This is a take off of the good and evil thread, how do you see the clans as in what you think makes them tick, how they get along with groups, their motives...kind of like what your headcanon is for them. I'll give an example...
Riots: While there are Bioshock references in Riotopolis, it's not Randian due to Pericles knowing what it's like to be screwed over by the market and the elites Rand would've praised. The Riots do praise logic over emotions and are atheists or to a lesser extent, agnostic. To many of the surface-dwellers, the clan might come off as snobby and they were for a while until the Riots were forced to eat a little humble pie when stuff like Christmas appealed to the kids and they saw that the surface-dwellers aren't all barbarians. Still, the clan has a lot of pride and are more open to sharing what they have in science and philosophy in hopes the Clintizens will learn something.
If you guys have different ideas about the Riots or have your own theories on the clans, I'd like to hear them. If you want, I can add what I believe the Riots think about the other clans.