Appeal Process and the Role of Judge
Yoshinobu Zasu∗

Abstract
We examine the non-benevolent judge under the appeal process and a role of judge as amediator between the ligation parties. As a member of the organization of court a judge has
to avoid appeals if she purses their future career. We consider the eﬀect of appeal process
on the non-benevolent judge. We introduce the constraints with regard to “appeal proof” toanalyze the judge who avoids appeal. We examine that the judge makes an eﬀort to create
the range by persuasion of the litigants when there is no range of appeal proof and consider
that the judge has a role, which solves the problem that the litigants cannot by themselves
seek the range and saves the social costs on appeals.

1

Introduction

We examine the non-benevolent judge under the appeal process and explore a role of judge as amediator between the ligation parties.
In the most models of law and economics, judge tends to be described to be benevolent andmaximize social welfare.1 In reality, however, some of them make a decision depending on theirown preference and consider the eﬀects of their judgement on their future career. In this paper,
judge is assumed to be non-benevolent or self-interested.
In addition, we assume that the court as a organization wants to avoid appeal. On one hand,the non-benevolent court may reduce the number of suits itself including appeals because suits
are just burden for judges. On the other hand, the benevolent court might prevent appeals of
the typical cases because of decreasing the social costs on suits. The court by nature, which isbenevolent or not, is tend to avoid appeals as an organization. As a member of the organization∗
Faculty of Economics, Kansai University, Yamate-cho 3-3-35, Suita-shi, Osaka, Japan. Tel.: +81-6-6368-0580.
Email: zasu@kansai-u.jp.
1
For example, in the standard litigation model, judge is likely to be assumed to be a “function” which inputs
litigation eﬀorts of parties and outputs judgement.

1

of court a judge has to avoid appeals if she purses their future career. We consider the eﬀect ofappeal process on the non-benevolent judge.
Recent studies include the non-benevolent judge and focus on the judge behavior by which
the judge maximizes her payoﬀ. Focus of these studies is not litigation parties’ behaviors: theevolution of common law, Wittman (2000); consideration of judge reputation, Levy (2005); theeﬀect of appeal process on the divergence of social welfare and individual preference, Shavell(2007). We follow these studies, especially Shavell (2007). He introduces the constraints withregard to “appeal proof” to analyze the judge who avoids appeal. In his model, there assumed toexist the range of appeal proof, which means that there is common judgement which both parties(plaintiﬀ and defendant) can accept. We consider that the judge seeks acceptable judgement or
the range of appeal proof when one of (or both) parties cannot accept the judgement ex ante.
Through this consideration, we examine a role of judge.
This study is related to the literature of economics of litigation.2 In the study, the “range ofsettlement” is well described as the scope of that the dispute parties can reach the settlement. So
if there does not exist the range, then there is no possibility that the parties reach the settlement
only by themselves. The range of appeal proof in our study is similar idea to that of settlement.
We examine that the judge makes an eﬀort to create the range by persuasion of the litigants when
there is no range of appeal proof and consider that the judge has a role, which solves the problem
that the litigants cannot by themselves seek the range and saves the social costs on appeals.

2The modelThere is one judge and the two litigant parties (plaintiﬀ and defendant). The judge oﬀers a judgment (damages) to the litigants. Both plaintiﬀ and defendant bear disutility from the judgement.
Letd = judgement or damages,′′′UP (d) = plaintiﬀ’s disutility of d (UP < 0, UP > 0 ),′′′UD (d) = defendant’s disutility of d (UD > 0, UD > 0).
After a judgement, the litigants choose whether to go to the appeal court, based on the theireach threshold level of disutility (or reservation utility). The judge chooses a level of eﬀort that
2See Miceli (1997) for introduction of economics of litigation and settlement.

2

aﬀect the litigants’s threshold of disutility. This eﬀort is interpreted as eﬀort to persuade thelitigants to accept d that she oﬀers. The judge bears (physical and psychological) costs on boththe eﬀort and judgement. Let
e = judge’s eﬀort to persuade the litigants,Ū (e) = threshold of disutility of litigants (Ū (0) ≥ 0, Ū ′ (e) > 0, Ū ′′ (e) > 0)
ˆ = judge’s costs of d and e given dˆ (Ce > 0, Cee > 0 and Cd > 0, Cdd > 0),C(d, e : d)where dˆ is the ideal damages of the judge.
ˆ That is, theWe assume that given e C(d, e) is quadratic function of d with minimum at d.
damages is more costly for the judge as the distance between d and dˆ is greater.

