Theoretical Economics Letters, 2013, 3, 40-44
http://dx.doi.org/10.4236/tel.2013.35A2007 Published Online September 2013 (http://www.scirp.org/journal/tel)
Re-election Concerns and the Failure of Plea Bargaining
Siddhartha Bandyopadhyay1, Bryan C. McCannon2
1University of Birmingham, Birmingham, United Kingdom
2St. Bonaventure University, New York, USA
Received July 31, 2013; revised: August 30, 2013; accepted September 9, 2013
Copyright © 2013 Siddhartha Bandyopadhyay, Bryan C. McCannon. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original
work is properly cited.
In this note, we provide a new explanation for the “failure” of plea bargaining. We show in a model of asymmetric in-
formation that a public prosecutor facing re-election takes cases to the courtro om to signal quality even when her wel-
fare (absent retention motivation) is always higher from plea bargaining.
Keywords: Plea Bargaining; Re-Election; Prosecutor
Trials in the United States are expensive and time con-
suming. The average cost of a trial is $10,000 per day.1
However, pretrial bargaining is an available option to
save on such costs. Not all disputes, though, are plea
bargained. We ask whether there are incentives for cases
to be taken to trial even when both prosecutor and de-
fendant know that plea bargaining is efficient. We focus
on the incentives of local prosecutors who in the US
handle 95% of all criminal cases (Simmons . Further,
in forty-seven states the chief prosecutor is elected (Perry
). We argue that a possible explanation for having
trials when plea bargaining is efficient is asymmetric
information regarding the quality of the public prosecutor.
Specifically, it is her desire to be retained in office that
leads her to signal her quality by us ing trials. We show in
a simple theoretical model that (absent her retention mo-
tivation) even if bargaining is preferable to the prosecu-
tor and for welfare there exist equilibria where trials oc-
cur. Convictions act as a signal to the vo ting public since
high-quality prosecutors are better able to obtain them.2
We also show that there are enviro nments where to ta l wel-
fares, even after incorporating future benefits of effect-
tively identi fying highl y capab le prosecutors, are reduced.
This provides a new exp lanation for the failure of plea
bargaining. A variety of reasons have been provided for
its effectiveness: resource conservation (Landes ),
insurance (Grossman and Katz ; Bjerk ), and
screening (Baker and Mezzetti, ; Bjerk ; Grossman
and Katz ; Reinganum, [10,11]). There are two exist-
ing explanations for its failure. First, individuals make
mistaken assessments. This comes from errors (Priest
and Klein ) or optimism (Shavell ). Second,
asymmetric information related to the trial creates a bar-
rier. It may be on the likelihood of success (Bebchuk
), costs and damages (Bebchuk ), or risk prefer-
ences (Farmer and Pecorino ) or a combination of
optimism and asymmetric information (Farmer and Pe-
corino ). Ancelot and Delacote  consider the plea
outcome under different fee schemes for prosecutors and
an altruistic defense attorney.
We contribute to the explanations for the failure of
plea bargaining by introducing retention motivations of
prosecutors. There are other papers on plea bargaining as
a signal (Reinganum [8,9]) , but they are not about its role
of signaling prosecutorial quality. There is evidence that
elected prosecutors obtain more convictions (Rasmusen,
Raghav and Ramseyer ) and those facing contested
elections increase their use of jury trials (Bandyopadhyay
and McCannon ), consistent with our theory that tri-
als are a signal of quality.3
1The 7th pwr.wordpress.com/categ ory/plea-bargain/.
2There exists evidence that for state-level elections convictions is an
important variable covered by media (Wright ) and in a theoretical
model retention incentives are shown to influence the investigation
decision by prosecutors (Gordon and Huber ) who recommend
making retention based on convict ions.
