t’s not the only way to do so, though; you can also require that the prior probabilities of statements (without corresponding opposite-utility statements) shrink at least as fast as utilities grow.
My favored solution. Incidentally, if your prior shrinks faster, then you can still be vulnerable. The mugger can simply split his offer up into a billion smaller offers, which will avoid the penalty of big offers disproportionately being discounted. So unless you would reject every single mugging offer of any magnitude (in which case isn’t that kind of arbitrary?), the faster shrinking doesn’t buy you anything.
Incidentally, if your prior shrinks faster, then you can still be vulnerable. The mugger can simply split his offer up into a billion smaller offers, which will avoid the penalty of big offers disproportionately being discounted. So unless you would reject every single mugging offer of any magnitude (in which case isn’t that kind of arbitrary?), the faster shrinking doesn’t buy you anything.
I believe a set of smaller offers would imply the existence of a statement which aggregates them and violates this formalization of the anti-mugging axiom.
On the other hand, you can potentially be forced to search the space of all functions for the one that diverges, and it might be possible (I don’t know whether it is) to mug in a way that makes finding that function computationally hard.
I believe a set of smaller offers would imply the existence of a statement which aggregates them and violates this formalization of the anti-mugging axiom.
I take the aggregating thing as a constructive proof that that class of priors + utility function is vulnerable; your version just seems to put it another way. We agree on that part, I think.
My favored solution. Incidentally, if your prior shrinks faster, then you can still be vulnerable. The mugger can simply split his offer up into a billion smaller offers, which will avoid the penalty of big offers disproportionately being discounted. So unless you would reject every single mugging offer of any magnitude (in which case isn’t that kind of arbitrary?), the faster shrinking doesn’t buy you anything.
I believe a set of smaller offers would imply the existence of a statement which aggregates them and violates this formalization of the anti-mugging axiom.
On the other hand, you can potentially be forced to search the space of all functions for the one that diverges, and it might be possible (I don’t know whether it is) to mug in a way that makes finding that function computationally hard.
I take the aggregating thing as a constructive proof that that class of priors + utility function is vulnerable; your version just seems to put it another way. We agree on that part, I think.