Consistency and social choice

We consider a model of preference aggregation when a single public good has to be chosen. We do not impose any restrictions on the preferences. We show the impossibility of contraction consistent (CC), anonymous and Pareto efficient social choice functions. We provide a characterization of the priority based social choice function (Priority Rule) which satisfies a weaker version of consistency called Efficient Dominance (ED). ED is a Weak Axiom of Revealed Preference (WARP) type of consistency criterion over the set of Pareto efficient alternatives. We show that the Priority Rule is the only social choice function that satisfies Pareto efficiency and Efficient Dominance.