Should arbitrators adjudicate on the basis of their own investigations, or invite the interested parities to make their cases and decide on the basis of the information so gathered? I call the former the inquisitorial procedure in arbitration and the latter the adversarial procedure. I conduct a welfare comparison of the two procedures by constructing a game-theoretic model of decision making by an arbitrator in the face of self-interested reporting strategies by the interested parties. Even it if is assume that the arbitrator is, on average, as well informed as the two opposing parties, the adversarial procedure is shown to be strictly superior. The source of this superiority lies in a non-convexity in the adversarial procedure. There are increasing marginal returns to improvements in the information of an interested party. There are no analogous increasing returns to the arbitrator's information under the inquisitorial procedure.