Thus, (a) the notion of ‘irrelevance’ is dealt with by considering the budget set, (b) the axiom can be named after what it properly does: pairwise decision making.
If we want to deal with possibly farfetched preferences of some citizens, which is the moral meaning of the axiom of universal preferences, then we should work towards practical procedures that work. Assuming inconsistent axioms is not a good way to deal with that moral question.
The following sections use formal logic.
A lemma
Lemma A.I: AF implies that a constitution p satisfies the property Op
p.
First proof: AF means that desires (Op) in conflict with reality (~p) are not entitled to consideration. But