dFigure 1: Disutilities of the parties

Since social litigation costs arise if a litigant easily goes to appeal court and appealing is justa pain for judge or the like, a main objective of the court (including appeal and lower courts)
as an organization is assumed to resolve disputes and to prevent the litigants from appealing.
This might be true at least for a typical case. In such an organization of court, the judge whoselitigants appeal earns the reputation as that she is not able. This reputation is established not
only when her judgement is disapproval in appeal court, but also when her judgement is accepted.
Therefore, the judge who cares about her reputation needs to get the litigants to accept damages
and needs to dissuade them from appealing. For the sake of appeal proof, the judge has to oﬀer
an agreeable damages, which prevents both litigants from going to the appeal court.
32.1

Appeal proof conditions

Each litigant (plaintiﬀ and defendant) has a level of threshold that is acceptable for her or him if
the disutility is smaller than that level, or a reservation utility Ū (e). That is, A litigant accepts
the judgement and will not appeal if the level of disutility is less than her (or his) threshold:UP (d) ≤ Ū (e) UD (d) ≤ Ū (e)(1)

We shall call these inequalities appeal proof conditions (APCs) and call such d in these inequalities
as appeal proof damages (or judgements). We ﬁnd such appeal proof d in Fig.2.

Ūdappeal proof dFigure 2: Range of appeal proof dUnfortunately, there always does not exist appeal proof damages, such as in Fig.3. In thissituation, any damages that the judge oﬀers is unacceptable for either (or both) litigant(s), anddefendant or plaintiﬀ (or both) go to the appeal court. The judge makes eﬀorts to persuade thelitigants to accept damages she oﬀers and this eﬀorts result in raising the level of reservation
utility: Ū ′ (e) > 0. In other words, the judge can ﬁnd the appeal proof damages d by raising thelevel of threshold. We can interpret the eﬀorts e as ones for searching a acceptable damages forthe litigants.

4Ūdappeal proof dfor D

appeal proof dfor P

Figure 3: Nonexistence of appeal proof d for both parties

2.2

The judge’s objective

Denoted by U summation of disutilities of the plaintiﬀ and defendant (i.e., U = UP (d) + UD (d)).
The judge cares about appeal proof conditions and chooses damages d and eﬀorts e in order tominimize the parties’s disutilities and her costs. That is, the judge’s objective is to minimize theweighted average of the disutility and cost under the APCs:
min W = ηU (d) + (1 − η)C(d, e)
d,esubject toAP Cs.

(2)
(3)

Let us consider this problem of judge intuitively by using the ﬁgures. The following analysis
classiﬁes into four cases, depending on whether the constraint(s) is(are) binding or not.31) Both APCs are non-binding (i.e., UP < Ū and UD < Ū )The judge can optimize her objective without consideration of appeal proof conditions. She is
not under pressure of appeal. So she need not make eﬀorts of persuasion e in order to enlarge
3See also Appendix.

5

WŪappeal proof ddd
appeal proof dd∗

Figure 4:

Figure 5:

the range of appeal proof. In this case, the judge has the freedom of decision on damages d∗ .
Therefore, in the equilibrium (d∗ , e∗ = 0) occurs.
2) APC of P is binding and APC of D is non-binding (i.e., UP = Ū and UD < Ū )This case is likely to occur when the judge’s preference is relatively pro-defendant. The judge
can optimize her objective by persuasion of the plaintiﬀ to accept the oﬀered damages. She canbe better oﬀ by enlarging the scope of appeal proof (See Fig. 6 and ??). Thus, the judge makes
positive eﬀorts and oﬀers damages that is acceptable for the plaintiﬀ. In the equilibrium, d∗ ande∗ such that UP (d∗ ) = Ū (e∗ ) occur.
3) APC of P is non-binding and APC of D is binding (i.e., UP < Ū and UD = Ū )This case is likely to occur when the judge’s preference is relatively pro-plaintiﬀ. The judge canoptimize her objective by persuasion of the defendant to accept the oﬀered damages. Thus, thejudge makes positive eﬀorts and oﬀers damages that is acceptable for the defendant as well as theplaintiﬀ. In the equilibrium, d∗ and e∗ such that UP (d∗ ) = Ū (e∗ ) occur.
4) Both APCs are binding (i.e., UP = Ū and UD = Ū )This case indicates that both parties’ reservation disutility Ū is low. This means that both parties
are not reluctant to go to the appeal court. The judge has to make persuasive eﬀorts for appeal
proof. In this case, d∗ and e∗ such that UP (d∗ ) = UD (d∗ ) = Ū (e∗ ) occurs in the equilibrium.
6

Ū

appeal proof dddd

new appeal proof d∗new appeal proof dFigure 7:Figure 6:

Ūappeal proof dddnew appeal proof d

new appeal proof dFigure 8:

Figure 9:7d∗Ū (e∗ )dappeal proof d = d∗Figure 10:

