The Reduced Form of Litigation Selection Models and the Plaintiff’s Win Rate

In this paper I develop a new approach—the reduced form approach—to studying the plaintiff’s win rate in one-shot litigation selection models. A reduced form requires three basic elements. First, a joint distribution of plaintiff’s and defendant’s beliefs concerning the probability that the plaintiff would win in the event a dispute were litigated. Second, a conditional win rate function that returns the actual probability the plaintiff would win if the case were litigated, given the parties’ subjective beliefs. Third, a reduced form requires a specification of a litigation rule, which tells us the probability that a case will be litigated given the two parties’ subjective probabilities. I use the reduced form to prove several general results. First, I show that the plaintiff’s win rate will always equal one-half when certain balance conditions on the conditional win rate function, joint density, and litigation rule all hold. Second, I show that when these balance conditions are systematically violated in the same direction, the plaintiff’s win rate will deviate from one-half in a predictable direction. Third, I prove that any plaintiff’s win rate between 0 and 1 is possible, even in the limit as party information becomes very good, and even without the kind of asymmetric information that Shavell (1996) has suggested is the key to generating this result. Fourth, I show via a simple constructive example that there is no reason to expect the plaintiff’s win rate to move in a predictable direction when legal rules change, contra the optimistic conclusions in Klerman & Lee (2014) concerning the empirical usefulness of plaintiff’s win rate data. ∗For helpful comments and suggestions, I thank Daniel Klerman, Jon Klick, Alex Lee, Rick Brooks, Charles Silver, Steven Salop, Sarath Sanga, David Schleicher, Joshua Teitelbaum, Abe Wickelgren, and participants at ALEA 2014, the Yale-Paris 2 Summer School in Law and Economics, and workshops at Georgetown and the University of Texas.