For the record I am in a poly triad.
We really honestly don't fight much. Seriously. The last one I remember was when I took a shower while one of my SOs was trying to sleep, several years ago... I didn't realize how much it bothered her, and she kept it in for several days before telling me. (Now our schedules are all over the place so we just HAVE to shower while people are sleeping, no other options.) So that was a heated argument.
So honestly, it's been years, and I think what was lacking there was communication. With proper communication and plenty of flexibility, I don't think we have fights. Honest to god.