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

In this paper I introduce what I call the reduced form approach to studying the plaintiff’s win rate in litigation selection models. A reduced form comprises 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; a conditional win rate function that tells us the actual probability of a plaintiff win in the event of litigation, given the parties’ subjective beliefs; and a litigation rule that provides the probability that a case will be litigated given the two parties’ beliefs. I show how models with very different-looking structure can be understood in common reduced form terms, and I then use the reduced form to prove several general results. First, a generalized version of the Priest-Klein model can be used to represent any other model’s reduced form, even though the Priest-Klein model uses the Landes-Posner-Gould (“LPG”) litigation rule while some other models do not. Second, Shavell’s famous any-win-rate result holds generally, even in models with party belief distributions that are both highly accurate and identical across plaintiffs and defendants. Third, there are only limited conditions under which the LPG litigation rule can be rejected empirically; this result undermines the case against the LPG rules’ admittedly non-optimizing approach to modeling litigation selection. Finally, I use the reduced form approach to clarify how selection effects complicate the use of data on the plaintiff’s win rate to measure changes in legal rules. The result, I suggest, is that recent work by Klerman & Lee advocating the use of such data is unduly optimistic. ∗For helpful comments and suggestions, I thank Albert Choi, Giuseppe Dari-Mattiacci, Avery Katz, Daniel Klerman, Jon Klick, Alex Lee, Rick Brooks, Bruce Kobayashi, Charles Silver, Steven Salop, Sarath Sanga, David Schleicher, Joshua Teitelbaum, Abe Wickelgren, and participants at ALEA 2014, the YaleParis 2 Summer School in Law and Economics, and workshops at Columbia, Georgetown and the University of Texas.