Appeal Process Lowers Litigation Costs?∗
Yoshinobu Zasu†

1Introduction

This paper explores the eﬀects of appeal process on the litigation eﬀorts of the plaintiﬀ anddefendant under the assumption of non-benevolent judge.
In the standard litigation model, the plaintiﬀ eﬀort level (litigation cost) is cancelled out by thedefendant eﬀort.1 judge tends to be described not as a self-interested player but as a “function”
which inputs litigation eﬀorts and outputs judgement. The judges are benevolent and maximizesocial welfare in the model. In reality, however, some of them make a decision depending on theirown preference and consider the eﬀects of their judgement on their future career.
On the other hand, 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: the evolution of common law, Wittman (2000); consideration of judge reputation, Levy(2005); the eﬀect of appeal process on the divergence of social welfare and individual preference,
Shavell (2007).
The present paper combines the litigation model with non-benevolent judge model, and examines the eﬀect of appeal process on litigation costs of the parties.

2The Model

We consider strategic behavior of a plaintiﬀ (P) and a defendant (D) in a lower court. In order togain damages, or judgment under the lower court, P hires a lawyer and spends time and money.
This litigation eﬀort of P to is x, which is count by dollars. That is, x is litigation cost of P.
Similarly, Litigation cost of D is y. Given the parties’ eﬀorts, a judge in the lower court makes∗

Preliminary. Comments are welcome!
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
See Katz (1988).
†1judgement v After the judgment of the lower court, if either of the parties would not be satisﬁedwith the judgment, he or she could appeal to a higher court.
Given that P receives harms from D, the timeline is describes as the following manner:
1. Potential D chooses level of care c, and accident occurs with probability p(c).
2. P decides whether he brings a suit or not.
3. P and D decide each litigation eﬀorts (x, y) under the lower court;
4. Judgment v is given by the judge of the court;
5. P and D consider whether to appeal the court’s decision;
6. If one of the parties appeal to a high court, judgment vA under the high court is given.
In order to satisfy the subgame perfection, we will examine decisions of each parties, including P,D, and lower court judge, in the reverse order.
We assume that judgment vA and litigation cost zA under higher court are common value
for parties. Given the judgment under lower court v, each party, who anticipates higher court
decision vA , consider whether to appeal. For the plaintiﬀ, he does not appeal when the expected
payoﬀ under higher court is lower than that under lower court;vA − zA ≤ v − x.

(1)

Similarly, the defendant does not appeal when cost under higher court is higher than that underlower court;vA + zA ≥ v + y.

2.1

(2)

Judge Behavior

Now let us consider judge decision under the lower court.2 Following Shavell (2006), we assume
that a lower court judge fears the penalty on the career track if a higher court judge denies thelower court decision, and dislikes the litigation parties appeal to higher court to avoid the higher
court decision. Therefore, the lower court judge prevents litigation parties from appealing to ahigher court.
2The argument of this subsection is based on Shavell (2006).

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To this end, a lower court judge will make a decision v to satisfy the condition that bothparties avoid to appeal, that is, conditions (1) and (2);vA − zA + x ≤ v ≤ vA + zA − y.

(3)This is similar condition to the “settlement range’ in the literature of economics of litigation.3
We call this condition appeal-proof condition (AC). For analytical usefulness, we deﬁne Ap =vA − zA + x and Ad = vA + zA − y. Ap and Ad are the appeal-proof conditions with respect to theplaintiﬀ and defendant, respectively. To make thing interesting, we assume that there exisits suchv that satisfy the condition. Given parties’ litigation eﬀorts (x, y), the judge bears costs c(v; x, y),which is given as (v − v̄(x, y))2 for analytical simplicity. From this functional form, v of longer
distance from v̄ means more costly for the judge. Exogenous variable v̄ represents preferrence ofthe judge. A judge with smaller (larger) v̄ means that she is more pro-defendant (pro-plaintiﬀ),
because it is less costly for the judge to give smaller (larger) judgement v.
Thus, the lower court judge makes decision v to prevent both litigants from appealing and tominimize her cost. Thus, the judge’s problem is described as follows;
min C(v; x, y)v

subject to(4)AC.

The decision v of the above prolem is depicted as v ∗ = v(x, y). From the discussion of Shavell(2006), we can classify the decisions of the judge into three cases, depending on whether AC isconstrained.
Case 1 is that AC is not constrained as in Fig.1. In this case, a lower court judge makes
a decision without caring about the ligation parties. This means that the lower court judge’sdecision is neither so far nor diﬀerent from that of higher court judge. It results in that there
is little possibility that she is punished. Given (x, y), the judge chooses her optimal decision asv ∗ = v̄(x, y).
Case 2 is that the left side of AC is constrained (Fig. 2). In this case, a lower court judge
has to consider the plaintiﬀ and to oﬀer judgement. The judge prefers to lesser damages, andmeans to be more pro-defendant. Unless the judge does not care about the plaintiﬀ, then hewill go to a higher court after lower court decision. The judge chooses her optimal decision as3See Miceli (1997) for introduction of economics of litigation and settlement.

