AN EXPLICIT TEST OF PLEA BARGAINING IN THE “SHADOW OF THE TRIAL”

• Date: 01 November 2014
• Author: ROBERT J. NORRIS,ALLISON D. REDLICH,SHAWN D. BUSHWAY
• DOI: http://doi.org/10.1111/1745-9125.12054
• Published date: 01 November 2014

AN EXPLICIT TEST OF PLEA BARGAINING IN THE

“SHADOW OF THE TRIAL”∗

SHAWN D. BUSHWAY,1ALLISON D. REDLICH,2

and ROBERT J. NORRIS2

1Rockefeller College of Public Affairs and Policy, University at Albany

2School of Criminal Justice, University at Albany

KEYWORDS: plea bargaining, rational choice, sentencing, experiments

Bargaining in the “shadow of the trial,” which hinges on the expectations of trial

outcomes, is the primary theory used by noncriminologists to explain variation in the

plea discount given to defendants who plead guilty. This study develops a formal math-

ematical representation of the theory and then presents an empirical test of the theory

using an innovative online survey with responses to a hypothetical case from 1,585

prosecutors, defense attorneys, and judges. The key outcomes are the probability that

the defendant will be convicted at trial, the sentence for the defendant if convicted,

and the best plea that the respondent would accept or offer. Variation in the outcomes

is created through experimental variation in the information presented to the respon-

dents. Structural regression models are estimated to fit the formal theoretical models,

and the instrumental variables method is used to correct for measurement error in the

estimate for probability of conviction. The data support the basic shadow model, with

minor modifications, for only prosecutors and defense attorneys. Controlling for the

characteristics of the individual actors and their jurisdictions adds explanatory value

to the model, although these control variables did not affect the key coefficients from

the shadow model.

Defendants who plead guilty usually receive substantially shorter sentences than

observably equivalent people convicted at trial.1The implication is that defendants re-

ceive a discount for pleading guilty or, alternatively, a penalty for going to trial.2The

∗Additional supporting information can be found in the listing for this article in the Wiley Online

Library at http://onlinelibrary.wiley.com/doi/10.1111/crim.2014.52.issue-4/issuetoc.

This research was supported by award 2009-IJ-CX-0035 from the National Institute of Justice,

Office of Justice Programs, U.S. Department of Justice. The opinions, findings, and conclusions

expressed in this publication are those of the authors and do not necessarily reflect the views of

the Department of Justice. The authors are extremely grateful to the organizations and individuals

who assisted us in obtaining our sample. We also want to thank Linda Truitt, Emily Owens, Greg

DeAngelo, the anonymous reviewers, and Eric Baumer for helping us to write the best possible

article. Direct correspondence to Shawn D. Bushway, Rockefeller College of Public Affairs and

Policy, University at Albany (SUNY), Milne Hall 220, 135 Western Avenue, Albany, NY 12203

(e-mail: sbushway@albany.edu).

1. A nonexhaustive list includes papers by Albonetti (1990, 1997); Bradley-Engen et al. (2012); Dixon

(1995); Smith (1986); Ulmer and Bradley (2006); and Ulmer, Eisenstein, and Johnson (2010). For

an exception that finds no trial penalty or plea discount, see Breen (2011).

2. These labels are field specific—criminologists and sociologists tend to talk about trial penalties,

whereas legal scholars, psychologists, and economists talk about plea discounts.

C2014 American Society of Criminology doi: 10.1111/1745-9125.12054

CRIMINOLOGY Volume 52 Number 4 723–754 2014 723

724 BUSHWAY, REDLICH, & NORRIS

size of this plea discount varies across individual cases (Bradley-Engen et al., 2012; Bush-

way and Redlich, 2012; Smith, 1986; Ulmer and Bradley, 2006; Ulmer, Eisenstein, and

Johnson, 2010). Criminological scholars have used perspectives such as focal concerns

to argue that this variation can be explained by case-level factors, such as race, criminal

history, crime type, and the probability of conviction, and institutional factors, such as

workgroup norms and workload. Empirical tests with standard sentencing data sets do

a reasonable job of “explaining” the size of the trial penalty with these explanatory fac-

tors included in multilevel models (Bradley-Engen et al., 2012; Ulmer and Bradley, 2006;

Ulmer, Eisenstein, and Johnson, 2010).

Outside of criminology, “bargaining in the shadow of the trial” (hereafter the “shadow”

model) is the primary model used to explain variation in the plea discount (Bibas, 2004;

Landes, 1971; Mnookin and Kornhauser, 1979; Nagel and Neef, 1979). In this model, a

defendant pleads guilty if the offered sentence is less than or equal to his or her expected

value of the trial. For example, if the expected sentence for a conviction at trial is 20 years

and the defendant believes his or her probability of conviction at trial is .8, then a plea

to a sentence of no more than 16 years (80 percent of 20) represents a rational choice

for a risk-neutral defendant. A risk-neutral defendant is not affected by the degree of

uncertainty in a choice, and therefore, this individual is indifferent to the choice between

accepting the plea bargain and going to trial as long as he or she has the same expected

outcome. In contrast, a risk-averse defendant would prefer the certainty of a plea bargain

to a choice to proceed to trial even when the expected sentence if the person goes to trial

is lower than the expected value of the plea bargain.