3There are also papers (Boylan , Boylan and Long ) which
show that prosecutors use experience in trials as a caree r advancement
mechanism, i.e. to improve their future payoffs.
opyright © 2013 SciRes. TEL
S. BANDYOPADHYAY, B. C. MCCANNON 41
There are two periods. In the first, there is an incumbent
of unknown quality who has to decide how to handle
cases. She may be one of two types
1. She is
high quality with probability . Let
denote the strength of evidence, she has against the de-
fendant in any given case4. Observing
for a case, she
may either take it to trial or plea bargain. Assume a large
number of cases come up in the first period, which may
be thought of as a term in office.
as the sanction if successful in the court-
room. It makes no difference for our analysis whether
is a constant or
. With judicial
discretion, parole, and appeals this may be thought of as
the expected sanction conditional on conviction. The
probability the prosecutor is successful depends on the
quality of the prosecutor and the evidence. A prosecutor
of quality wins at trial with probability
If she takes the case to trial, a cost is experienced.
as the plea agreement with 0
. As the prosecutor type is private informa-
tion to the defend ant, sanc tions can not be cond itione d on
type though it can be shown (calculations available on
request) that there are no substantive changes in the equi-
librium analysis if better prosecutors can negotiate b etter
plea agreements, i.e. if increases with q. One would
expect that the evidence affects the bargain since it de-
termines the size of the surplus to be negotiated over.
Similarly, the cost incurred reduces this surplus; and
therefore, presumably affects the plea bargaining out-
Denote as welfare from a case resulting in ,
, or 0 depending on whether a
case is plea bargained, taken to trial and won or taken to
trial and lost. Thus, expected welfare from a case at trial
make things as stark as possible, we consider a situation
where plea bargaining is always efficient, i.e. we con-
sider an environment where
Thus, plea bargaining is better for society for every
case, even for a high-quality prosecutor who is more
successful. We assume that the plea bargain is a fraction
of the expected penalty at trial which seems a natural
assumption.6 One way to rationalize, this is to assume
discounting; trials are time consuming so if the expected
, the defendant is indifferent to that
and an immediate sanction of
along with d0
z. Thus, the gap be-
tween the value of plea bargaining and the expected wel-
fare from trial diminishes with better evidence.
Denote as the first period expected welfare. Let
be the distribution function in which
the evidence for each case is (independently) drawn. As-
sume a large number of cases arise in the term so that the
expected welfare from a case equals the average welfare
generated from all cases over the term. Thus, first-period
welfare equals the expected welfare from a case. Hence,
if a prosecutor chooses to take every case to trial where
and plea those with
Finally, if her type is known, second-period welfare is
q, while it is
if the type is not,
L. Hence, if a prosecutor’s type becomes
known and she is re-elected , seco nd period welf ar e is q
while if she is replaced we assume that the person who
replaces her has an expected quality . The interpre-
tation is simple, society benefits from a more capable
prosecutor as a more capable prosecutor can dispense
society’s objectives more efficiently, i.e. we assume a
positive correlation between a prosecutor’s ability at trial
6In fact, Black’s Law Dictionary defines plea bargaining as “the proc-
ess whereby the accused and the prosecutor in a criminal case work out
a mutually satisfactory disposition of the case subject to court approval
It usually involves the defendant’s pleading guilty to a lesser offense o
to only one or some of the counts of a multi-count indictment inreturn
for a lighter sentence than that possible for the graver charge”.
7A similar result can be obtained with optimism bias on the part of the
4We assume that the decision to file charges has already been made.
Thus, only cases strong enough to file charges are considered.
5One may presume that
wz incorporates wrongful convictions and
acquittals along with
incorporating the quality of the defense.
Copyright © 2013 SciRes. TEL
S. BANDYOPADHYAY, B. C. MCCANNON
and her efficiency in othe r aspe cts of her work.8
2.2. Asymmetric Information
Suppose voters do not know the incumbent’s typ e. While
it is best if every case is plea bargained, with private in-
formation a retention agent cannot distinguish between
high and low-quality incu mbents. If some cases are taken
to trial, success in the courtroom would be a reasonable
metric to use to evaluate her since th e types differ in their
ability to obtain a conv iction. We are interested in estab-
lishing whether there exist environments in which waste-
fully cases are taken to trial for the purpose of being
The preference of the prosecutor needs to be consid-
ered. We propose the most favorable preferences for wel-
fare. Specifically, assume the utility she derives is pro-
portional to the welfare, or rather,
. Thus, absent motivation to be retained she is in-
terested in “dispensing justice”. Additionally, she re-
ceives a bonus from being retained, . Assume the bo-
nus is independent of the prosecutor’ s quality. If a prose-
cutor does take cases to trial, then she takes those more
likely to win and where there is less welfare lost. Hence,
if she proceeds to trial when an d only when
her expected utility if not retained is
If she is retained, her utility is q. Hence, ab-
sent the retention motivation the prosecutor is interested
in bargaining every case. We solve for the separating
equilibria that arise as Perfect Bayesian equilibria.9
3. Separating Equilibrium
Suppose the incumbent is retained if and only if the
number of convictions achieved is greater than or equal
to a threshold, , or rather, if10 n
The question here is whether there exist equilibria
where , i.e. we get inefficient trials even when
both parties would have preferred to plea.