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Figure 1: Non-contrained ACv ∗ = Ap (= vA − zA + x).
In Case 3, the judge prefers to more damages and is more pro-plaintiﬀ. The right side of ACis constrained (Fig. 3) in this case. The judge cares about whether the defendant will appeal to ahigher court. In order to prevent the defendant to go to the higher court, the judge has to choosev ∗ = Ad = vA + zA − y less than her ﬁrst best decision v̄.
From the above discussion, we can ﬁnd that appeal process mitigates the lower court judge
to make a moderate judgment particularly when she tends to be a extremely pro-defenandant or
pro-plaintiﬀ. Given the analysis of the self-interested judge, we will consider the eﬀect of appeal
process on the parties’ behaviors in the next section.

Figure 2: Constrained AC (Ap )Figure 3: Constrained AC (Ad )4

3The Eﬀect of Appeal Process

3.1

Litigation Costs

Let us examine litigation eﬀorts of the parties. The plaintiﬀ and defendant anticipate the lower
court’s judgement v(x, y) and decide their litigation eﬀorts (x, y), respectively:
The plaintiﬀ’s problem

max v(x, y) − x;(5)

The defendant’s problem

min v(x, y) + y.

(6)

xy

The lower judge decision v(x, y) depends on whether appeal-proof condition is constrained (Case1, 2, and 3). We consider litigation eﬀorts of the parties in each case.
In Case 1, An increase of x leads to an increase of v̄, and in addition to an increase of Ap (SeeFig.4). The judge chooses v̄ as long as an incremental of Ap is not larger than that of v̄. Theparties’ problems are described as follows:
The plaintiﬀ’s problem

max v̄(x, y) − x;(7)

The defendant’s problem

min v̄(x, y) + y.

(8)

xy

It is assumed that in these problems solutions (x∗ , y ∗ ) are positive and unique, respectively. The∂v̄
plaintiﬀ decides x∗ > 0 such as ∂x= 1 of the ﬁrst order condition of Eq.5. Similarly, the defendant∂v̄
= 1 of the ﬁrst order condition of Eq.6. Therefore, in Nash Equilibrium
selects y ∗ > 0 such as ∂y(x∗ (> 0), y ∗ (> 0)) is occurred. This is the same result as the standard litigation eﬀort model. In
this case, there is no diﬀerence of litigation costs between under existence of appeal process andunder inexistence.

Figure 4: Channel to v ∗Now let us consider the litigation eﬀorts in Case 2, where Ap is constrained. As x increases,5

v(x, y) increases and Ap also increases. If the marginal eﬀect of x on v is larger than that onAp , then this become the same situation as Case 1. Thus, we focus on the situation wheremarginal eﬀect of x on v is not larger than that on Ap :∆v̄
∆x

<∆Ap
∆x .

Since the judge chooses∗v ∗ = vA − zA + x in this case, the plaintiﬀ equalizes marginal beneﬁt ∂v∂x to marginal cost 1. Infact, the marginal beneﬁt is 1, and the marginal cost is also 1. Thus, the plaintiﬀ decides any x∗
satisﬁes 0 ≤ x∗ < 2zA . This value follows vA − zA + x < vA + zA . Since it is indiﬀerent for theplaintiﬀ to choose whether x∗ = 0 or x∗ = 2zA − ϵ, where ϵ is suﬃciently small positive value, we
assume that for simplicity x∗ = 0. The defendant cannot make an eﬀect on the judgement because∗of the judge’s decision v ∗ = vA − zA + x. The marginal beneﬁt is ∂v∂y = 0 and marginal cost is 1.
Thus, the defendant chooses y ∗ = 0. As a result, (0, 0) as Nash Equilibrium can occur. Therefore,
under inexistence of appeal process, the litigation parties choose positive litigation costs as Nashequilibrium (x∗ (> 0), y ∗ (> 0)). On the other hand, the litigation parties can spend little costs
under appeal process in this case.
We consider the litigation eﬀorts of Case 3, where Ad is constrained. Similar analysis applies,
and we ﬁnd that in Nash Equilibrium (0, 0) can occur.
In this subsection, we can summarize that appeal process can help litigation costs of parties
to lower in some cases (Case 2 and 3). Incorporating the incentive of the judge into analysis oflitigation eﬀort makes us new insight. The lower court judge does not care about the parties’litigation cost but just care about her preference. She is neither benevolent nor intends not tolower litigation costs. In spite of this, as a result the existence of appeal process contributes tolower litigation costs in some cases. Intuitive reason why litigation costs is lower in Case 2 and3 is the following: There is strategic relationship between the plaintiﬀ and defendant in Case 1.
On the other hand, in Case 2 and 3 the judge is concerned only one party and the other party
cannot inﬂuence the judgement. As a result, the appeal process cuts oﬀ the strategic relationshipbetween the litigation parties. The lower court judge’s preference is far diﬀerent from the upper
one in Case 2 and 3. In these cases, the lower court judge has to shift from her best to the upper
court preference through the appeal proof condition, and has no choice to oﬀer judgment that islower than is desirable for her. From the above analysis, we summarize the results as the followingproposition.
Proposition 1
a. If the judge has no eﬀect of appeal court, litigants choose positive litigation costs.
b. If the judge has eﬀect of appeal court, litigants can make no litigation eﬀorts.
63.2

