Edit: Moved to main at ThrustVectoring's suggestion.

A suggestion as to how to split the gains from trade in some situations.

The problem of Power

A year or so ago, people in the FHI embarked on a grand project: to try and find out if there was a single way of resolving negotiations, or a single way of merging competing moral theories. This project made a lot of progress in finding out how hard this was, but very little in terms of solving it. It seemed evident that the correct solution was to weigh the different utility functions, and then for everyone maximise the weighted sum, but all ways of weighting had their problems (the weighting with the most good properties was a very silly one: use the "min-max" weighting that sets your maximal attainable utility to 1 and your minimal to 0).

One thing that we didn't get close to addressing is the concept of power. If two partners in the negotiation have very different levels of power, then abstractly comparing their utilities seems the wrong solution (more to the point: it wouldn't be accepted by the powerful party).

The New Republic spans the Galaxy, with Jedi knights, battle fleets, armies, general coolness, and the manufacturing and human resources of countless systems at its command. The dull slug, ARthUrpHilIpDenu, moves very slowly around a plant, and possibly owns one leaf (or not - he can't produce the paperwork). Both these entities have preferences, but if they meet up, and their utilities are normalised abstractly, then ARthUrpHilIpDenu's preferences will weigh in far too much: a sizeable fraction of the galaxy's production will go towards satisfying the slug. Even if you think this is "fair", consider that the New Republic is the merging of countless individual preferences, so it doesn't make any sense that the two utilities get weighted equally.