Because there are 2 threads instead of one I'll ask you this question here, talking about " discussing the Faction " you ment to create a sort of background for the Factions as well as a background for the conflict, and trying to put in evidence what this Faction is made by, meaning elements and mechanics, right? So to starting to create something concrete to this project..
If so a way to talking about Factions is really start to talk from the beginnings, before the Conflict started..
I think creating thematic background is a good way to develop the factions in addition to actually fleshing out the actual cards. However keep in mind this is at its core a series of ETG cards we are making (apparently with heavy flavor), not a story based around the elements.
storyteller has a good portion his interpretation of the backstory defined, so I expect he will post with his opinion soon.
It might be a good idea to split the faction threads into sections devoted to theme and sections devoted to mechanics.
