Discussion: We have enlarged the commodity domain with constitutions, and hence the axiom of feasibility becomes a bit stronger. The extension itself is rather weak, since we only extend on consistency (and not empirical validity). Our criterion is as that a reasonable society would stick to its rules. The gap between Is and Ought still exists in principle, but can in practice be bridged by the human effort to attain one’s ends.
Rejection of the Arrow Moral Claim (AMC)
Theorem A.1: For a reasonable society, the AMC is invalid.
First proof by rationality & moral consistency (DA): Assume Oa. But a
~a, and with DA we get O~a. But this gives a preference inconsistency Oa & O~a. Hence ~Oa. Q.E.D.
Second proof by rationality & moral consistency (DA): Assume Oa. Since a
falsum we find Ofalsum. Thus for some p0 we have O(p0 & ~p0). But this means Op0 & O~p0, and that is a preference inconsistency. Hence ~Oa. Q.E.D.
First proof by realism (AF): Assume Oa. By the lemma