That’s not necessary for the parallel to work. In my post, the insurer is stating how things look from your side of the deal, in a way that shows the mapping to the counterfactual mugger. (And by the way, if insurers predict your house will burn down they don’t offer you a policy—not one as cheap as $1000. If they sell you one at all, they sell at a price equal to the payout, in which case it’s just shuffling money around.)
What creates a mapping to Newcomb’s problem (and by transition, the counterfactual mugging) is the inability to selectively set a policy so that it only applies at just the right time to benefit you. With a perfect predictor (Omega), you can’t “have a policy of one-boxing” yet conceal your intent to actually two-box.
This same dilemma arises in insurance, without having to assume a perfect, near-acausal predictor: you can’t “decide against buying insurance” and then make an exception over the time period where the disaster occurs. All that’s necessary for you to be in that situation is that you can’t predict the disaster significantly better than the insurer (assuming away for now the problems of insurance fraud and liability insurance, which introduce other considerations).
The analogy is that both situations use expected utility to make a decision. The principal difference is that when you are buying insurance, you do expect your house to burn to the ground, with a small probability. Counterfactual mugging suggests an improbable conclusion that the updated probability distribution is not what you should base your decisions on, and this aspect is clearly absent from normal insurance.
Counterfactual mugging suggests an improbable conclusion that the updated probability distribution is not what you should base your decisions on, and this aspect is clearly absent from normal insurance.
No, normal insurance has this aspect too: you don’t regret buying insurance once you learn the updated probability distribution, so you shouldn’t base your decision on it either.
you don’t regret buying insurance once you learn the updated probability distribution
I don’t regret it, because I remember that it was the best I could do given the information I had at the time. But if I knew when deciding whether or not to buy insurance that I would not be sued or become liable for large amounts, then I wouldn’t buy it. And I don’t want to change my decision algorithm to ignore information just because I didn’t have it some other time.
Where did I suggest that throwing away information is somehow optimal or of different optimality than in Newcomb’s problem or the counterfactual mugging?
I don’t know whether or not you intended to say that. But if you didn’t, then what did you mean by
normal insurance has this aspect too: you don’t regret buying insurance once you learn the updated probability distribution, so you shouldn’t base your decision on it either
To me that looks like you are saying that it doesn’t matter if you decide whether to buy insurance before or after you learn what will happen next year.
Please read it in the context of the comment I was replying to. Vladimir_Nesov was trying to show how my mapping of insurance to Newcomb didn’t carry over one important aspect, and my reply was that when you consistently carry over the mapping, it does.
That is the context that I read it in. He pointed out that counterfactual mugging is equivalent to insurance only if you fail to update on the information about which way the coin fell before deciding (not) to play. You responded that this made no difference because you didn’t regret buying insurance a year later (when you have the information but don’t get to reverse the purchase).
I guess I should have asked for clarification on what he meant by the “improbable conclusion” that the counterfactual mugging suggests. I thought he meant that the possibility of being counterfactually mugged implies the conclusion that you should pre-commit to paying the mugger, and not change your action based upon finding that you were on the losing side.
If that’s not the case, we’re starting from different premises.
In any case, I think the salient aspect is the same between the two cases: it is optimal to precommit to paying, even if it seems like being able to change course later would make you better off.
That’s not necessary for the parallel to work. In my post, the insurer is stating how things look from your side of the deal, in a way that shows the mapping to the counterfactual mugger. (And by the way, if insurers predict your house will burn down they don’t offer you a policy—not one as cheap as $1000. If they sell you one at all, they sell at a price equal to the payout, in which case it’s just shuffling money around.)
What creates a mapping to Newcomb’s problem (and by transition, the counterfactual mugging) is the inability to selectively set a policy so that it only applies at just the right time to benefit you. With a perfect predictor (Omega), you can’t “have a policy of one-boxing” yet conceal your intent to actually two-box.
This same dilemma arises in insurance, without having to assume a perfect, near-acausal predictor: you can’t “decide against buying insurance” and then make an exception over the time period where the disaster occurs. All that’s necessary for you to be in that situation is that you can’t predict the disaster significantly better than the insurer (assuming away for now the problems of insurance fraud and liability insurance, which introduce other considerations).
I see your point.
The analogy is that both situations use expected utility to make a decision. The principal difference is that when you are buying insurance, you do expect your house to burn to the ground, with a small probability. Counterfactual mugging suggests an improbable conclusion that the updated probability distribution is not what you should base your decisions on, and this aspect is clearly absent from normal insurance.
No, normal insurance has this aspect too: you don’t regret buying insurance once you learn the updated probability distribution, so you shouldn’t base your decision on it either.
I don’t regret it, because I remember that it was the best I could do given the information I had at the time. But if I knew when deciding whether or not to buy insurance that I would not be sued or become liable for large amounts, then I wouldn’t buy it. And I don’t want to change my decision algorithm to ignore information just because I didn’t have it some other time.
Where did I suggest that throwing away information is somehow optimal or of different optimality than in Newcomb’s problem or the counterfactual mugging?
I don’t know whether or not you intended to say that. But if you didn’t, then what did you mean by
To me that looks like you are saying that it doesn’t matter if you decide whether to buy insurance before or after you learn what will happen next year.
Please read it in the context of the comment I was replying to. Vladimir_Nesov was trying to show how my mapping of insurance to Newcomb didn’t carry over one important aspect, and my reply was that when you consistently carry over the mapping, it does.
That is the context that I read it in. He pointed out that counterfactual mugging is equivalent to insurance only if you fail to update on the information about which way the coin fell before deciding (not) to play. You responded that this made no difference because you didn’t regret buying insurance a year later (when you have the information but don’t get to reverse the purchase).
I guess I should have asked for clarification on what he meant by the “improbable conclusion” that the counterfactual mugging suggests. I thought he meant that the possibility of being counterfactually mugged implies the conclusion that you should pre-commit to paying the mugger, and not change your action based upon finding that you were on the losing side.
If that’s not the case, we’re starting from different premises.
In any case, I think the salient aspect is the same between the two cases: it is optimal to precommit to paying, even if it seems like being able to change course later would make you better off.