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Larks comments on Gains from trade: Slug versus Galaxy - how much would I give up to control you? - Less Wrong
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It's even worse. Suppose Alice and Carol are as you say, with Alice having x more resources than Carol. Before the trade, Alice is given the chance to benefit them both; if she accepts the offer, she will gain y resources, and Carol will gain y+2x. This is a pareto improvement, and prima facie it seems she should do so.
But alas! If she does so, Carol will have x more resources that Alice does - so all the resources will go to Carol! So Alice definitely does not want to accept the offer - even though accepting Omega's offer could leave them both better off post-trade.
Ideally the default point would be set before Omega's offer. After all, that is a decision point of Alice's, that Carol woul value being able to decide...