1 Forthcoming in the Journal of the Philosophy of Sport On the Rationality of Inconsistent Predictions: The March Madness Paradox Rory Smead Department of Philosophy & Religion Northeastern University June 15, 2015 ABSTRACT: There are circumstances in which we want to predict a series of interrelated events. Faced with such a prediction task, it is natural to consider logically inconsistent predictions to be irrational. However, it is possible to find cases where an inconsistent prediction has higher expected accuracy than any consistent prediction. Predicting tournaments in sports provides a striking example of such a case and I argue that logical consistency should not be a norm of rational predictions in these situations. Keywords: Rationality, Prediction, Decision Theory, Logical Consistency, Expected Utility, Tournaments Logical consistency is often assumed to be a necessary condition for rationality. However, when attempting to predict an interrelated set of events, such as a sequence of game outcomes in a sports tournament, there are circumstances where rationality seems to require making inconsistent predictions. Here, I will provide an example where decision-theoretic rationality, in the sense of maximizing expected utility (von Neumann and Morgenstern 2007), conflicts with logical consistency. From a pragmatic perspective, inconsistency may, in some cases, be more rational than consistency. Every March, the sports world in the United States is abuzz with the NCAA collegiate basketball tournament. The tournament has a simple structure: 64 teams are seeded in a single elimination bracket. The last team standing is the champion. Many fans, both serious and casual, partake in prediction contests. These contests usually charge the participants with the herculean task of correctly predicting, at the outset of the tournament, the winner of every game. The difficulty of this task and the inevitable surprises of the tournament give weight to the tournament’s other name: “March Madness.” The miniscule chance of a perfect bracket prediction means that the real goal is to give a more accurate prediction than one’s competitors. Suppose you are tasked with such a challenge: generate a complete prediction set that maximizes the expected number of correctly predicted games. Speaking more generally, you must provide a prediction for a sequence of interdependent events and your goal is to maximize the accuracy of your prediction. We will suppose that the relevant measure of accuracy is simply the number of correctly predicted individual events. For tractability, assume that there are only four teams in the tournament. In the first round, team A will play team B and team C will play team D. The winners of each game will play in the