A Thought on Pascal's Mugging

The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3.

Is your utility function such that there is some scenario for which you assign -3^^^^3 utils? If so, then the Kolmogorov complexity of "3^^^^3 units of disutility" can't be greater than K(your brain) + K(3^^^^3), since I can write a program to output such a scenario by iterating through all possible scenarios until I find one which your brain assigns -3^^^^3 utils.

A prior of 2^-(K(your brain) + K(3^^^^3)) is not nearly small enough, compared to the utility -3^^^^3, to make this problem go away.

Come to think of it, the problem with this argument is that it assumes that my brain can compute the utility it assigns. But if it's assigning utility according to Kolmogorov complexity (effectively the proposal in the post), that's impossible.

The same issue arises with having probability depend on complexity.

0komponisto9yProbably not, if "you" is interpreted strictly to refer to my current human brain, as opposed to including more complex "enhancements" of the latter.

A Thought on Pascal's Mugging

by komponisto 1 min read10th Dec 2010159 comments

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For background, see here.

In a comment on the original Pascal's mugging post, Nick Tarleton writes:

[Y]ou could replace "kill 3^^^^3 people" with "create 3^^^^3 units of disutility according to your utility function". (I respectfully suggest that we all start using this form of the problem.)

Michael Vassar has suggested that we should consider any number of identical lives to have the same utility as one life. That could be a solution, as it's impossible to create 3^^^^3 distinct humans. But, this also is irrelevant to the create-3^^^^3-disutility-units form.

Coming across this again recently, it occurred to me that there might be a way to generalize Vassar's suggestion in such a way as to deal with Tarleton's more abstract formulation of the problem. I'm curious about the extent to which folks have thought about this. (Looking further through the comments on the original post, I found essentially the same idea in a comment by g, but it wasn't discussed further.)

The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3. That is, the utility function should grow only according to the complexity of the scenario being evaluated, and not (say) linearly in the number of people involved. Furthermore, the domain of the utility function should consist of low-level descriptions of the state of the world, which won't refer directly to words uttered by muggers, in such a way that a mere discussion of "3^^^^3 units of disutility" by a mugger will not typically be (anywhere near) enough evidence to promote an actual "3^^^^3-disutilon" hypothesis to attention.

This seems to imply that the intuition responsible for the problem is a kind of fake simplicity, ignoring the complexity of value (negative value in this case). A confusion of levels also appears implicated (talking about utility does not itself significantly affect utility; you don't suddenly make 3^^^^3-disutilon scenarios probable by talking about "3^^^^3 disutilons").

What do folks think of this? Any obvious problems? 

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