Well, the goal would be to let each party air their grievances one at the time and then arbitrate as a neutral party. When I hear disputes at Winterfell, I allow each to speak and present their side of things without interruption from the other. It helps that I am their ruler on authority of the King in the North. We have no such social status here.

( This, of course, makes things more difficult. )

However, if we do things for each side and show we can be a help to them, perhaps they will respect us enough to allow us to mediate.