Inferences from Litigated Cases

Dan Klerman & Yoon-Ho Alex LeeConference 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 literatureNO. 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-p STANDARD PRO-D STANDARD

DISTRIBUTION OF ALL DISPUTES (SETTLED OR LITIGATED)

Distributions of litigated disputes if parties make small errors

p WINS (BLUE)

p WINS(BLUE)

Distributions of litigated disputes if parties make moderate errors

DEGREE OF D FAULT

DEGREE OF DFAULT

Priest-Klein Model: Overview

Priest-Klein Model: Overview

PROPOSITION 1 (INFERENCES UNDER THE PRIEST-KLEIN MODEL). Under the Priest-Klein model, if the distribution of disputes has a log concave CDF, then p’s win-rate among litigated cases increases as the decision standard becomes more pro-p.

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-D, p’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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Low liability defendant

Probability that will lose, if case goes to trial 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 10K, if case does not settle• Plaintiff makes take it or leave it offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Low liability defendant

Probability that will lose, if case goes to trial 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 10K, if case does not settle• Plaintiff makes take it or leave it offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 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 10K, if case does not settle• Plaintiff makes take it or leave it offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 30%

Expected liability 30K

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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 30%

Expected liability 30K

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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 30%

Expected liability 30K

Accepts settlement offers ≤ 40K

Plaintiff’s optimal settlement offer 80K

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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 30%

Expected liability 30K

Accepts settlement offers ≤ 40K

Plaintiff’s optimal settlement offer 80K

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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70% 80%

Expected liability 70K

Accepts settlement offers ≤ 80K

Low liability defendant

Probability that will lose, if case goes to trial 30% 40%

Expected liability 30K

Accepts settlement offers ≤ 40K

Plaintiff’s optimal settlement offer 80K

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 offerHigh liability Defendant

Probability that will lose, if case goes to trial 70% 80%

Expected liability 70K 80K

Accepts settlement offers ≤ 80K 90K

Low liability defendant

Probability that will lose, if case goes to trial 30% 40%

Expected liability 30K 40K

Accepts settlement offers ≤ 40K 50K

Plaintiff’s optimal settlement offer 80K 90K

High liability defendants settle

Low liability defendants litigate

Observed plaintiff win rate (trials) 30% 40%

Pro-plaintiff shift in law

Screening Model

PROPOSITION 2 (INFERENCES UNDER THE SCREENING MODEL). The probability that p 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

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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

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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

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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