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shminux comments on On accepting an argument if you have limited computational power. - Less Wrong
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You can assign credence to the claim and still assign little enough that a quadrillion humans won't overload it. I think the claim the be able to simulate a quadrillion humans is a lot more probable than the claim to be able to simulate 3^^^3 (you'd need technology that almost certainly doesn't exist, but not outside-the-Matrix powers,) but I'd still rate it as being so improbable as to only account for a tiny fraction of an expected death.
I'm settling for just one quadrillion to avoid dealing with the contingency of "3^^^3 is impossible because complexity". The requirement of testability is not affected by the contingency.
If you assign the threat a probability of, say, 10^-20, the mugger is extorting considerably more dead children from you than you should expect to die if you don't comply.