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HopeFox comments on Pascal's Mugging: Tiny Probabilities of Vast Utilities - Less Wrong
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But that is precisely it - it's no longer a Pascal mugging if the threat is credible. That is, in order to be successful, the mugger needs to be able to up the utility claim arbitrarily! It is assumed that we already know how to handle a credible threat, what we didn't know how to deal with was a mugger who could always make up a bigger number, to a degree where the seeming impossibility of the claim no longer offsets the claimed utility. But as I showed, this only works if you don't enter the mugger's thought process into the calculation.
This actually brings up an important corollary to my earlier point: The higher the number, the less likely the coupling is between the mugger's claim and the mugger's intent.
A person who can kill another person might well want 5$, for whatever reason. In contrast, a person who can use power from beyond the Matrix to torture 3^^^3 people already has IMMENSE power. Clearly such a person has all the money they want, and even more than that in the influence that money represents. They can probably create the money out of nothing. So already their claims don't make sense if taken at face value.
Maybe the mugger just wants me to surrender to an arbitrary threat? But in that case, why me? If the mugger really has immense power, they could create a person they know would cave in to their demands.
Maybe I'm special for some reason. But if the mugger is REALLY that powerful, wouldn't they be able to predict my actions beforehand, a-la Omega?
Each rise in claimed utility brings with it a host of assumptions that need to be made for the action-claimed reaction link to be maintained. And remember, the mugger's ability is not the only thing dictating expected utility, but also the mugger's intentions. Each such assumption not only weakens the probability of the mugger carrying out their threat because they can't, it also raises the probability of the mugger rewarding refusal and/or punishing compliance. Just because the off-chance comes true and the mugger contacting me actually CAN carry out the threat, does not make them sincere; the mugger might be testing my rationality skills, for instance, and could severely punish me for failing the test.
As the claimed utility approaches infinity, so does the scenario approach Pascal's Wager: An unknowable, symmetrical situation, where an infinite number of possible outcomes cancel each other out. The one outcome that isn't canceled out is the loss of 5$. So the net utility is negative. So I don't comply with the mugger.
I'm still not sure I'm fully satisfied with the level of math my explanation has, even though I've tried to set the solution in terms of limits and attractors. But I think I can draw a graph that dips under zero utility fairly quickly (or maybe doesn't really ever go over it?), and never goes back up - asymptotic at -5$ utility. Am I wrong?
Ah, my mistake. You're arguing based on the intent of a legitimate mugger, rather than the fakes. Yes, that makes sense. If we let f(N) be the probability that somebody has the power to kill N people on demand, and g(N) be the probability that somebody who has the power to kill N people on demand would threaten to do so if he doesn't get his $5, then it seems highly likely that Nf(N)g(N) approaches zero as N approaches infinity. What's even better news is that, while f(N) may only approach zero slowly for easily constructed values of N like 3^^^^3 and 4^^^^4 because of their low Kolmogorov complexity, g(N) should scale with 1/N or something similar, because the more power someone has, the less likely they are to execute such a miniscule, petty threat. You're also quite right in stating that the more power the mugger has, the more likely it is that they'll reward refusal, punish compliance or otherwise decouple the wording of the threat from their actual intentions, thus making g(N) go to zero even more quickly.
So, yeah, I'm pretty satisfied that Nf(N)g(N) will asymptote to zero, taking all of the above into account.
(In more unrelated news, my boyfriend claims that he'd pay the mugger, on account of him obviously being mentally ill. So that's two out of three in my household. I hope this doesn't catch on.)