A generalization of Campbell and Kelly's trade-off theorem

This paper considers social choice theory without the Pareto principle. We revisit the trade-off theorem developed by Campbell and Kelly (Econometrica 61:1355– 1365, 1993), and generalize their result. By introducing an alternative criterion of power structure, a dominance relation, we show that if a social welfare function on the unrestricted domain satisfies the independence of irrelevant alternatives, then it must be exist either maldistribution of power or too many pairs of alternatives which social ranking is fixed independently of individual preferences. Moreover, we offer two applications of our main result. JEL classification D61; D71