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Wei_Dai comments on indexical uncertainty and the Axiom of Independence - Less Wrong
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Agents don't need to merge by changing anything in their individual preferences, merging is just a way of looking at the system, like in process algebra. Three agents can be considered as three separate agents cooperating with each other, or as two agents, one a merge of the first two of the original ones, or as one merged agent. All different perspectives on the same system, revealing its structure.
The crucial relation in this picture is that the global cooperation must be a Pareto improvement over cooperations (merges) among any subset of the agents. This is a possible origin for the structure of fair coopertive strategy. More than that, if each agent that could otherwise be considered as individual is divided in this manner on a set of elementary preferences, and all of these elementary preferences are then dumped together in the global cooperation, this may provide all the detail the precise choice of the fair cooperative strategy might need. The "weights" come from the control that each of the elementary agents has over the world.
Are you familiar with Cooperative Game Theory? I'm just learning it now, but it sounds very similar to what you're talking about, and maybe you can reused some of its theory and math. (For some reason I've only paid attention to non-cooperative game theory until recently.) Here's a quote from page 356 of "Handbook of Game Theory with Economic Applications, Vol 1":
I couldn't find anything that "clicked" with cooperation in PD. Above, I wasn't talking about a kind of Nash equilibrium protected from coalition deviations. The correlated strategy needs to be a Pareto improvement over possible coalition strategies run by subsets of the agents, but it doesn't need to be stable in any sense. It can be strictly dominated, for example, by either individual or coalition deviations.
A core in Cooperative Game Theory doesn't have to be a Nash equilibrium. Take a PD game with payoffs (2,2) (-1,3) (3,-1) (0,0). In Cooperative Game Theory, (-1,3) and (3,-1) are not considered improvements that a player can make over (2,2) by acting for himself. Maybe one way to think about it is that there is an agreement phase, and an action phase, and the core is the set of agreements that no subset of players can improve upon by publicly going off (and forming their own agreement) during the agreement phase. Once an agreement is reached, there is no deviation allowed in the action phase.
Again, I'm just learning Cooperative Game Theory, but that's my understanding and it seems to correspond exactly to your concept.
Sounds interesting, thank you.