of the members of a group, K.J. Arrow imposed the following five conditions on the ordering of the outcomes as a function of the preferences of the individual group members, and then proved that the conditions are logically inconsistent:- The...