Statistical evidence and the problem of robust litigation

• Author: Jesse Bull,Joel Watson
• Date: 01 December 2019
• Published date: 01 December 2019
• DOI: http://doi.org/10.1111/1756-2171.12302

RAND Journal of Economics

Vol.50, No. 4, Winter 2019

pp. 974–1003

Statistical evidence and the problem

of robust litigation

Jesse Bull∗

and

Joel Watson∗∗

We propose a new model of disclosure, interpretation, and management of hard evidence in the

context of litigation and similar applications. A litigant has private information and may also

possess hard evidence that can be disclosed to a fact-finder, who interprets the evidence and

decides a finding in the case. We identify conditions under which hard evidence generates value

that is robust to the scope of rational reasoning and behavior. These fail if the litigant’s private

information is sufficiently strong relative to the “face-value signal” of evidence, and then hard

evidence may be misleading. Rules that exclude some relevant hard evidence can be justified.

1. Introduction

In common-law countries, judges have latitude to exclude relevant evidence from being

presented at trial and from being considered by juries. The United States’ Federal Rules of

Evidence (FRE) Rule 403 describes various circumstances that warrant exclusion, and it offers a

limited explanation:

The court may exclude relevant evidence if its probative value is substantially outweighed

by a danger of one or more of the following: unfair prejudice, confusing the issues, mis-

leading the jury, undue delay, wasting time, or needlessly presenting cumulative evidence.

The related Rule 404 provides for a particular circumstance in stating that “Evidence of

a person’s character or character trait is not admissible to prove that on a particular occasion

∗Florida International University; bullj@fiu.edu.

∗∗UC San Diego; jwatson@ucsd.edu.

The authors are grateful to Kathy Spier (the Editor in charge of this article), and two anonymous referees for their many

thoughtful and detailed comments, which stimulated significant improvements of this article. The authors thank Alex

Weiss for superb research assistance and also the following people for their input: Navin Kartik, Dan Klerman, Aaron

Kolb, Alex Lee, Herb Newhouse, Joel Sobel, Eric Talley, Simon Wilkie,and seminar participants at Indiana University,

USC, UC Riverside, UCF, the 2015 Law and Economic Theory Conference at Duke University, the 2017 American

Law and Economics Association Conference at Yale University, the 2016 Canadian Law and Economics Association

Conference at the University of Toronto,the Fall 2017 Midwest Economic Theory Conference at the Southern Methodist

University,and the 2018 Canadian Economic Theory Conference at the University of Toronto.

974 C2019, The RAND Corporation.

BULL AND WATSON / 975

the person acted in accordance with the character or trait.” Both of these rules have origins in

common-law tradition. The existence of these rules, and the broad judicial practice of excluding

certain types of evidence, raises two questions: How can excluding relevant evidence improve

accuracy in the deliberations of a jury, as Rule 403 suggests, and what kinds of evidence should

be excluded?

We address these questions with a theoretical model that explores the interaction between a

single litigant and a fact-finder whom we take to be a jury. Both the litigant and the fact-finder

are sophisticated and rational. The fact-finder must evaluate a claim being made by the litigant,

which amounts to estimating the value of an underlying state of the world.The litigant has private

unverifiable information, described as the litigant’s type. In some contingencies, the litigant also

possesses hard evidence and must decide whether to disclose it, if allowed.The fact-finder reviews

whatever hard evidence is presented, updates its beliefs about the state (obeying Bayes’ rule), and

then issues a finding in the case. Applications extend beyond litigation, as we describe below.

In our model, the meaning of hard evidence is endogenous because the fact-finder must

assess the litigant’s disclosure strategy in order to interpret evidence. We show that constructive

hard evidence requires the litigant and fact-finder to have similar beliefs about this interpretation.

In some circumstances, it is possible for beliefs to be out of alignment and, as a consequence,

hard evidence can mislead the fact-finder and reduce social welfare by more than the value of

evidence. For a court that is sensitive to such a worst-case scenario, which we refer to as seeking

“robust litigation,” it is optimal to exclude relevant hard evidence under some conditions.

To delve into the logic, note that hard evidence is, by definition, statistical in nature: an

individual piece of evidence exists with differentprobabilities in various states of the world. Hard

evidence rarely provides definitive proof (that is, certainty) that the state is in some set, but it

gives a signal that allows a fact-finder to update from a prior to a posterior probability distribution

of the state.

Consider, for example, a trial that focuses on the question of whether the defendant robbed

a particular store at 10:00 p.m. on a given date. The defendant may enter into evidence a time-

stamped surveillance video showing him at a stadium 20 miles away at 9:20 p.m. on the same date

(the hard evidence in this example). This piece of hard evidence does not prove with certainty

that the defendant is innocent. It is possible that traffic conditions on the day of the crime were

such that the defendant could, by leaving the stadium at 9:25 p.m. and speeding through the city,

reach the store before 10:00 p.m.1However, the defendant’s image on the stadium’s 9:20 p.m.

surveillance video is perhaps more likely to exist in the state of the world in which the defendant

did not rob the store than it would in the state of the world in which he did.

Weobserve that hard evidence produces information through two channels. The first channel

is the exogenous signal providedby the simple existence or nonexistence of the hard evidence. We

call this the face-value signal. The second channel is the signal that disclosure or nondisclosure

of hard evidence provides about the litigant’s privateinfor mation, and so we call this the litigant-

type signal. The litigant-type signal has an endogenous element because the fact-finder’s posterior

belief about the litigant’s type depends on the fact-finder’s assessment of the litigant’s disclosure

strategy (the probability that each type of litigant would disclose the hard evidence when it

exists). It is informative if different types of the litigant would disclose hard evidence with

different probabilities.

Let us use the robbery sketch described above to illustrate these two channels and to show

how evidence can be misleading. If the jury is assured of seeing the time-stamped video of the

defendant at the stadium whenever such a video exists, then the jury would extract from its

disclosure (or nondisclosure) exactly the face-value signal. In this case, disclosure of the video

would cause the jury to revise upward its probability assessment that the defendant is innocent.

However, suppose the jury believes that a type of defendant who likely knows he committed the

crime (the “bad type”) would disclose the video evidence with high probability when it exists,

1There may also be errors in the estimate of the time of the robbery and/or the video time stamp.

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