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CarlShulman comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
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Comments (34)
1: Well, part of the issue is that feelings can very well be right. The feeling is that the claim is too outrageous, that's a genuine thing but it is too hard to pin any probabilities onto.
One would think that the probability should fall off with the outrageousness of the claim, super-linearly. I.e. suppose that no claim is made; you are to give, or not to give, $5, to a random person who have not claimed that $5 will save 3^^^3 people. It is clear enough that the probability of this $5 saving 3^^^3 people got to be very small then, and would fall off with the claimed number, it's reasonable that it would fall off super-linearly. Then, the person making that claim is just a piece of evidence that can't boost the prior probability by whole lot; see the posts here on Bayesian statistics. Indeed, if one is to give to mugger $5, one should give $5 to people who didn't even ask for money.
Actually, to think about it, i might've just nailed it and also nailed the problem with using probabilistic reasoning in practice. You can easily pick some random hypothesis out of enormously huge space, which gives it very small prior, but then you forget about this enormous space.
2: I don't see how it's overly specific. If we consider (coin or a person), one randomly chosen (coin or a person) affecting 3^^^^3 (coin or a person) is unlikely. Still, the explanation is indeed somewhat problematic.
1: Well my reasoning is that the more people the mugger threatens to kill, the less likely his claims are to be true. In the same way that if I were to claim that a row of 3^^^^3 coins would all turn up heads; it would be far less likely to come true than if I predicted two coins would come up heads. At least that's what I'm trying to get across in this post.
2: It seems overly specific to me because it seems like a bit too much of a hack, if you get my meaning?
As you see more and more heads, you become increasingly convinced the coins are biased. What's the bias? With what probability p will a given flip come up heads? At the start you assign some mass to p=1, and some to lesser biases. After 10^1000 heads you can basically ignore the possibility that the coins are fair, and most of the weight you might have initially placed on a minor bias. Going from 10^1000 to 3^^^^3 coins, you will get to clobber hypotheses like "p=1-10^2000", but you will get no evidence whatsoever against "p=1". So as long as you assigned any non-infinitesimal, non-gerrymandered credence to p=1 at the start, longer sequences can't get probabilities approaching zero.
True, but that is as you see more heads. You can't actually update your value for p based on evidence you haven't seen yet, longer sequences would still have probabilities approaching zero.
Can someone let me know why this has negative votes please? Thanks.
Because its likes/dislikes not votes. The number of dislikes is greater than number of likes by 1. That being said, as the estimate of bias in coin increases, so does your likehood of future throws being HHHHH. Not sure I understand what is your point.
Hover over the thumbs-up / thumbs-down icons, they say "Vote up" and "Vote down". Anyway I was wondering what it was that I'd said that was wrong and thus deserved to be voted down.
Yes, I agree. However what I was trying to point out is that if you start off with no evidence of the coin being biased then you estimate of the bias won’t increase before you start flipping coins.
By the same merits, your estimate of how likely it is the mugger will kill x number of people won’t change because every person he kills is evidence toward him killing them all successfully as you're making the prediction before he does anything. If you read the above comments I believe it makes sense in context.
We have a saying in Russian, along the lines of ' the wall of a shed says [certain swearword common in graffiti, refers to a reproductive organ] but this body part is not present inside the shed ' . edit: anyhow, i kind of don't see anything wrong about what you said.