Note that the judge has no freedom to decide (d, e). The judge just makes eﬀorts to persuadeboth parties until she ﬁnds acceptable damages for both parties. Given the eﬀorts of persuasion,
the judge just sets such appeal proof damages, rather than optimizes her objective. If the judge
makes no eﬀorts, there does not exist the range of appeal proof and any damages the judge oﬀers
is unacceptable for both parties. Therefore, by such persuasion the judge creates the range ofappeal proof and prevents both parties from appealing.
In the literature of ‘litigation and settlement,’ if there does not exist the scope of ‘settlement,’
both parties do not compromise and cannot help bringing the suit. The scope of appeal proof
in our study is a similar idea to that of settlement. There is no choice but brtinging suits undernonexistence of the range of settlement. On the contrary, when there does not exist the range ofappeal proof, the judge can seek out the acceptable damages by persuasion of the parties. Though
this function to persuade parties is from self-interest of judge, from the point of view of social
costs, it helps to save the costs. We can say that this is the role of judge.

3

Concluding remarks

This paper considers non-benevolent judge and explores a role of judge. Under the appeal court
system, the judge cares about her reputation and prevents the litigants from going to appeal
court. We focus on the judgement that prevent the litigants from appealing, that is, the appealproof judgement. Allowing for the range of appeal proof to both litigants, the judge needs to oﬀer
a judgement. Through the consideration of such judges, we explore a role of judge. When theplaintiﬀ and defendant are optimistic, there might not be the range of appeal proof. Under such8

a situation, the judge makes eﬀorts to legally persuade the litigants to accept the judgement sheoﬀers and from appealing. Although this is from self-interest of the judge rather than from social
interest, this might contribute to saving social costs on litigation.
Appendix
The Lagrangian is deﬁned as
L = η (UP (d) + UD (d)) + (1 − η)C(d, e) + λ1 (UP (d) − Ū (e)) + λ2 (UD (d) − Ū (e)).

(4)

The Kuhn-Tucker conditions reduce to()∂L′′= η UP′ (d) + UD(d) + (1 − η)Cd (d, e) + λ1 (UP′ (d)) + λ2 (UD(d)) = 0∂d∂L= (1 − η)Ce (d, e) + λ1 (Ū ′ (e)) + λ2 (Ū ′ (e)) = 0∂e(5)(6)λ1 ≥ 0with λ1 = 0if Ū (e) − UP (d) ≥ 0(7)λ2 ≥ 0with λ2 = 0if Ū (e) − UD (d) ≥ 0(8)1) Both APCs are non-binding (i.e., UP < Ū and UD < Ū )Conditions (7) and (8) yield λ1 = λ2 = 0. Then from (6) we have (1 − θ)Ce (d, e) = 0, which
gives e∗ = 0 under the assumption of Ce (d, 0) = 0 for any d. From (5) we have d∗ > 0 such that′ (d)) + (1 − η)C (d, 0) = 0.
η (UP′ (d) + UDd2) APC of P is binding and APC of D is non-binding (i.e., UP = Ū and UD < Ū )e (d,e)Conditions (7) and (8) yield λ1 > 0 and λ2 = 0. Then (6) yields λ1 = (1−η)C. InsertedŪ ′ (e)into (5) and (7) give d∗ > 0 and e∗ ≥ 0, which satisfy UP (d∗ ) = Ū (e∗ ).
3) APC of P is non-binding and APC of D is binding (i.e., UP < Ū and UD = Ū )e (d,e). Inserted
Conditions (7) and (8) yield λ1 = 0 and λ2 > 0. Then (6) yields λ2 = (1−η)CŪ ′ (e)into (5) and (7) give d∗ > 0 and e∗ ≥ 0, which satisfy UD (d∗ ) = Ū (e∗ ).
4) Both APCs are binding (i.e., UP = Ū and UD = Ū )Conditions (7) and (8) yield λ1 > 0 and λ2 > 0, which give d∗ > 0 and e∗ ≥ 0 such thatŪ (e∗ ) = UP (d∗ ) = UD (d∗ ).

9References[1] Katz, A.W. Judicial decision-making and Litigation Expenditure. International Review of Lawand Economics, vol.8, pp.127–143.
[2] Levy, Gilat. 2005. Careerist Judges and the Appeal Process. Rand Journal of Economics,
vol.36, no.2. pp.275–297.
[3] Shavell, Steven. 2006. The Appeals Process and Adjudicator Incentives. Journal of LegalStudies, vol.35, pp.1–29.
[4] Wittman, Douglas Glen. 2000. Evolution of the Common Law and the Emergence of Compromise. Journal of Legal Studies, vol.24, pp.753–781.

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