If you are challenged to a duel and you avoid it, you ought to be branded a coward and doors shut in your face. (then it becomes a matter of that chars political strength, but let's stay in a general sense). This way, dueling acts like the deterrent it was meant to be - don't want to be killed in a duel, best watch your language.
This is the best solution by far. It means people will only be dicks either if they can afford to do so, or if the thing they want to be dickish about is important.