Your “walking by in the street” example is interesting. But the point of weighting your utilities is to split the gains from every single future transaction and interaction with them. Since you’re both part of the same economic system, they will have (implicit or explicit) interactions in the future. Though I don’t yet know the best way of normalising multiple agents utilities, which we’d need to make this fully rigorous.
And seeing how much world GDP is dependent on trade, I’d say the gains from trade are immense! I note your treasure hunting example has rather large gains from trade...
So, what we do know:
1) If everyone has utility equally linear in every resource (which we know is false), then the more powerful player wins everything (note that this one of the rare cases where there is an unarguable “most powerful player”)
It’s a proof based on premises of uncertain validity. So it certainly proves something, in some situations—the question is whether these situations are narrow, or broad.
Would it be possible to make those clearer in the post?
I had thought, from the way you phrased it, that the assumption was that for any game, I would be equally likelly to encounter a game with the choices and power levels of the original game reversed. This struck me as plausible, or at least a good point to start from.
What you in fact seem to need, is that I am equally likely to encounter a game with the outcome under this scheme reversed, but the power levels kept the same. This continues to strike me as a very substansive and almost certainly false assertion about the games I am likely to face.
Your “walking by in the street” example is interesting. But the point of weighting your utilities is to split the gains from every single future transaction and interaction with them. Since you’re both part of the same economic system, they will have (implicit or explicit) interactions in the future. Though I don’t yet know the best way of normalising multiple agents utilities, which we’d need to make this fully rigorous.
And seeing how much world GDP is dependent on trade, I’d say the gains from trade are immense! I note your treasure hunting example has rather large gains from trade...
So, what we do know:
1) If everyone has utility equally linear in every resource (which we know is false), then the more powerful player wins everything (note that this one of the rare cases where there is an unarguable “most powerful player”)
2) In general, to within the usual constraints of not losing more than you can win, any player can get anything out of the deal (http://lesswrong.com/r/discussion/lw/i20/even_with_default_points_systems_remain/ , but you consider these utilities naturally occurring, rather than the product of lying)
I don’t therefore see strong evidence I should reject my informal proof at this point.
I think you and I have very different understandings of the word ‘proof’.
It’s a proof based on premises of uncertain validity. So it certainly proves something, in some situations—the question is whether these situations are narrow, or broad.
Would it be possible to make those clearer in the post?
I had thought, from the way you phrased it, that the assumption was that for any game, I would be equally likelly to encounter a game with the choices and power levels of the original game reversed. This struck me as plausible, or at least a good point to start from.
What you in fact seem to need, is that I am equally likely to encounter a game with the outcome under this scheme reversed, but the power levels kept the same. This continues to strike me as a very substansive and almost certainly false assertion about the games I am likely to face.
After the baby, when I have time to do it properly :-)
Fair enough