Basically, Duel of Wits resolves intractable arguments between players. You break into two sides, and each state the argument you're trying to make. Your argument has a "body" (i.e., hit points), and you then make a series of verbal manuevers (which you must roleplay) that whittle down your opponent's body of argument. When one BoA reaches zero, you have a loser. The winner's argument holds, although he must make concessions commensuate with the "body points" lost in the course of the argument.
You don't necessarily convince your opponent that you are right; you just force him to agree to your demands. Of course, he can always escalate to violence (in-character) if he's really upset with the outcome.
