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twanvl comments on Cooperating with agents with different ideas of fairness, while resisting exploitation - Less Wrong Discussion
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In general, you can not compare the utilities for two different agents, since a linear transformation doesn't change the agent's behavior. So (12, 12) is really (12a+a₀, 12b+b₀). How would you even count the utility for another agent without doing it in their terms?
We don't have this problem in practice, because we are all humans, and have similar enough utility functions. So I can estimate your utility as "my utility if I were in your shoes". A second factor is perhaps that we often use dollars as a stand-in for utilons, and dollars really can be exchanged between agents. Though a dollar for me might still have a higher impact than a dollar for you.
Hence "Suppose a magical solution N to the bargaining problem." We're not solving the N part, we're asking how to implement N if we have it. If we can specify a good implementation with properties like this, we might be able to work back from there to N (that was the second problem I wrote on the whiteboard).