We had
an interesting talk about grudges that quickly went over groups because, well, grudges only start being Fun when several persons are implied.
I think the less specific the system is, the more numerous different situations able to emerge from said system are, which implies more sources of Fun. So I'll try to remain as generic as possible.
A group's influence could be described through three things : its economical power (how much money does it disposes of), its political power (the sum of the power of the politic people among its followers, military power included) and its social influence (how many followers does it count).
Also, so as to reflect alliances, a group would add to its influence a part of allied influence, depending on how tights their bounds are.
I don't really know what such a number would be useful for, though. During worldgen, as a shortcut, or when deciding who to fight or fear, whether victory over some group is possible ?
Goals would be what mainly distinct a group from another. I don't really know how to chose these goals, but I have an idea about how to use them. Basically, each member of a group would have happy thoughts when its group achieves one of his goal, or a step toward it. Of course, when a group fails to achieve a goal or takes too much time to do so, they would have an unhappy thought about it too.
A group could order some laws its members would have to respect (this would be particularly useful for religions and political parties). Someone who does not respect these laws would attract a grudge from this group (so from its members, too). Then there's the idea of punishments, possibly a member being banned from the group (bad thought depending on how much he liked the group).
Now, the part where it all becomes interesting is at the individual level : someone would want to please groups he is a member of. Simplest way to do this would be to try and reach happy thoughts instead of just merely receiving them. This way, you just have to define an occasion of having a happy thought and you're done.
So, members would want their groups to achieve their goals. For this, they would ask themselves "what can I do so my family/guild/clan succeeds ?"
They'd check a list of what they can do, and the repercutions over every of their groups' goals and also over their OWN goals.
Then, we would have to calculate some sort of average/bayesian product and chose what to do depending on the individual personality traits and determination to achieve said goals (which would depend on how close they feel to each group and goal).
Having a difference between personnal goals and groups' goals is crucial here : dilemnas and tension and drama would come out of this. Along with corruption, deception, brother-killing, decision making, not-making-a-decision-because-that's-still-your-daughter-the-elves-have-captured-and-you-can't-order-magma-to-be-released.
Like skill rust, an individual would tend to forget its bounds to a group. They would have to be maintained by trying to act for the group (happy thought for the one who tried) and succeeding in helping the group (happy thoughts for everyone !). This way, a group which fails in everything would quickly lose influence, but someone whose goal matches the group's goal would still be committed.
In short, a member's opinion about something would be influenced by what its groups think of it as well as about his opinion.
Let's take the example of Urist McAverageDwarf. A new Mayor is elected, Dulcim McFamilyKilledDuringElfRush. Dulcim declares war to the elves. What would Urist do ? She doesn't think of anything about elves, nor war. So, mostly "meh, why not". But, she pretty much likes Dulcim. In fact, her family likes Dulcim, her friends like Dulcim, the priests of OdilNom like Dulcim. So, its gonna affect a little her choice, and she's gonna trust Dulcim.
Meanwhile, Dolum is a merchant whose main buyers are elves. As a merchant, he wants to keep having money, so he wants elves to buy him stone mugs. If his fortress declares war to his source of income, he'll no longer have a source of income ! Holly gosh, even if everyone thinks Dulcim is awesome, he doesn't want his family to be poor !
So he'll try to react.