Pareto optimality and the decisive power structure with expansion consistency conditions (Q1066782)

Let X be a finite set of social states (at least four), and N a finite set of voters (at least two). Let C be a social choice function satisfying the independence condition and Pareto optimality. C satisfies strong dominance if C(B)\(\subseteq C(A)\cap B\), where A and B are subsets of X, and B contains exactly two elements. The main result is that such a strongly dominant C has a dictator.