Debates and decisions: On a rationale of argumentation rules

We view a debate as a mechanism by which an uninformed decision maker (the listener) extracts information from two informed debaters, who hold contradicting positions regarding the right decision. During the debate, the debaters raise arguments and, based on these arguments, the listener reaches a conclusion. Using a simple example, we investigate the mechanism design problem of constructing rules of debate that maximize the probability that the listener reaches the right conclusion, subject to constraints on the form and length of the debate. It is shown that optimal debate rules have the property that the conclusion drawn by the listener is not necessarily the same as the conclusion he would have drawn, had he interpreted the information revealed to him or her during the debate literally. The optimal design of debate rules requires that the information elicited from a counterargument depends on the argument it counterargues. We also link our discussion with the pragmatics literature.