There are many practical advantages to dueling, as opposed to litigation, as a means of conflict resolution. This makes for much fairer, and vastly less expensive, combat. The most famous rules of dueling, the Irish code Duello, easily fits on four typed pages, with plenty of space to spare. Compare that brevity to the American legal code, which can barely fit in the infinite space of the Internet. Litigation takes years.
Duels take place the morning following the challenge, at dawn.
Dueling allows both parties to survive with honor, as long as they play according to the rules of the game. Litigation does not allow either party to survive with honor, and no one can figure out the rules of the game. On the other hand, it's possible, though not likely, that both participants in a duel may perish. Thus we could at least hope for the demise of both Bill Clinton and Paula Jones in one brief melee. If the Gods were feeling benevolent that morning, it's even possible that both of their public relations counselors could join in, and also exit this vale of tears.