I agree with the suggestion that our judgment about the *rationality* of acceding to the mugger's demand is more secure than our judgment about the *likelihood* of his carrying through with his threat. But I don't think this is enough to escape the problem that arises from the fact that the mugger can multiply the threat. Because he can multiply the threat, we have to ask ourselves: "Supposing that it was initially irrational for me to accede to the threat, would it still be irrational if the threat was multiplied by [arbitrarily high number]?" And I don't think *this* question prompts a secure negative judgment. On the face of it, a low expected utility can always be multiplied into a high expected utility. So I don't think we can escape the problem just by relying on our secure judgments about rationality.

I wonder what you think about a different way of escaping the problem. The way I think of it, when the mugger confronts you, there are at least three possible situations you might be in:

Normal: The mugger is just lying.

Demon Mugger: The mugger is actually a demon/wizard/god/whatever capable of carrying through on his threat, and will do so.

Demonic Test: The situation with the mugger is a test set up by an evil demon/wizard/god/whatever, and if you accede to the mugger's threat, the demon/wizard/god will do whatever the mugger threatened to do.

Demon Mugger and Demonic Test are both unbelievably unlikely, and more to the point, neither of them seems any more likely than the other. So they cancel each other out in the decision calculus. And while the mugger can keep increasing his threat, for every such threat there's an equal and opposite Demonic Test. So we can ignore any crazy threat the mugger might make (unless and until he gives some evidence that these threats should be taken more seriously than the corresponding Demonic Test scenarios!)