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...
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...