Manfred comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong

43 08 May 2013 12:43AM

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Comment author: 06 May 2013 04:40:35AM *  16 points [-]

Hm, a linear "leverage penalty" sounds an awful lot like adding the complexity of locating you of the pool of possibilities to the total complexity.

Thing 2: consider the case of the other people on that street when the Pascal's Muggle-ing happens. Suppose they could overhear what is being said. Since they have no leverage of their own, are they free to assign a high probability to the muggle helping 3^^^3 people? Do a few of them start forward to interfere, only to be held back by the cooler heads who realize that all who interfere will suddenly have the probability of success reduced by a factor of 3^^^3?

Comment author: 06 May 2013 04:47:44AM 6 points [-]

This is indeed a good argument for viewing the leverage penalty as a special case of a locational penalty (which I think is more or less what Hanson proposed to begin with).

Comment author: 06 May 2013 09:48:47AM *  10 points [-]

Suppose we had a planet of 3^^^3 people (their universe has novel physical laws). There is a planet-wide lottery. Catherine wins. There was a 1/3^^^3 chance of this happening. The lotto representative comes up to her and asks her to hand over her ID card for verification.

All over the planet, as a fun prank, a small proportion of people have been dressing up as lotto representatives and running away with peoples' ID cards. This is very rare - only one person in 3^^3 does this today.

If the lottery prize is 3^^3 times better than getting your ID card stolen, should Catherine trust the lotto official? No, because there are 3^^^3/3^^3 pranksters, and only 1 real official, and 3^^^3/3^^3 is 3^^(3^^3 - 3), which is a whole lot of pranksters. She hangs on to her card, and doesn't get the prize. Maybe if the reward were 3^^^3 times greater than the penalty, we could finally get some lottery winners to actually collect their winnings.

All of which is to say, I don't think there's any locational penalty - the crowd near the muggle should have exactly the same probability assignments as her, just as the crowd near Catherine has the same probability assignments as her about whether this is a prankster or the real official. I think the penalty is the ratio of lotto officials to pranksters (conditional on a hypothesis like "the lottery has taken place"). If the hypothesis is clever, though, it could probably evade this penalty (hypothesize a smaller population with a reward of 3^^^3 years of utility-satisfaction, maybe, or 3^^^3 new people created), and so what intuitively seems like a defense against pascal's mugging may not be.

Comment author: 06 May 2013 04:53:48AM -2 points [-]

Really? I was going to say that the argument need not mention the muggle at all, since the mugger is also one person among 3^^^3.