Ok, so I see that probability plays a role in determining one's "bargaining power", which makes sense. We still need a rule that outputs a compromise set of preferences when given a set of agents, their probabilities, individual preferences, and resources as input, right? Does the rule need to be uniquely fair or obvious, so that everyone can agree to it without discussion? Do you have a suggestion for what this rule should be?

Edit: I see you've answered some of my questions already in the other reply. This is really interesting stuff!