Inferences from Litigated Cases Dan Klerman & Yoon-Ho Alex Lee Conference on Empirical Legal Studies October 24, 2013

Motivating Questions Can empirical legal scholars use the plaintiff trial win rate to draw inferences about the law? Would a change in the law lead to a predictable change in the plaintiff trial win rate?

Answers in the literature NO. Plaintiffs will win 50% regardless of the legal standard. - Priest & Klein (1984) NO. If there are deviations from 50%, they are caused by asymmetric stakes or other factors unrelated to the law. - Priest & Klein (1984) Any plaintiff trial win rate is possible under asymmetric information models. - Shavell (1996)

Our Answer Sometimes Under all standard settlement models, change in legal standard, under plausible assumptions, will lead to predictable changes in plaintiff trial win rate – Priest-Klein divergent expectations model – Bebchuk screening model – Reinganum-Wilde signaling model Pro-plaintiff change in law will lead to increase in plaintiff trial win rate Good news for empirical legal scholars

PRO-  STANDARD PRO-  STANDARD DISTRIBUTION OF ALL DISPUTES (SETTLED OR LITIGATED) Distributions of litigated disputes if parties make small errors  WINS (BLUE)  WINS (BLUE) Distributions of litigated disputes if parties make moderate errors DEGREE OF  FAULT Priest-Klein Model: Overview

P ROPOSITION 1 (I NFERENCES U NDER THE P RIEST -K LEIN M ODEL ). Under the Priest-Klein model, if the distribution of disputes has a log concave CDF, then  ’s win-rate among litigated cases increases as the decision standard becomes more pro- . PDFs with Log-Concave CDFs: normal, generalized normal, skew normal, exponential, logistic, Laplace, chi, beta, gamma, log-normal, Weibull… PDFs with Log-Concave CDFs: normal, generalized normal, skew normal, exponential, logistic, Laplace, chi, beta, gamma, log-normal, Weibull…

Priest-Klein Model As legal standard becomes more pro- ,  ’s win-rate decreases Effect varies with standard deviation of prediction error Paper presents evidence that standard deviation is large

Screening Model 2 types of defendants – High liability defendants 70% probability that will lose at trial – Low liability defendants 30% probability that will lose at trial – 50% of each kind Defendant knows type – Plaintiff does not – Plaintiff knows overall proportions Damages 100K Each side has litigation costs of 10K – if case does not settle Plaintiff makes take it or leave it offer

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Low liability defendant Probability that will lose, if case goes to trial30%

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Low liability defendant Probability that will lose, if case goes to trial30%

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30%

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30% Expected liability30K

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30% Expected liability30K Accepts settlement offers ≤40K

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 10K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30% Expected liability30K Accepts settlement offers ≤40K Plaintiff’s optimal settlement offer80K High liability defendants settle Low liability defendants litigate

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 30K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30% Expected liability30K Accepts settlement offers ≤40K Plaintiff’s optimal settlement offer80K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)30%

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 30K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70%80% Expected liability70K Accepts settlement offers ≤80K Low liability defendant Probability that will lose, if case goes to trial30%40% Expected liability30K Accepts settlement offers ≤40K Plaintiff’s optimal settlement offer80K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)30% Pro-plaintiff shift in law

Screening Model 2 types: High liability defendants, low liability defendants (equal probability) Defendant knows type, but plaintiff does not (but knows distribution) Damages 100K Each side has litigation costs of 30K, if case does not settle Plaintiff makes take it or leave it offer High liability Defendant Probability that will lose, if case goes to trial70%80% Expected liability70K80K Accepts settlement offers ≤80K90K Low liability defendant Probability that will lose, if case goes to trial30%40% Expected liability30K40K Accepts settlement offers ≤40K50K Plaintiff’s optimal settlement offer80K90K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)30%40% Pro-plaintiff shift in law

Screening Model P ROPOSITION 2 (I NFERENCES U NDER THE S CREENING M ODEL ). The probability that  will prevail in litigated cases is strictly higher under a more pro-plaintiff legal standard, as characterized by case distributions that satisfy the monotone likelihood ratio property. Holds whether plaintiff or defendant has informational advantage. PDF Families over [0,1] Exhibiting MLRP: uniform, exponential, binomial, Poisson, beta, rising triangle, falling triangle PDF Families over [0,1] Exhibiting MLRP: uniform, exponential, binomial, Poisson, beta, rising triangle, falling triangle

19 Extensions Signaling model Effect of different decisionmakers – Republican versus Democratic judges – Male versus female judges – 6 or 12 person jury Whether factor affects trial outcome – Race or gender of plaintiff – Instate or out-of0state defendant – Law firm quality

20 Caveats Assumes that distribution of underlying behavior doesn’t change – Not usually true – Exceptions Retroactive legal change Uninformed defendants – Advice to empiricists Worry less about settlement selection Worry more about changes in behavior Distribution of disputes (litigated & settled) – Logconcave for Priest-Klein – Monotone likelihood ratio property for asymmetric information

21 Conclusions Selection effects are real But may be able to draw valid inferences from litigated cases – Measure legal change – Measure biases of decision makers – Identify factors affecting outcomes Good news for empirical legal studies