Good catch on Cox’s theorem; that is now fixed. Do you know if the dutch book argument corresponds to a named theorem?
There is a whole class of dutch book arguments, so I’m not sure which one you mean by the dutch book argument.
In any case, Susan Vineberg’s formulation of the Dutch Book Theorem goes like this:
Given a set of betting quotients that fails to satisfy the probability axioms, there is a set of bets with those quotients that guarantees a net loss to one side.
Then you might think you could have inconsistent betting prices that would harm the person you bet with, but not you, which sounds fine.
Rather: “If your betting prices don’t obey the laws of probability theory, then you will either accept combinations of bets that are sure losses, or pass up combinations of bets that are sure gains.”
There is a whole class of dutch book arguments, so I’m not sure which one you mean by the dutch book argument.
In any case, Susan Vineberg’s formulation of the Dutch Book Theorem goes like this:
Yes, that is the one I had in mind. Thanks!
Then you might think you could have inconsistent betting prices that would harm the person you bet with, but not you, which sounds fine.
Rather: “If your betting prices don’t obey the laws of probability theory, then you will either accept combinations of bets that are sure losses, or pass up combinations of bets that are sure gains.”