There, one wants the opposing party to believe that you don’t have the option; and this is often only possible if you in fact don’t have the option (without strong legible proof of not having the option, the opponent will be worried about deception).
In this money pump (I think it’s close enough to count), that’s not happening.
“paying to avoid being given more options looks enough like being dominated that I’d want to keep the axiom of transitivity around”
Maybe offtopic but paying to avoid being given more options is a common strategy in negotiation.
There, one wants the opposing party to believe that you don’t have the option; and this is often only possible if you in fact don’t have the option (without strong legible proof of not having the option, the opponent will be worried about deception).
In this money pump (I think it’s close enough to count), that’s not happening.