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nerzhin comments on Fair Division of Black-Hole Negentropy: an Introduction to Cooperative Game Theory - Less Wrong
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I was really confused by this article, so I looked up Shapley value and re-thought the example. This is repetitive, but maybe someone will find it useful.
Society wants to dump matter in a black hole. It (society as a whole) gets a payoff of (total matter dumped)^2 for doing so. If Alice agrees to dump 3 kg, the payoff is 9. Then Bob agrees to dump 2 kg, and the total societal payoff jumps to 25.
In some sense Alice contributed 9 and Bob 16, but it doesn't seem fair to reward them that way. We don't want order of contribution to matter that much. So you imagine doing it in the opposite order. In that case, Alice's marginal contribution is 21 and Bob's is 4.
Then you average over all possible orderings. In this example, Alice gets (9+21)/2 = 15, and Bob gets (16 + 4)/2 = 10.
Right, except it's not that society wants to dump matter in black holes. We just compute the entropy of a black hole with all the mass dumped into it because that's an upper bound on how much negentropy society originally had.