ABSTRACT
The argument in the last chapter tells us that a ‘voting paradox’ can be found not only in pairwise simple majority voting, but also in any democratic social decision functions based on pairwise comparison. We may now further inquire whether or not the same phenomenon occurs in a still wider class of social decision functions than a democracy based on pairwise comparison. Indeed, even Arrow’s original proof established an inconsistency for that set of conditions which is weaker than a democracy by our definition. We are led to doubt that Arrow’s set of conditions is the weakest that can induce an inconsistency.