If the incumbent does not act to be retained, then since
utility is proportional to welfare she chooses to plea all
cases. Thus, retention is preferable if
is the value of
which results in q
This reduces to
. Denote q
as the value of
(6) holds with equality. Define q
as the value of
that arises if q
For a separating equilibrium to exist only a high-qua-
lity prosecutor is willing to achieve the required thre-
shold. Hence, if
, then (6) holds for
a high-quality, but not for a low-quality prosecutor. Thus,
we are left only to verify that there exists an n
is greater than
pected welfare loss to proceeding to court is less. In other
words, if both types use the same cutoff
, then the
RHS of (6) is less for qH
. Therefore, it must be that
, a high-quality prosecutor is still willing to act
to be retained. As a result,
Proposition 1: There exist separating equilibria where
a high-quality prosecutor achieves
retained, while a low-quality prosecutor engages in plea
bargaining in every case and is not retained.
8The model assumes both types receive the same outcome with plea
bargaining and that it is efficient. Hence, one might expect voters to be
indifferent between the types,
VV. However, there is a positive
enefit to having a higher quality prosecutor in office as we assume he
is more efficient in all other related prosecutorial activities which we
have not explicitly modeled but is captured by
it can be shown that the results remain if (so long
as (1) continues to hold). The assumption of
In all separating equilibria, it is the low-quality prose-
cutor who selects the first-best amount of prosecution,
while it is the high-quality prosecutor who is engaging in
an excessive number of trials. Furthermore, while the
model presented assumes the number of convictions is
the metric used to make the retention decision, an equi-
valent result is obtained if the median voter uses the ag-
gregate sentences obtained by the prosecutor as the met-
ric on which to base her re-election decision.
VV can thus be
9Pooling equilibria are not considered here since our objective is to
establish the existence of equilibria where the high-quality prosecutors
behave wastefully to be distinguished and retained.
10We choose to define on the expected number of convictions.
With the assumption that there are a large number of cases in a term,
this does not impose any problems for the anal ysis.
The final issue to consider is whether the separating
equilibria are, in fact, worse for total welfare than pleaing
all cases. If the type is identified, then the second-period
V if qH
and if . Total EV qL
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S. BANDYOPADHYAY, B. C. MCCANNON 43
welfare is less in a separating equilibrium if
Proposition 2: If the cost of trial is substantial, the li-
kelihood of the replacement being low quality is great,
the probability of success in trial is small, or the gain to
having a high-quality prosecutor in office is small rela-
tive to the actions of a low-quality incumbent, i.e. (7)
holds, then the separating equilibria generate a lower
total welfare (in terms of median voter’s utility) than the
outcome of plea bargaining every case.
In this note, we have analyzed a stark environment, viz.
one where in each case, welfare generated from plea bar-
gaining is greater than from going to trial11. We show
that unlike a standard bargaining environment where
efficient outcomes are obtained, the asymmetric informa-
tion on the skills of the incumbent prosecutor who wishes
to be retained leads to some cases being taken to trial.
The voters, due to the informational constraint, cannot
take into account all relevant payoff components. Thus,
this provides an alternate explanation for why all cases
are not plea bargained. The result calls into question the
effectiveness of popular elections to select and retain
public prosecutors. Additional analysis is needed to in-
vestigate whether other metrics can be used to provide
proper incentives and whether alternative institutions,
such as appointments, do not suffer from similar distor-
tions. These, though, are reserved for future investiga-
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S. BANDYOPADHYAY, B. C. MCCANNON
Copyright © 2013 SciRes. TEL
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