I'm not sure I get your example. If groups A and B have 2 members each, but one of the members cares about the group status, while the other one doesn't, don't

I'm not sure I get your example. If groups A and B have 2 members each, but one of the members cares about the group status, while the other one doesn't, don't they effectively have only 1 member? I.e. group of "me and someone who doesn't care" would just be a group of "me". Then that group isn't useful to be high status in, since it doesn't offer any extra benefits (a group of "me" can't do more than just me). If the weights weren't 1 and 0 for A and B respectively, but something like 1 and 0.5, then the group's value would just be (status within the group) * sum(participants sans self * their weight * their influence). (assuming influence can be quantified somehow) Then if I gain status in a group, and other members of the group lose a bit of their status, I can evaluate the gains and losses and the sum will be 0. To get the global status I just sum the results for all the groups I'm part of, and compare to other people. So a person A can be highly regarded in a paper airplane folding club, but unless there's a surprising number of top politicians/lobbyists/whatever who care about the club a lot, person B who plays golf with Donald Trump will probably have higher global status. ----- Looking at it now, I guess you could say that the global status is technically non-zero sum, since it will inflate with creation of new groups. Maybe the weights representing how much people care should need to sum to 1 for every person, that would solve the inflation? Then it only inflates when new people appear. Anyway, the global status is just a ranking showing who can "move the most pieces", as it were.