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Vladimir_Nesov comments on Fairness and Geometry - Less Wrong
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Since AIs can self-modify, one nice property would be if no player can obtain a better outcome for itself by modifying its utility function ahead of time. In this case, if I take the pure outcome that most favors me, and change my utility function so that I value it less, I can increase my bargaining power and possibly get a better outcome under your proposed solution. Right?
It's like with unfair coins: there are unfair utility functions as well. ;-) You'd have to look at what the utility could be, as with the prior probability of Omega's coin. All the AI can do is adapt its utility to environment, while there is also a "prior" utility, that describes how it looks at all possible environments, how it chose this particular utility for this particular environment.