Larks comments on Gains from trade: Slug versus Galaxy - how much would I give up to control you? - Less Wrong
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Here's another strange property of the bargaining solution. (Again I would appreciate confirmation that I'm understanding it correctly.) Suppose Alice and Carol both have linear utility, and Alice owns a tiny bit more resources than Carol. Then Alice's utility function gets normalized to have a higher marginal utility than Carol, and all the resources go to Alice. If Carol instead brought a tiny bit more resources to the table, then all the resources would go to Carol.
I find it puzzling that the post is getting upvoted so much with so little discussion. Is anyone else looking at whether the solution produces outcomes that make intuitive sense?
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...