Inferences from Litigated Cases Dan Klerman USC Law School Alex Lee USC Law School SCELS USC Law School June 7, 2013

2 Introduction Priest & Klein (1984) – Most cases settle – Litigated cases are non-random sample – Expect 50% win rate – Deviations from 50% caused by factors other than law Asymmetric stakes – Can’t draw inferences about law from win rate – Highly cited – Closes off much empirical work Klerman & Lee – Can draw inferences from litigated cases – Priest-Klein prediction is limiting result – Asymmetric information models

Pro-plaintiff decision standard Pro-defendant decision standard Distribution of all disputes, whether settled or litigated Distribution of litigated disputes if parties make small estimation errors Plaintiff victories Distribution of litigated disputes if parties make larger estimation errors Degree of defendant fault Priest-Klein Model

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Screening Model 2 types of defendants – High liability defendants Likely to lose at trial – Low liability defendants Likely to win at trial – 50% of each kind Defendant knows type – Plaintiff does not – Plaintiff knows overall proportions Damages 100K Each side has litigation costs of 30K – 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 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% Low liability defendant Probability that will lose, if case goes to trial40%

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 Low liability defendant Probability that will lose, if case goes to trial40%

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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40%

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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40% Expected liability40K

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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40% Expected liability40K Accepts settlement offers ≤70K

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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40% Expected liability40K Accepts settlement offers ≤70K Plaintiff’s optimal settlement offer100K 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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40% Expected liability40K Accepts settlement offers ≤70K Plaintiff’s optimal settlement offer100K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)40%

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 ≤100K Low liability defendant Probability that will lose, if case goes to trial40%50% Expected liability40K Accepts settlement offers ≤70K Plaintiff’s optimal settlement offer100K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)40% 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 ≤100K110K Low liability defendant Probability that will lose, if case goes to trial40%50% Expected liability40K50K Accepts settlement offers ≤70K80K Plaintiff’s optimal settlement offer100K110K High liability defendants settle Low liability defendants litigate Observed plaintiff win rate (trials)40%50% Pro-plaintiff shift in law

Screening Model With Continuous Distributions Legal Standard (α) Percentage of Plaintiff Wins at trial

16 Extensions and Caveats Priest & Klein model – Lots of simulations – Working on analytical proof Screening model – Proven analytically Signaling model Caveat – Assume that distribution of underlying behavior doesn’t change Not usually true Exceptions – Retroactive legal change – Uninformed defendants – Advice to empiricists Worry more about change in behavior Worry less about settlement selection

17 Regression Analysis of Trial Outcomes Might try to estimate effect of Factor X on trial outcomes – E.g. Jury bias against out-of-state defendants Priest & Klein: Won’t work – Party settlement behavior will take bias into account – Expect 50% win rate against in-state defendants – Expect 50% win rate against out-of state defendants Even if jury very biased Even if control for all observable factors Klerman & Lee: Regressions will work – Selection will make win-rates look more similar But differences will remain – Regression will under-estimate effect of jury bias So effect is larger than actually observed

18 Conclusions Selection effects are real But can draw valid inferences from litigated cases – Can measure legal change – Can measure factors affecting plaintiff win rates Good news for empirical studies of law