Despite the prevalence of this theory in the legal literature, there were no explicit tests

of the theory prior to 2012. Legal scholars such as Bibas (2004) also have begun to raise

important questions about the face validity of the model. In its simplest incarnation, the

theory assumes that actors in the criminal justices system act rationally; yet behavioral

economists and psychologists now routinely show that people, including professionals in

the criminal justice system, do not act in strictly rational ways (Guthrie, Rachlinski, and

Wistrich, 2001; Plous, 1993; Tversky and Kahneman, 1974). No systematic attempt has

been made to integrate these ideas into the basic “shadow” model. More generally, Bibas

(2004) questioned whether the complex institutional choices involved in bargaining are

congruent with the simple shadow model.

Bushway and Redlich (2012) formally introduced the shadow model into criminology

and provided the first-known attempt to test the shadow model using individual case

record data.3To conduct such a test, the researcher needs the following three pieces of

information: the probability of conviction at trial, the sentence at trial (which together

produce the expected value of the trial), and the value of the plea bargain. Obviously,

these data are not available for each person because each defendant either pleads guilty

or goes to trial. Bushway and Redlich (2012) overcame this problem by using statistical

models to create predicted counterfactuals for those who pled guilty based on the data

from people who actually went to trial. At the aggregate level, their initial result provided

support for the shadow model—the average plea sentence for the sample was equivalent

3. Bushway and Redlich (2012) used a well-known plea bargaining data set collected by Miller,

McDonald, and Cramer (1978). The main difference between this data set and the standard crimi-

nological conviction data set is that it starts at indictment rather than at conviction, and it includes

data on evidence that influences likelihood of conviction.

BARGAINING IN THE “SHADOW OF THE TRIAL” 725

to the average sentence at trial discounted by the probability of conviction for the sample.

A paper by Abrams (2011) with different administrative data found a contrasting result:

the average plea value was actually higher than the average expected value of the trial

(the sentence at trial discounted by the probability of conviction).

At the individual level, the results from Bushway and Redlich (2012) did not support

the shadow model. In many cases, a defendant’s actual plea value was not at all similar to

the estimate of that defendant’s discounted probability of a sentence at trial. Individual

estimates of the probability of conviction at trial for those who pled guilty were either

uncorrelated with key pieces of evidence known to increase the probability of conviction

at trial, such as confessions, or correlated in the opposite direction than the one predicted

by the shadow theory. This unexplained noise at the individual level leaves open the pos-

sibility that other theories, including criminological theories that focus on interjurisdic-

tional differences in plea outcomes, may be needed to explain individual-level variation

in the size of plea discounts.

Bushway and Redlich (2012) cautioned against making too many conclusions based on

their study and called for replication. They used 35-year-old data that were considerably

less detailed than the norm in modern criminological data sets. In addition, the econo-

metric methods used to create the counterfactuals for those who pled guilty required a

nontestable assumption that those who pled guilty are observationally equivalent to those

who went to trial after controlling for case characteristics.

In this article, we attempt to advance understanding of plea bargaining by resurrect-

ing and revitalizing a survey approach with a hypothetical case first used by Miller,

McDonald, and Cramer (1978). Attorneys and judges were asked to review the case and

provide their best estimates for the three main components of the shadow of the trial:

the probability of conviction at trial, the outcome at trial, and the plea deal they would

advocate for in this situation (all within their own jurisdiction). Because the study uses

hypothetical rather than real case data, this approach does not require estimation to test

the shadow of the trial model—the key parameters are obtained directly from the respon-

dents. More broadly, there is no need to assume that cases convicted at trial and by guilty

plea are observationally equivalent, as in traditional empirical studies using case data.

The trade-off is that concerns about external validity become more prominent. Actors

may respond to questions in a hypothetical survey differently from how they would act

when faced with the constraints of a real case, constraints that include the need to negoti-

ate with other actors. We start the next section by comparing the criminological approach

with the shadow model. After explaining the model, we describe the data more fully and

then present the study results.

THEORETICAL FRAMEWORK

The criminological approach to the study of sentencing starts with an organizational

paradigm that emphasizes that judges, prosecutors, and defense attorneys within a juris-

diction are part of an interdependent workgroup working together toward shared goals

such as disposing of cases efficiently and minimizing uncertainty (Eisenstein and Jacob,

1977). Within this framework, criminologists predict that the workgroup will establish

norms, or going rates, that are less than the punishment at trial for defendants who are

willing to plead guilty. These plea discounts save time and resources while reducing uncer-

tainty. Over time, theorists have extended this basic framework. Dixon (1995) and Engen