Wei_Dai comments on Fairness and Geometry - Less Wrong
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Comments (34)
My understanding is that cousin_it is suggesting just such a base decision algorithm, which works like this:
We can all probably see a whole bunch of difficulties here, both technical and philosophical. But Eliezer, it's not clear from reading your comment what your objection is exactly.
ETA: I just noticed that cousin it's proposed "good and fair" formula doesn't actually ensure my point above in parenthesis (that anyone who doesn't follow the decision algorithm will fail to maximize its utility). To see this, suppose in PD one of the players can choose a third option, which is not Pareto-optimal but unilaterally gives it a higher payoff than assigned by cousin_it's formula.
cousin_it, if you're reading this, please see http://lesswrong.com/lw/102/indexical_uncertainty_and_the_axiom_of/sk8 , where Vladimir Nesov proposed a notion that turns out to coincide with the concept of the core in cooperative game theory. This is necessary to ensure that the "good and fair" solution will be self-enforcing.
If one of the PD players has a third option of "get two bucks guaranteed and screw everyone else" - if the game structure doesn't allow other players to punish him - then no algorithm at all can punish him. Or did you mean something else?
Yep, I know what the core is, and it does seem relevant. But seeing as my solution is definitely wrong for stability reasons, I'm currently trying to think of any stable solution (continuous under small changes in game payoffs), and failing so far. Will think about the core later.
The "good and fair" solution needs to offer him a Pareto improvement over the outcome that he can reach by himself.
Wei Dai, thanks. I gave some thought to your comments and they seem to constitute a proof that any "purely geometric" construction (that depends only on the Pareto set) fails your criterion. Amending the post.
Sorry, I was being stupid. You're right.