To add unto the break down that
@azakhi kindly provided, once a proposal is made, relationship (with the sponsor / proposer) plays a role in how much other clans are willing to invest with their vote. That is to say, they wouldn't vote for the opposite of what their "rational" interest is (this is determined first), but they may choose to spend more or less (or no) influence on something they like/dislike depending on who proposed the decision.
The specific logic differs per decision type (policy / war&peace / succession / etc) and I believe that war & peace, for instance, does look at the honor trait as well. One challenge here is simply balance as clan interests can overlap notably in terms of rationality (honor or even political preference don't qualify for this).
Do take this with a grain of salt as I am writing this from memory and changes may have happened to the related systems since.
I would like to share another update, yes, however, I think it's a bit too early still. If you want to know something about a specific topic, don't hesitate to ask though. If I can, I will try to clarify.