Arrow (1951, pp. 28–29), an Imposed Constitution is a constitution such that for some alternative social states x and y and for any set of orderings , ..., in the domain and corresponding social ordering R, the social ranking is x R y. Non-imposition N (Citizens' Sovereignty): A constitution is not to be imposed. Under imposition, for every set of orderings in the domain, the social ranking for at least one x and y is only x R y. The vote makes no difference to the outcome. Proof The proof is in two parts (Arrow, 1963, pp. 97–100). The first part considers the hypothetical case of some one voter's ordering that prevails ('is decisive') as to the social choice for some pair of social states no matter what that voter's preference for the pair, despite all other voters opposing. It is shown that, for a constitution satisfying Unrestricted Domain, Pareto and Independence, that voter's ordering would prevail for every pair of social states, no matter what the orderings of others. So, the voter would be a Dictator. Thus, Nondictatorship requires postulating that no one would so prevail for even one pair of social states. The second part considers more generally a set of voters that would prevail for some pair of social states, despite all other voters (if any) preferring otherwise. Pareto and Unrestricted Domain for a constitution imply that such a set would at least include the entire set of voters. By Nondictatorship, the set must have at least 2 voters. Among all such sets, postulate a set such that no other set is smaller. Such a set can be constructed with Unrestricted Domain and an adaptation of the voting paradox to imply a still smaller set. This contradicts the postulate and so proves the theorem. Summary, interpretation, and aftereffects The book proposes some apparently reasonable conditions for a "voting" rule, in particular, a 'constitution', to make consistent, feasible social choices in a welfarist context. But then any constitution that allows dictatorship requires it, and any constitution that requires nondictatorship contradicts one of the other conditions. Hence, the paradox of social choice. The set of conditions across different possible votes refined welfare economics and differentiated Arrow's constitution from the pre-Arrow social welfare function. In so doing, it also ruled out any one consistent social ordering to which an agent or official might appeal in trying to implement social welfare