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
Priest-Klein Model: Overview
DISTRIBUTION OF ALL DISPUTES (SETTLED OR LITIGATED)
p WINS
(BLUE)
p WINS
(BLUE)
DEGREE
OF D
FAULT
PRO-p STANDARD
Distributions of litigated disputes
if parties make moderate errors
Distributions of litigated disputes
if parties make small errors
DEGREE
OF D
FAULT
PRO-D STANDARD
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 offer
High 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 offer
High 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 offer
High 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 offer
High 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 offer
High 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 offer
High 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
High liability defendants settle
Low liability defendants litigate
80K
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 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
Pro-plaintiff
Each side has litigation costs of 30K, if case does not settle
shift in law
Plaintiff makes take it or leave it offer
High liability Defendant
Probability that will lose, if case goes to trial
70%
Expected liability
70K
Accepts settlement offers ≤
80K
80%
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%
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
Pro-plaintiff
Each side has litigation costs of 30K, if case does not settle
shift in law
Plaintiff makes take it or leave it offer
High liability Defendant
Probability that will lose, if case goes to trial
70%
80%
Expected liability
70K
80K
Accepts settlement offers ≤
80K
90K
Probability that will lose, if case goes to trial
30%
40%
Expected liability
30K
40K
Accepts settlement offers ≤
40K
50K
80K
90K
30%
40%
Low liability defendant
Plaintiff’s optimal settlement offer
High liability defendants settle
Low liability defendants litigate
Observed plaintiff win rate (trials)
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.
PDF Families over [0,1] Exhibiting MLRP:
uniform, exponential, binomial, Poisson,
beta, rising triangle, falling triangle
Holds whether plaintiff or defendant has informational
advantage.
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
19
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
20
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
21