"Call for champions and be done with it" is a phrase often used in Arvum - meaning to resolve any petty or minor dispute, to put some small injury to bed and allow everyone to move on with their lives. It derives from a much more literal practice popular among the great houses.
While technically any noble house could appeal to their lieges and all the way up to the crown for any dispute, in practice very minor conflicts such as social slights, insults, or omissions are beneath the notice of the great lords that run houses. This is not, however, to say they are not dangerous. More than one war has started over a minor incident that led to serious animosity that led to someone dead that then led to a war (such as House Redrain's 'Alespill War'), but the Peerage of the Compact places a great deal of importance on resolving petty slights before they get out of hand. This in turn leads to the popularity of champions, particularly those for hire, representing nobles in minor incidents and settling an issue.
Somewhat counter to the intuition of those unfamiliar with the practice, most nobles in these minor incidents rarely represent themselves (though some warriors insist on doing so), simply because having anyone stand willingly to champion a noble's complaint and demand satisfaction is at least a symbolic representation that at least one other person believes the complaint has merit and is willing to fight to prove it, even if a great number of champions are just paid to do so. Similarly, if a demand for satisfaction goes unanswered, the assumption by the peers of the realm is that no one, not even the accused, saw fit to dispute the accusation, and it must have a ring of truth to it. Serious matters are, of course, usually brought for resolution between the liege lords of those involved, or in the most serious of cases, before a magistrate of the crown.
But for anything else, and for the minor and trivial, they call for champions and are done with it. In practice, this means that kerfuffles between nobles are often resolved by one party or the other naming a Champion and requesting an honor duel (often to first wound, see help duel). If Princess Pants is mad at Duke Dick for holding the door for four courtiers and then letting it slam in her face, she can name a Champion and inform him of his duty to answer the slight. Conversely, if Princess Pants takes her anger out in other ways, such as drawing in members of her family to make trouble for Duke Dick's family, Duke Dick would probably name a Champion and challenge her.
In Arx, this is how things are handled. It keeps the Champions busy, and it keeps minor scuffles that happen when you group so many people together from turning into drama explosions.