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dankane comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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Fine if you think that Omega would have told me about the previous coin flip consider this:
There are two different supernatural entities who can correctly predict my response to the counterfactual mugging. There's Omega and Z.
Two things could theoretically happen to me:
a) Omega could present me with the counterfactual mugging problem.
b) Z could decide to steal $1000000 from me if and only if I would have given Omega $1000 in the counterfactual mugging.
When I am trying to decide on policy for dealing with counterfactual muggings I should note that my policy will affect my outcome in both situation (a) and (b). The policy of giving Omega money will win me $499500 (expected) in situation (a), but it will lose me $1000000 in situation (b). Unless I have a reason to suspect that (a) is at least twice as likely as (b), I have no reason to prefer the policy of giving Omega money.
The basis of the dilemma is that you know that Omega, who is honest about the dilemmas he presents, exists. You have no evidence that Z exists. You can posit his existence, but it doesn't make the dilemma symmetrical.
But if instead Z exists, shows up on your doorstep and says (in his perfectly trustworthy way) "I will take your money if and only if you would have given money to Omega in the counterfactual mugging", then you have evidence that Z exists but no evidence that Omega does.
The point is that you need to make your policy before either entity shows up. Therefore unless you have evidence now that one is more likely than the other, not paying Omega is the better policy (unless you think of more hypothetical entities).
Agreed. Neither is likely to happen, but the chance of something analogous happening may be relevant when forming a general policy. Omega in Newcombe's problem is basically asking you to guard something for pay without looking at it or stealing it. The unrealistic part is being a perfect predictor and perfectly trustworthy and you therefore knowing the exact situation.
Is there a more everyday analogue to Omega as the Counterfactual Mugger?
People taking bets for you in your absence.
It's probably a good exercise to develop a real-world analogue to all philosophical puzzles such as this wherever you encounter them; the purpose of such thought experiments is not to create entirely new situations, but to strip away extraneous concerns and heuristics like "but I trust my friends" or "but nobody is that cold-hearted" or "but nobody would give away a million dollars for the hell of it, there must be a trick".
Good point. On the other hand I think that Omega being a perfect predictor through some completely unspecified mechanism is one of the most confusing parts of this problem. Also as I was saying, it is also complicating issue that you do not know anything about the statistical behavior of possible Omegas (though I guess that there are ways to fix that in the problem statement).
It may be a truly magical power, but any other method of stipulating better-than-random prediction has a hole in it that lets people ignore the actual decision in favor of finding a method to outsmart said prediction method. Parfit's Hitchhiker, as usually formalised on LessWrong, involves a more believable good-enough lie-detector - but prediction is much harder than lie-detection, we don't have solid methods of prediction that aren't gameable, and so forth, until it's easier to just postulate Omega to get people to engage with the decision instead of the formulation.
Now if the method of prediction were totally irrelevant, I think I would agree with you. On the other hand, method of prediction can be the difference between your choice directly putting the money in the box in Newcomb's problem and a smoking lesion problem. If the method of prediction is relevant, than requiring an unrealistic perfect predictor is going to leave you with something pretty unintuitive. I guess that a perfect simulation or a perfect lie detector would be reasonable though. On the other hand outsmarting the prediction method may not be an option. Maybe they give you a psychology test, and only afterwords offer you a Newcomb problem. In any case I feel like confusing bits of problem statement are perhaps just being moved around.
There is one Omega, Omega and Newcomb's problem gives his profile!