Dmytry comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
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Well, few things to note:
Making up reasons against pascal's mugging based on 'it must be wrong' feeling sounds awful lot like rationalization. One got to stick to really solid logic; only in mathematics can you believe rather strongly in a conjecture, be motivated to prove it, and then make a valid proof.
One man's decision affecting 3^^^^3 people, got to be very rare occurrence to find yourself in; you're much more likely to be among those 3^^^^3 . You got to adjust your prior for that. This should be enough for not giving $5
Other issue is that it is a hostage situation, and even in normal human hostage situations, whenever you should, or should not give the money to the hostage holder, depends solely to whenever you have higher probability that the hostages will be killed (or tortured) if money are given, than if money are not given. Without further information about people whom hold 3^^^^3 beings hostage for $5, you can not make any prediction - the expected effect of giving $5 on the suffering of 3^^^^3 beings is 3^^^^3 * 0 = 0, and thus the expected utility of giving $5 is equal to expected utility of not giving $5 , minus the utility of having $5 in your hands rather than in mugger's hands. It does not matter how many up arrows the mugger stacks; it may well be that on average, giving money gets hostages killed in the situation when the kidnapper is this psychopathic. Then one may estimate that giving the money has immense dis-utility. Caveat: one can imagine the inconvenient world where psychopaths hold their words and release hostages when demands are met.
Actually in real life, we also consider the future consequences of unspecified potential future hostage takers who may be motivated to take hostages if they see a hostage taker paid off. This is ostensibly why the USG will not (directly) pay off a hostage taker.
Also, we have to consider the value of the money, and our next best alternative to saving a hostages life. For example, if Dr. Evil is holding a hostage (doesn't matter who) for $1B, and you know we will not catch him if you pay him off, then you should probably just let him execute the hostage and use the money to buy food for a few thousand starving people somewhere who are just as desperate.
Yep. Well, those aspects of it are not so relevant to the 3^^^3 case as they don't scale with N