· There is more clarity now, by the distinction between the theorem proper (a
falsum), the moral claim (Oa) and the claim on reasonableness (AF and I(~a)).
· The arguments above on rationality and morality have a destructive character since they reject the accepted view. In another perspective they are constructive, since they allow the formalisation of (meta) notions, and bring these back into mathematics again (notably the voting on constitutions).
· From a mathematical point of view, the Arrow axioms are incomplete for decision making in a reasonable society.
· It has been shown that the APDM is undesirable. Dropping APDM is not a sad state of affairs, as is sometimes suggested in the literature, but a sign of understanding group decision making.
· The Arrow axiomatisation does not capture the truly desirable properties required for a constitution, both by incompleteness and APDM.
· There are detail results, such as the distinction between voting and deciding, the integration of preference theory and deontic logic, and a proof of Arrow’s Theorem that shows clearly the abuse by APDM.
· We have given examples of consistent constitutions that many might regard as optimal.