In the presence of Pareto, non-dictatorship, full domain, and transitivity, an extremely weak independence condition disallows both anonymity and neutrality.

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...