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wedrifid 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?
That is backward. It is only a Pascal mugging if the threat is credible. Like one made by Omega, who you mention later on.
No, then it's just a normal mugging.
If the threat is not credible from the perspective of the target it may only be an attempted mugging - not a proper mugging at all.
Huh? Isn't the whole point of Pascal's mugging that it isn't likely and the mugger makes up for the lack of credibility by making the threat massive? If the mugger is making a credible threat we just call that a mugging.
The threat has to be credible at the level of probability it is assigned. It doesn't have to be likely.
How are you defining credible? It may be that we are using different notions of what this means. I'm using it to mean something like "capable of being believed" or "could be plausibly believed by a somewhat rational individual" but these have meanings that are close to "likely".
"The threat has to be credible at the level of probability it is assigned. "
And what, precisely, does THAT mean? If I try to taboo some words here, I get "we must evaluate the likelihood of something happening as the likelihood we assigned for it to happen". That's simply tautological.
No probability is exactly zero except for self-contradictory statements. So "credible" can't mean "of zero probability" or "impossible to believe". To me, "credible" means "something I would not have a hard time believing without requiring extraordinary evidence", which in itself translates pretty much to ">0.1% probability". If you have some reason for distinguishing between a threat that is not credible and a threat with exceedingly low probability of being carried out, please state it. Also please note that my use of the word makes sense within the original context of my reply to HopeFox, who was discussing the implications of a world where such threats were not incredible.
Pascal's mugging happens when the probability you would assign disregarding manipulation is very low (not a credible threat by normal standards), with the claimed utility being arbitrarily high to offset this. If that is not the case, it's a non-challenge and is not particularly relevant to our discussion. Does that clarify my original statement?
That makes sense. Whereas my statement roughly meant "Pascal's wager isn't about someone writing BusyBeaver<8>(3^^^3)" - that's not even a decision problem worth mentioning.