> "It's hard to say anything about their likelihoods, other than they are all absurdly unlikely. So it's not clear to me that one is more likely than the other."
Yeah, I agree it's not clear. But it's especially not clear that they are precisely equal in likelihood. And if Test is even *slightly* more unlikely then the cancelling out move…
> "It's hard to say anything about their likelihoods, other than they are all absurdly unlikely. So it's not clear to me that one is more likely than the other."
Yeah, I agree it's not clear. But it's especially not clear that they are precisely equal in likelihood. And if Test is even *slightly* more unlikely then the cancelling out move fails.
> "Does it seem more trustworthy when we assume that the low expected utility is finitely small?"
Probably, but I don't think we should assume that the mugger's claim warrants finite credence. I'm dubious of the Bayesian claim that nothing can count as evidence for zero probability events.
Simple counterexample: suppose God runs a fair lottery over the natural numbers. You should assign p = 0 that the number 1 will be picked (any finite credence would be too large). Then God tells you that the winning number was, in fact, 1. You should now assign this much higher credence. It's difficult to model this mathematically. But it seems clearly correct nonetheless.
> "It's hard to say anything about their likelihoods, other than they are all absurdly unlikely. So it's not clear to me that one is more likely than the other."
Yeah, I agree it's not clear. But it's especially not clear that they are precisely equal in likelihood. And if Test is even *slightly* more unlikely then the cancelling out move fails.
> "Does it seem more trustworthy when we assume that the low expected utility is finitely small?"
Probably, but I don't think we should assume that the mugger's claim warrants finite credence. I'm dubious of the Bayesian claim that nothing can count as evidence for zero probability events.
Simple counterexample: suppose God runs a fair lottery over the natural numbers. You should assign p = 0 that the number 1 will be picked (any finite credence would be too large). Then God tells you that the winning number was, in fact, 1. You should now assign this much higher credence. It's difficult to model this mathematically. But it seems clearly correct nonetheless.