Alternate approaches to Pascal's Mugging

Most of these are just a failure to consider the Least Convenient Possible world, all may be valid arguments in that specific case but fail to address the general problem.

The mugger can also just say "Give me $5 or I will cause you to lose 3^^^3 times more utility than that $5 is worth." This makes the issue a bit clearer, though I'm sure one can still fail to answer the challenge head-on.

Presumably upon reflection everyone here could already assign a probability (possibly zero if that's your thing) to me torturing a kajillion Matrix people or causing specifically you to lose lots of disutility or whatever.

Does this probability really change significantly if I make a bunch of cheap and familiar statements about how I'm going to do this if you don't give me $5?

It seems like the "mugging" step of Pascal's Mugging isn't really that important. If you'd be vulnerable to it, then you can mug yourself just fine without my help.

"Give me five dollars, and I will use my outside-the-Matrix powers to make your wildest dreams come true, including living for 3^^^3 years of eudaimonic existence and, yes, even telling you about the true substrate of existence. Hey, I'll top it off and let you out of the box, if only you decide to give me five of your simulated dollars."

For your kinds of arguments to work, it seems that there must be nothing that the mugger could possibly promise or threaten to do and that, if it came true, you would rate as making a difference of 3^^^3 utils (where declining the offer and continuing your normal life is 0 utils, and giving five dollars to a jokester is -5 utils). It seems like a minor variation on the arguments in Eliezer's original post to say that if your utility function does assign utilities differing by 3^^^3 to some scenarios, then it seems extremely unlikely that the probability of each of these coming true will balance out just so that the expected utility of paying the mugger is always smaller than zero, no matter what the mugger promises or threatens. If your utility function doesn't assign utilities so great or small to any outcome, then you have a bounded utility function, which is one of the standard answers to the Mugging.

My own current position is that perhaps I really do have a bounded utility function. If it were only the mugging, I would perhaps still hold out more hope for a satisfactory solution that doesn't involve bounded utility, but there's also the unpalatability of having to prefer a (googolplex-1)/googolplex chance of everyone being tortured for a thousand years and all life in the multiverse ending after that + a 1/googolplex chance of 4^^^^4 years of positive post-singularity humanity to the certainty of a mere 3^^^3 years of positive post-singularity humanity, given that 3^^^3 years is far more than enough to cycle through every possible configuration of a present-day human brain. Yes, having more space to expand into post-singularity is always better than less, but is it really that much better?

(ObNote: In order not too make this seem one-sided, I should also mention the standard counter to that, especially since it was a real eye-opener the first time I read Eliezer explain it -- namely, with G := googolplex, I would then also have to accept that I'd prefer a 1/G chance of living (G + 1) years + a (G-1)/G chance of living 3^^^3 years to a 1/G chance of living G years + a (G-1)/G chance of living 4^^^^4 years -- in other words, I'll prefer a near-certainty of an unimaginably smaller existence, if I get for that a miniscule increase of existence in a scenario that only has a miniscule chance of happening in the first place. But I've started to think that, perhaps, the unimaginably large difference between these lifetimes possibly really might be that unimportant, given that I can cycle through all of current-brain-size human mindspace many times in a mere 3^^^3 years, and given the also-unpalatable conclusions from the unbounded utility function.)

I'm not sure if this is out of left field or not, but I think I currently have the approach below:

If a Pascal Mugger can mug you for n utils, it seems like A Pascal Mugger can mug you for 2n utils by restructuring the math of his statement slightly. Or alternatively, he can just mug you for n utils again.

There doesn't appear to be any obvious limit to the above. If my evaluation of the math says I should give in to a Pascal mugger for 5 dollars, it also seems to indicate I should give in to a Pascal mugger for 10 dollars, 100 dollars, my house, a year of slavery, or allowing myself to be a mind controlled puppet for the rest of my life, if the mugger phrases the numbers correctly. It seems like I can be mugged for anything (Another way to say this might be that there is no clear upper limit on the maximum amount of utility I can be Pascal mugged for if I can be Pascal mugged for 5 utility.)

It does not seem reasonable to become a mind controlled puppet for the rest of my life because anyone says:

"Pascal's Mugging, A=#, P(a)=#, B=#, P(b)=#, C=Mind controlled puppetry for the rest of your life."

So I guess I'm left with:

A: If my utility function is such that it is correct to give into Pascal's Mugging, then it is correct to give into Pascal's Larger Mugging. (By the argument above) B: Giving into Pascal's Larger Mugging is incorrect according to my utility function. (This just appears to be the case. I mean I could be that submissive to absolutely any math student who had a function capable of generating a generically copiable string of numbers, but it does not seem correct to do so.) C: So giving into Pascal's Mugging is incorrect according to my utility function. (By Modus Tollens)

Now, there are alternatives to that. If for instance, The circumstance causing Pascal's mugging does not appear to be a sentient capable of modifying the dilemma to turn you into a slave for itself, (Pascal's Incoming Meteor?) Then that's entirely different. It does seem reasonable to give 5 dollars to help build a meteor deflection system under some circumstances.

So I suppose I could say "I will allow myself to be Pascal Mugged if and only if it does not appear likely to turn me into a utility pump for lots of people." Which also makes sense, because if your utility function is unbounded, then allowing millions of people to steal as much utility from you as they want whenever they want seems rather catastrophically bad, since as bad as making any one decision incorrectly is, allowing your decision making process to be subverted for all of your next decisions seems likely to be worse, and there is no limit to how bad it can get with an unbounded utility function.

Does that seem reasonable?

To put it bluntly... why should I care? Even if the Mugger's claim is accurate, the entities he threatens to simulate and calls 'people' don't seem as if they will have any opportunity to interact with my portion of the Matrix; they will never have any opportunity to offer me any benefit or any harm. How would it benefit myself to treat such entities as if they not only had a right to life, but that I had an obligation to try to defend their right?

This is easily remedied: The 3^^^3 people will all be put into the exact same simulated Pascal's Mugging scenario, and each will be given some previous life experiences that may or may not be like your own, but that the simulated person will assume as his/her own. Their choice won't actually affect what happens to them, but depending on the original non-simulated person's choice, they'll either lead a happy simulated life, or be killed (dependent on the original's choice, not their own). Overall, 3^^^3 + 1 choices, only one of which counts (the original's).

Now, you'd have to assume that you yourself are not in the original PM situation, but one of the simulated ones (self sampling assumption). This means that while you'd have to expect your choice not to have any impact (since the original already made the choice that counts), even the tiny probability of being the original would cause you to pay the 5$, counting on TDT reasoning to ensure the best outcome for all simulated muggees - and thus for yourself (Possibly contributing towards not getting killed yourself would outweigh the 5$ you'd expect to be simulated anyways.)

To put it bluntly... why should I care?

(Putting things bluntly or expressing opinions based on unclear considerations is usually not helpful for forming robust understanding of subtle questions.)

Never mind.