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 …
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!)
Demonic Test strikes me as even more unlikely. However unlikely it is that the mugger has magical demonic powers, the Test hypothesis requires the *additional* implausibility of their lying about their plans for no obvious reason. This is a small difference in plausibility compared to the immense implausibility of having demonic powers in the first place. But even a small difference in plausibility prevents a "cancelling out" story from working.
(This differs from Pascal's Wager, where I think it is substantively more plausible that an all-powerful God would reward honest inquiry than that one would jealously punish reasonable non-believers.)
> "the problem that arises from the fact that the mugger can multiply the threat..."
I guess I just have different intuitions from you here. No matter how ludicrously high a number of people the mugger claims to affect, it doesn't seem rational to me to grant them proportionate credence (because it definitely doesn't seem rational to assign high EV to complying).
> "On the face of it, a low expected utility can always be multiplied into a high expected utility"
That sort of abstract theoretical claim strikes me as much less trustworthy. You might retain it by assigning lower credence the more people the mugger claims to affect. But if you need to give a constant credence at some point (e.g. to the generic claim that the mugger can affect *any* number of lives), then I think your credence ought to be lower than 1/N for any N whatsoever. Maybe it ought to be literally zero.
(Some zero probability events are, in some sense, more likely than others. Like, God's randomly picking the number '1' from amongst all the natural numbers, vs. randomly picking either '1' or '2'. Both have p = 0, but the former is even less likely. Demonic Test and Demonic Mugger might be like that.)
> Demonic Test strikes me as even more unlikely. However unlikely it is that the mugger has magical demonic powers, the Test hypothesis requires the *additional* implausibility of their lying about their plans for no obvious reason.
I'm actually not sure we do have any rational grounds for thinking that Demonic Test is more unlikely. It's not as if Demonic Test includes everything that is implausible about Demonic Mugger, *plus* an additional implausibility. The implausibilities are just different. In Demonic Mugger we have to ask "why might it be that this mugger has crazy evil powers, and will punish me for refusing his threat?" (Maybe he somehow can't use his powers to get the money himself, and he has to carry out his threats in order to guarantee future compliance. Absurdly unlikely, but perhaps!) In Demonic Test we have to ask, "why might it be that this mugger has crazy evil powers, and will punish me for complying with his threat"? (Maybe he hates people who are weak and spineless, or who are irrational from the standpoint of decision theory. Again absurdly unlikely, but perhaps!) The possibilities we are considering are simply different. The Demonic Test scenarios aren't just (Demonic Mugger + something else). 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.
> "That sort of abstract theoretical claim strikes me as much less trustworthy."
Does it seem more trustworthy when we assume that the low expected utility is finitely small? I was assuming that your credence in the mugger's threat is finitely small, because I think weird things happen if it's infinitesimal. E.g. if your credence is infinitely small, then for you nothing will count as evidence in favor of the mugger's threat (I think?) Could definitely be mistaken about this! Anyway thanks for the response.
> "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.
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!)
Demonic Test strikes me as even more unlikely. However unlikely it is that the mugger has magical demonic powers, the Test hypothesis requires the *additional* implausibility of their lying about their plans for no obvious reason. This is a small difference in plausibility compared to the immense implausibility of having demonic powers in the first place. But even a small difference in plausibility prevents a "cancelling out" story from working.
(This differs from Pascal's Wager, where I think it is substantively more plausible that an all-powerful God would reward honest inquiry than that one would jealously punish reasonable non-believers.)
> "the problem that arises from the fact that the mugger can multiply the threat..."
I guess I just have different intuitions from you here. No matter how ludicrously high a number of people the mugger claims to affect, it doesn't seem rational to me to grant them proportionate credence (because it definitely doesn't seem rational to assign high EV to complying).
> "On the face of it, a low expected utility can always be multiplied into a high expected utility"
That sort of abstract theoretical claim strikes me as much less trustworthy. You might retain it by assigning lower credence the more people the mugger claims to affect. But if you need to give a constant credence at some point (e.g. to the generic claim that the mugger can affect *any* number of lives), then I think your credence ought to be lower than 1/N for any N whatsoever. Maybe it ought to be literally zero.
(Some zero probability events are, in some sense, more likely than others. Like, God's randomly picking the number '1' from amongst all the natural numbers, vs. randomly picking either '1' or '2'. Both have p = 0, but the former is even less likely. Demonic Test and Demonic Mugger might be like that.)
> Demonic Test strikes me as even more unlikely. However unlikely it is that the mugger has magical demonic powers, the Test hypothesis requires the *additional* implausibility of their lying about their plans for no obvious reason.
I'm actually not sure we do have any rational grounds for thinking that Demonic Test is more unlikely. It's not as if Demonic Test includes everything that is implausible about Demonic Mugger, *plus* an additional implausibility. The implausibilities are just different. In Demonic Mugger we have to ask "why might it be that this mugger has crazy evil powers, and will punish me for refusing his threat?" (Maybe he somehow can't use his powers to get the money himself, and he has to carry out his threats in order to guarantee future compliance. Absurdly unlikely, but perhaps!) In Demonic Test we have to ask, "why might it be that this mugger has crazy evil powers, and will punish me for complying with his threat"? (Maybe he hates people who are weak and spineless, or who are irrational from the standpoint of decision theory. Again absurdly unlikely, but perhaps!) The possibilities we are considering are simply different. The Demonic Test scenarios aren't just (Demonic Mugger + something else). 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.
> "That sort of abstract theoretical claim strikes me as much less trustworthy."
Does it seem more trustworthy when we assume that the low expected utility is finitely small? I was assuming that your credence in the mugger's threat is finitely small, because I think weird things happen if it's infinitesimal. E.g. if your credence is infinitely small, then for you nothing will count as evidence in favor of the mugger's threat (I think?) Could definitely be mistaken about this! Anyway thanks for the response.
> "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.