Filing a Suit

Let us consider the plaintiﬀ’s ﬁling decision. The plaintiﬀ bring a suit if v ∗ − x∗ − k ≥ 0, where
k is the ﬁxed cost to ﬁle a case. We assume that k varies across potential plaintiﬀs with thecumulative distribution F and the density f . We deﬁnes k̂ = v ∗ − x∗ , and a plaintiﬀ with k(≤ k̂)
brings a suit. We are interested in the comparison between the results with appeal process andwithout. K̂ denotes the following: a plaintiﬀ with k(≤ K̂) brings a suit under no appeal process,where K̂ = v ∗ − x∗ = v̄ − x∗ .
In the following analysis, since there is no diﬀerence in analysis between existence of appeal
process and inexistence, we focus on the interesting cases: Case 2 and 3.
In Case 2, if there is appeal process,k̂ = v ∗ − x∗
= vA − zA .

(9)

On the other hand, if there is no appeal process,K̂ = v ∗ − x∗= v̄ − x∗(10)

In this case, we know that v̄ < vA − zA , and ﬁnd that K̂ < k̂. This indicates that more plaintiﬀs
bring a suit under the existence of appeal process than under inexistence.
Similarly in Case 3, under the existence of appeal process, we know thatk̂ = v ∗ − x∗
= vA − zA .

(11)

On the other hand, if there is no appeal process,K̂ = v ∗ − x∗= v̄ − x∗ .

(12)These conditions lead to the result where the eﬀect of appeal process is unclear. More plaintiﬀs(or less plaintiﬀs) may bring a suit under the existence of appeal process. We summarize the7

result as follows.
Proposition 2
The eﬀect of appeal process on the number of ﬁling cases is unclear: more plaintiﬀs ﬁle a caseunder appeal court than under inexistence in Case 2; more plaintiﬀs may ﬁle a case under appeal
court than under inexistence in Case 3.

3.3

Injurer’s (Defendant’s) Preventive Activity

Now let us examine potential defendant’s level of care before accident. The potential defendant (injurer) chooses level of care c, accident occurs with probability p(c) and harms a victim(plaintiﬀ). The injurer expects the future results (x∗ , y ∗ , v ∗ ) and minimizes her costs:
min c + p(c)[F (k̂)(v ∗ + y ∗ )].

(13)

c

The ﬁrst order condition is described as
1 + p′ (c)[F (k̂)(v ∗ + y ∗ )] = 0.

(14)

From this, we ﬁnd that larger k̂, v ∗ , and y ∗ are, larger c∗ is.
In Case 2, under appeal process since v ∗ + y ∗ = vA − zA , the judgment v ∗ and the threshold ofﬁling a suit k̂ are larger, and the defendant’s litigation cost y ∗ is smaller, we ﬁnd that the eﬀectof appeal process on the deterrence is unclear. Finally, the level of care is higher under appeal
process than under inexistence if the following condition is satisﬁed:
1F (k̂)(vA − zA )<1F (K̂)(v̄ + y ∗ )

.

(15)

Since this condition holds when Ap > v̄ + y, if the diﬀerence between v̄ and vA is suﬃciently
large and/or y ∗ under inexistence is suﬃciently small, then the deterrence is larger under appeal
process.
In Case 3, under appeal process since v ∗ is smaller and the threshold of ﬁling a suit k̂ isunclear, the eﬀect of appeal process on the deterrence is unclear. The level of care c∗ is smaller8

under appeal process than under inexitence if the following condition holds:
1F (k̂)(vA + zA )<1
F (K̂)(v̄ + y ∗ )

.

(16)

This condition is satisﬁed if the diﬀerence between litigation cost of upper court zA and litigation
cost under inexistence of appeal court y ∗ is suﬃciently small. If there is no particular reason why
the diﬀerence is large, the deterrence under appeal process is weaker than under inexistence ofappeal process. Therefore, we have the following result in this subsection.
Proposition 3
The eﬀect of appeal process on deterrence is unclear.

4Concluding Remarks

This paper ﬁnds that appeal process can mitigate litigation costs through cutting oﬀ the strategic
relation between the parties. As in the setting of the model, even if a lower court judge has nointention to reduce the litigation costs of parties, she follows her self-interests and the litigation
parties predict her such behavior. As a result, appeal process can lead to cheaper litigation.

References[1] Katz, A.W. Judicial decision-making and Litigation Expenditure. International Review of Law
and 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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