Can you explain why “the only measure available is indeed the ordinary amplitude-squared measure”?
Also, I’m confused about this:
Continuity: If you prefer |A> to |B> and |B> to |C>, there’s some quantum-mechanical measure (note that this is a change from “probability”) X such that you’re indifferent between (1-X)|A> + X|C> and |B>.
According to the Wikipedia entry you linked to, a probability measure is a real-valued function, but X here is apparently just a number? What’s the significance of your parenthetical note here?
This seems relevant: