Trial and Settlement under Cumulative Prospect Theory
Eric Terry
Ted Rogers School of Business Management
Ryerson University
350 Victoria Street
Toronto ON
Canada M5B 2K3 eterry@ryerson.ca
Phone : 416-979-5000 ext.2452
Fax : 416-979-5266
This version: May 30, 2008

Eric Terry is an Associate Professor of Finance at Ryerson University in Toronto, Ontario. A previous version of this paper was entitled Trial and Settlement under Loss Aversion

Trial and Settlement under Cumulative Prospect Theory
Abstract
It is well-known that if the parties in a legal dispute agree about the likelihood of potential trial outcomes then they will be inclined to settle vs. going to trial in order to reduce litigation costs and risk. In this paper, we assume that both plaintiff and defendant evaluate this decision in accordance with Cumulative Prospect Theory. It is found that the two parties will sometimes be unable to reach settlement, instead preferring to incur litigation costs for the opportunity to minimize their losses by prevailing at trial. We derive and characterize the conditions under which settlement is Pareto efficient vs. going to trial.
1

Trial and Settlement under Cumulative Prospect Theory
1. Introduction
It is well-known that if the parties in a legal dispute will be inclined to settle vs. going to trial if they: (i) agree about the likelihood of potential trial outcomes and (ii) are either risk averse or risk neutral.
1
Settlement both reduces litigation costs and the risk associated with an uncertain trial result. The traditional rationale for some lawsuits going to trial is that one or both sides have information relevant to the trial outcome that the other side does not have. A number of asymmetric information models of the settlement vs. trial decision have been developed, most notably the screening model of Bebchuk (1984) and the signaling model of Reinganum and
Wilde (1986). A weakness of such models is that they require the informational asymmetries to persist until trial. As Hay (1995) notes, discovery rules generally force both sides to disclose any privileged information that they process before trial, which would then afford the parties an opportunity to settle.
2
In this paper, we take a new approach to the settlement vs. trial decision. Instead of assuming that the parties to the suit are either risk averse or risk neutral, it is assumed that they evaluate the settlement vs. trial decision using Cumulative Prospect Theory (Tversky &
Kahneman, 1992). Despite the tremendous growth of behavioral economics, the application of behavioral economics to the issue of lawsuits has largely been overlooked. Exceptions are Bigus
(2006), Eide (2005), Sunstein, Kahneman, and Schkade (2000), and Teitelbaum (2007).
However, none of these papers uses Cumulative Prospect Theory (CPT) to examine the issue of lawsuits nor do any of them directly examine the settlement vs. trial decision.
Under CPT, both parties are willing to trade off litigation costs against the opportunity to minimize their losses by prevailing at trial. We derive the conditions under which settlement is
2

Pareto efficient vs. going to trial. It is found that the two parties are more likely to favor trial when litigation costs are low. As well, the two parties are more likely to favor trial when they have high curvature in their utility functions and/or probability weighting functions. The settlement vs. trial decision is more sensitive to the curvature of the utility function than to the curvature of the probability weighting function. Furthermore, this choice tends to be more sensitive to the curvature of the utility function when the plaintiff is likely to prevail at trial than when the defendant is likely to prevail. In contrast, the sensitivity of this decision to the curvature of the probability weighting function is not significantly affected by the probability of the plaintiff prevailing at trial. Loss aversion has no impact on the settlement vs. trial decision in cases that do not involve punitive damages. When punitive damages are possible, greater loss aversion implies increased odds of a settlement.
In the model, the lawsuit is more likely to proceed to trial when full (vs. partial) restoration of the plaintiff’s loss is expected if the defendant is found liable. However, the likelihood of the suit proceeding to trial is negatively related to the amount of punitive damages that may be awarded. Uncertainty in the potential court award is found to increase the likelihood of a trial in cases where no punitive damages will be awarded, decrease the likelihood of a trial in cases where punitive damages may or may not be awarded if the plaintiff prevails, and have little effect of the likelihood of the suit going to trial in cases where punitive damages are certain to be assessed if the defendant is found liable.
Finally, for suits that do not involve potential punitive damages, the model predicts that the likelihood of the case going to trial is greatest when the two parties have approximately the same likelihood of prevailing. When punitive damages may be awarded by the court, trial is
3

most likely when the odds of the plaintiff prevailing are slightly unfavorable (somewhere in the range of 30% to 50%, depending on the amount of potential punitive damages).
The paper is organized as follows. Section 2 presents a short review of Cumulative
Prospect Theory. The basic model of the settlement vs. trial decision is developed in section 3.
Comparative statics are presented in section 4. The model is extended to allow for punitive damages and uncertainty in the amount of any court award in section 5. The impact of the rules for assigning litigation costs is also discussed. Finally, section 6 concludes the paper.
2. A Review of Cumulative Prospect Theory
Prospect Theory (Kahneman & Tversky, 1979) and later CPT (Tversky & Kahneman, 1992) were developed to account for several empirical phenomena that could not be explained well by expected utility theory. First, it has been observed that individuals tend to be risk averse when evaluating gains and risk seeking when evaluating losses.
3
This phenomenon is referred to as the reflection effect. Second, individuals appear be to loss averse, i.e., they are more sensitive to losses in wealth than to equivalent gains.
4
Together, the reflection effect and loss aversion imply a utility function of the shape shown in Figure 1(a). Utility is measured relative to some reference point which is used to distinguish positive outcomes (gains) from negative outcomes
(losses). This reference point is usually assumed to be the current status quo but it does not need to be. In the case of a lawsuit, a natural reference point for the plaintiff would be the status quo prior to suffering the losses that led to the suit. The utility function u(x) is concave for gains, convex for gains, and steeper for losses than for gains. Mathematically, the utility function is usually assumed to be of the power form:

 x
 for x


0
( x )
 for x 0
, (1)
4

where

< 1 captures the curvature of the utility function over the gains and losses domains and

> 1 captures the degree of loss-aversion.
5
A lower value of

implies more curvature in the utility function. There has been wide variation in the estimated value of

, with estimates ranging from 0.19 to 0.88; see Stott (2006) for a summary. The value of

is usually estimated to be around 2.5, which implies that individuals are 2.5 times as sensitive to losses as to gains.
Insert Figure 1 about here
Another empirical phenomenon is that individuals appear to overweight extreme but low probability events, as evidenced by the willingness of individuals to take unfair low-probability gambles on the one hand yet buy insurance on the other hand. This has led researchers to posit a probability weighting function w(p) with an inverse S-shape, as shown in Figure 1(b). Empirical evidence for a probability weighting function with this shape is widespread.
6
A number of different functional forms for the probability weighting function have been proposed. Stott
(2006) conducted an experimental test of various forms of the CPT and found that the probability weighting function which was proposed by Preclec (1998),
( )
 exp
 ln( )
 

, (2) with

< 1, provided the best fit to the data. A lower value of

implies greater curvature , i.e., a more pronounced inverse S-shape, for this probability weighting function. The estimated value of

has ranged from 0.53 to 0.94 (Stott, 2006).
In CPT, the utility function and probability weighting function are combined to compute the value of economic choices as follows. Consider an economic choice that has potential outcomes given by the vector x and associated probabilities given by the vector p . Let n be the number of potential outcomes that are positive (gains) and m be the number of negative potential
5

outcomes (losses). Then, the value of this choice is equal to the sum of the contributions of the payoffs over the gains and losses domains:
( ; )

V

( ; )

V

( ; ), (3) where the value functions over gains and losses are given by
V

( ; )

( n
) ( n
)
 k n  

1

 w


 j k

0 p

  w


  k j

1 

0 p




 ( ) and
V
 x p
 w p
 m u x
 m
)
 k m  

1

 w


 j k

0 p
 

  w


  k j

1 

0 p
 





 
) respectively. Although Tversky and Kahneman (1992) allow for different probability weighting functions over the gains and losses domains, the above formulation asumes the same weighting function for both domains, which is commonly done in applications of CPT.
3. The Basic Model
A lawsuit has been filed against the defendant by a plaintiff who has suffered a loss of L . If a settlement cannot be reached and the case goes to trial, the likelihood that the plaintiff will prevail and be awarded damages is given by p . Let A represent the amount that will be awarded by the court if it finds the defendant liable. We assume that A ≤ L , i.e., the court may award partial or full restitution of the plaintiff’s loss but will not impose any punitive damages. Total litigation costs of C will be incurred by the two sides if a trial ensues. These costs are assumed to be fixed, with the losing side being ordered to pay the costs of the other side. Finally, the values of L , p , A , and C are assumed to be common knowledge, which precludes any incentive for the plaintiff and defendant (or their agents) to settle or go to trial due to asymmetric information.
6

Before proceeding further, a few comments about this model should be made. The assumption that the amount of liability faced by the defendant is fixed at A ≤ L is made solely for mathematical convenience and will be relaxed later in the paper. In practice, the amount of effort put into case preparation – and thus the amount of litigation costs – by each side will have an impact on the probability of a favorable court verdict. The total litigation costs of C in the model are assumed to be based on the optimal amount of effort by both sides. The prevailing arrangement under American law is that each side bears its own costs, whereas the usual rule under the British system is that the losing side bears costs. Our assumption that the losing side bears costs, which conforms to the British system, is made solely to reduce the number of variables in the analysis by one and has no qualitative impact on the results of the paper.
Instead of going to trial, the two parties can negotiate a settlement for some amount S .
For ease of exposition, it is convenient to express the potential settlement amount, as well as the expected court award and costs of trial, in proportion to the plaintiff’s loss: s

/ , a

/ , and c

/ . Thus, the payoff to the plaintiff (net of the initial loss) will be
 s

1

L if a settlement is reached. Alternatively, if the case proceeds to trial, the plaintiff will have a net payoff of
 a

1

L if the defendant is found liable by the court and

1

if the defendant prevails. The corresponding payoff to the defendant will be
 sL if a settlement is reached,
  a
 
if the defendant is found liable at trial, and 0 is the defendant prevails at trial. Having described the potential outcomes for the plaintiff and defendant, we can proceed to examine the conditions under which trial rather than a settlement is pareto-optimal.
3.1. Trial and Settlement under Risk-Neutrality
7

We begin by briefly reviewing the case in which both parties are risk-neutral. The expected payout by the defendant if the case goes to trial is (

) , and so the defendant would be willing to settle for s

(

) . Meanwhile, the expected payoff to the plaintiff is
(

1) L
  p )(1

)
 
( c )

, which implies that the plaintiff would be willing to settle for s

(
  c . Consequently, settlement is always pareto-optimal for the two parties, with the optimal settlement amount s
* lying within the range
( c s * (

) .
The precise amount of the settlement would depend on the structure of the settlement negotiations; see Bebchuk (1984) and Nalebuff (1987) for a discussion of this issue. This result carries over to the case in which one or both parties are risk-averse; settlement will be paretooptimal both to save on litigation costs (as in the risk-neutral case) and to resolve uncertainty.
3.2. Trial and Settlement under Cumulative Prospect Theory
We now assume that both parties to the lawsuit are loss averse and evaluate the choice between settling and going to trial according to CPT value function (3). For simplicity, it is assumed that both the functional form and the parameters of the value function are the same for the two parties. The form of the utility function is assumed to be given by (1), whereas no specific form for the probability weighting function is assumed. It is further assumed that the plaintiff measures gains and losses relative to the status quo prior to suffering the loss of L . This is a natural reference point for the plaintiff to adopt because the lawsuit is focused on this loss.
8

Under these assumptions, the value to the defendant of going to trial is
      
( ) a c L , while the value of settling the suit is
  s L . Therefore, the defendant will prefer to settle for any amount s that satisfies the inequality
      
( ) a c L
  
, which can be rewritten as s
 w

( )
1/
  a
 c

.
(4)
For the plaintiff, the value of going to trial is
 w (1
 p
  c ) L
 w (1
 p )
  
1
 a
 
L
 and the value of settling is
 
(1

)
  s L .
7
Therefore, the plaintiff will be willing to settle for any amount s that satisfies
 w (1
 p
  c ) L
 w (1
 p )
  
1
 a
 
L
   
(1
 s ) L .
This condition can be simplified to s
  w (1
 p )(1
 c )
  w (1
 p ) 1
 a
  1/

.
(5)
Combining inequalities (4) and (5), we arrive at the following result.
Proposition 1.
When (i) the court will not award punitive damages, (ii) the amount awarded if the defendant is found liable is known with certainty, (iii) both parties have CPT value functions with identical functional forms and parameters, and (iv) the plaintiff measures gains and losses relative to the status quo prior to the loss that led to the lawsuit, settlement is pareto-optimal if and only if
B

( )
1/
   w (1
 p )(1
 c )
  w (1
 p ) 1
 a
   1/


1.
(6)
Because the variable λ does not enter into inequality (6), the decision to settle or go to trial is independent of the coefficient of loss aversion for the two sides. (Later in the paper, it will be shown that this result does not hold either when the court may award punitive damages or when
9

the amount awarded if the defendant is found liable is uncertain.) When a = 1, i.e., the court will award full restitution if the defendant is found liable, inequality (6) can be reduced to the condition c

1/

1
 w (1
 p )
1/


1.
(7)
By inspection, the conditions under which settlement or trial is optimal for the two parties are symmetric around p = 0.5 for this special case. The characteristics of the indifference boundary between settling and going to trial are explored in the next section.
4. Comparative Statics
It is easy to see that the function B in (6) is an increasing function of the litigation costs c .
Consequently, if the two parties are willing to settle when litigation costs are c
0
, the two parties will also be willing to settle when litigation costs are c
1
≥ c
0
. Thus, the model gives the common-sense result that high litigation costs favor settlement rather than trial.
Suppose that both parties to the lawsuit have probability weighting function (2). This assumption is solely for making numeric computations; the qualitative results in this section hold for alternative probability weighting functions. Let the function c min a p
   max{0,
* c a p
  where
*
 
is implicitly specified by the equation
B a p
  c a p
   represent the minimum level of litigation costs at which settlement is pareto-optimal. By the preceding argument, this function is well-defined. The two parties will prefer to settle if expected litigation costs are above c min
 
and will prefer to go to trial if expected
10

litigation costs are below this level. Because the properties of this indifference surface are difficult to derive analytically except in special cases, we rely instead upon numeric analysis.
The behavior of c min
 
when the potential court award is 50% of the plaintiff’s loss is presented in Figure 2.
8
This figure reveals that the two parties may prefer to go to trial rather than settle even when litigation costs total half of the potential court award (which translates to 25% of the plaintiff’s loss). The indifference surface is decreasing in 
, i.e., trial is more (less) attractive to the plaintiff and defendant when their utility functions display more
(less) curvature. This result can be explained as follows. Greater curvature in the utility function implies more risk-seeking behavior with respect to losses. Thus, both parties are more willing to take a chance on the outcome of a trial and less willing to settle in order to save on litigation costs. The indifference surface is more sensitive to

when the plaintiff is likely to prevail at trial than when the defendant is likely to be found not liable by the court. This is due to the fact that the loss suffered by the plaintiff is larger than the potential court award against the defendant.
Insert Figure 2 about here
The indifference surface is also decreasing in

, which implies that trial is more (less) attractive to the two parties when their probability weighting functions display more (less) curvature. This can be explained by recalling that a favorable trial outcome for one party is an adverse outcome for the other party. Greater curvature in the probability weighting functions of the two parties implies greater disparity in the weights that the two parties attach to the potential trial outcomes. This makes it more difficult for the parties to reach a mutually agreeable settlement unless litigation costs are high. The sensitivity of the indifference surface to
 is not significantly affected by either the level of
 or the probability of the plaintiff prevailing at trial.
11

Comparing Figures 2(a) and 2(b), the indifference surface is less sensitive to the curvature of the probability weighting function than to the curvature of the utility function.
The value of c min
 
is highest when the probability of the defendant being found liable at trial is approximately 50%. In other words, the suit is most likely to proceed to trial when the plaintiff and defendant have nearly equal odds of prevailing in the suit. Conversely, settlement becomes more appealing as the probability of a favorable trial outcome shifts significantly in favor of either party. When the two parties have about the same likelihood of prevailing at trial, both parties will underweight the probability of losing the suit and thus will disagree over the value of a fair settlement, which makes the case more likely to go to trial. In contrast, when the probability of one party prevailing at trial is low, both sides will overweight this outcome (and underweight the other) and so there will be less disagreement between them regarding a fair settlement amount.
Insert Figure 3 about here
Similar results were found for other levels of the potential court award. Figure 3 displays the behavior of the indifference surface when the court will award full restitution of the plaintiff’s loss if the defendant is found liable. As before, the two parties are more likely to favor trial when they have high curvature in their utility functions and/or high curvature in their probability weighting functions. The indifference surface is again more sensitive to

when the plaintiff is likely to prevail at trial than when the defendant is likely to prevail. In contrast, the sensitivity of the indifference surface to
 is not significantly affected by either the level of
 or the probability of the plaintiff prevailing at trial. Furthermore, the indifference surface is less sensitive to the curvature of the probability weighting function than to the curvature of the utility function.
12

As in the case of partial damages, the suit is most likely to proceed to trial when the two parties have approximately the same likelihood of prevailing. Conversely, settlement becomes more likely as the probability of prevailing at trial shifts in favor of one of the parties. One key difference between this scenario and the previous one is that the values of c min
 
are much higher here. Thus, the suit is more likely to go to trial when the amount of the potential court award is a greater percentage of the plaintiff’s loss. This relationship will be explored in more detail later in the paper.
5. Extensions of the Model
In this section, we extend the basic model to allow for punitive damages and/or uncertainty in the amount of damages that will be awarded to the plaintiff if the defendant is found liable at trial.
We also consider the impact of having each side bear its own costs rather than the losing side bearing all costs.
5.1. Punitive Damages
The basic model assumed that the plaintiff could only expect partial or full restoration of the suffered loss. Now, assume that the court will award punitive damages if the defendant is found guilty, i.e., a > 1. Under punitive damages, the formulas expressing the value to the defendant of settling or going to trial remain unchanged and thus inequality (4) continues to describe the conditions under the defendant would prefer to settle. The value to the plaintiff of settling becomes
V
S
 
(1
 s ) L
 ( s

1)
 
L if s

1 otherwise
, while the value of going to trial changes to
V
T
  w (1
 p
  c ) L

( )
 
1
 
L

.
(8)
13

Note that the value of going to trial can be either positive or negative, depending on the size of potential punitive damages and probability of the plaintiff receiving them. Comparing these two amounts, we find that V
S
> V
T
and thus the plaintiff would prefer to settle if s

V / I
T V

1/

,
L
(9) where I
V
is an indicator variable that equals 1 if V
T
≥ 0 and –λ otherwise. Combining inequalities (4) and (9), we arrive at the following result.
Proposition 2.
When (i) the court will award punitive damages, (ii) the amount awarded if the defendant is found liable is known with certainty, (iii) both parties have CPT value functions with identical functional forms and parameters, and (iv) the plaintiff measures gains/losses relative to the status quo prior to the loss that lead to the lawsuit, settlement is pareto-optimal if and only if
B

( )
1/
  

V / I
T V

1/


1,
L
(10) where V
T
is given by equation (8).
Because V
T is a function of λ , the coefficient of loss aversion for the two parties will impact the decision to settle or go to trial.
As before, suppose that both parties to the lawsuit have probability weighting function (2) and define c min
  
as the minimum level of litigation costs at which settlement is pareto-optimal. Most of the properties for the indifference surface that were found in the previous section continue to hold.
9
Specifically, the two parties are more likely to favor trial when they have high curvature in their utility functions and/or probability weighting functions.
The indifference surface is more sensitive to the curvature of the utility function than to the curvature of the probability weighting function. As well, the indifference surface tends to be more sensitive to

when the plaintiff is likely to prevail at trial than when the defendant is likely
14

to prevail. Meanwhile, the sensitivity of the indifference surface to
 is not significantly affected by either the level of
 or the probability of the plaintiff prevailing at trial. p
 
Insert Figure 4 about here
The behavior of
*
  
is given in Figure 4 for representative values of

. Although the indifference surface is increasing in the amount for which the court could find the defendant liable over the range of restorative court awards (a ≤ 100%), the indifference surface is generally decreasing in the amount of any punitive awards when the plaintiff has a reasonable probability of prevailing at trial. Thus, the greater the potential punitive damages, the more favorable it is in general for the two parties to settle rather than proceed to trial. The rationale is that punitive damages represent a potential gain (net of the suffered loss) to the plaintiff and thus this individual will exhibit less risk seeking behavior, which includes being more willing to settle rather than take his or her chances in court.
As well, the greater the probability of receiving punitive damages, the less risk seeking the plaintiff will become. For this reason, the sensitivity of the indifference surface to the size of the potential punitive award increases with the probability of receiving this award (except, of course, when the floor of zero is reached, at which point settlement becomes a certainty).
Consequently, the model predicts that cases involving significant punitive damages that go to trial will tend to be ones in which the plaintiff has low odds of prevailing. This differs from the case of restorative damages where the suit is most likely to proceed to trial when the two parties have approximately the same likelihood of prevailing.
Comparing Figures 4(a) and 4(b), the values of c min
 
are lower over the punitive damages spectrum when the coefficient of loss aversion,
λ
, increases. When punitive damages are possible, greater loss aversion makes the plaintiff accentuate the possibility of
15

losing at trial. Added to the reduced risk seeking behavior discussed above, the plaintiff will be even more willing to settle rather than risk a negative outcome at trial and so will be more willing to settle at terms that are acceptable to the defendant.
5.2. Uncertainty in Awarded Damages
Now, consider the case in which there is uncertainty amount of damages that will be awarded by the court if the defendant is found liable. To capture such uncertainty succinctly, it is assumed that the amount of any awarded damages is equally likely to be either A(1+d) or A(1-d) , where d represents the deviation of the actual award from its expectation. Going through the same steps as before, we find that the defendant will prefer to settle if
 
/ 2
   a (1
 d )
 c
 
L
  
( )

( / 2)
    a (1 d ) c L
   
, which implies that s



/ 2
  a (1
 d )
 c
 
( )

( / 2)
 a (1
 d )
 c
 

1/

.
(11)
The value to the plaintiff of settling is
V
S
    
(1 s ) L
 ( s

1)
 
L if s

1 otherwise.
Meanwhile, the value to the plaintiff of going to trial depends on the size of A(1+d) and A(1-d) .
There are three possible cases: both potential amounts are greater than one (and thus in the gains domain), both potential amounts are less than one (and thus in the losses domain), and the larger amount is greater than one but the smaller amount is less than one (and thus the first is in the gains domain but the second is in the loss domain). In terms of model parameters, the value of going to trial to the plaintiff is given by
16

V
T














 w w w
(1
(1
(1


 p

 p p



 


( )
 w
 c c
(1
 c
( / 2)
)
)


)
 
  a
L
L p
L

1

( / 2)

/ 2)


 d

( / 2) w
 w



1
(1


1
1





1 p p
 a

L
 a
/ 2
/ 2)
 d
1


1




 d

1
 d w w

 


(1
(1

L
L



1

 p p

)
)

L





1
1

 a a


1
1

 d d
 
 


L
L


  d
 
1
  d
 
1
(12) o therwise.
The value of going to trial can be either positive or negative, depending on the potential amount of damages and probability of the plaintiff receiving them. Comparing the value of settling and going to trial, we find that the plaintiff will prefer to settle if s

V
T
/ I
V

1/

,
L
(13) where I
V
is an indicator variable that equals 1 if V
T
≥ 0 and –λ otherwise. Combining inequalities (11) and (13), we arrive at the following result.
Proposition 3.
When (i) the amount awarded if the defendant is found liable can be one of two equally-likely values, (ii) both parties have CPT value functions with identical functional forms and parameters, and (iii) the plaintiff measures gains/losses relative to the status quo prior to the loss that lead to the lawsuit, settlement is pareto-optimal if and only if
B



/ 2
  a (1
 d )
 c
 
( )

( / 2)
 a (1
 d )
 c
 

1/



V / I
T V

1/

L

1, (14) where V
T
is given by equation (12).
When there is uncertainty in the potential court award, the properties for the indifference surface that were found previously continue to hold. The direct impact of uncertainty in the potential court award on the indifference surface is shown in Figure 5 for representative values
  
. For cases in which no punitive damages will be awarded, as in Figure 5(a), the indifference surface is increasing in the amount of uncertainty in the potential court award.
17

Basically, greater uncertainty regarding the potential court award implies a greater spread in potential outcomes and so greater risk seeking behavior on the part of the two parties. Thus, litigation costs need to be higher in order for the parties to prefer to settle rather than go to trial.
When the court may or may not impose punitive damages, as in Figure 5(b), greater uncertainty over the amount of potential damages causes the loss-averse plaintiff to be less willing to take a chance on an uncertain trail outcome that could result in a net gain or net loss. As a result, the plaintiff will be more willing to settle at terms that are acceptable to the defendant rather than risk an uncertain trial. Finally, there is the case in which the court is certain to impose punitive damages if the defendant is found liable, as in Figure 5(c) when the percentage uncertainty is under 50%. In this case, uncertainty in amount of punitive damages has a negligible effect on the indifferent surface. Basically, uncertainty in the potential court award causes the plaintiff to become more risk averse (since any amount of punitive damages represents a net gain) but the defendant to become more risk seeking, and these two effect tend to negate each other.
Insert Figure 5 about here
5.3. Sharing of Litigation costs
It has been assumed for computational simplicity that the losing side bears costs. When each side must bear its own costs, the difference in net wealth between winning and losing at trial is significantly reduced. This implies that both parties will be less willing to trade off litigation costs against the opportunity to minimize their losses by prevailing at trial. Consequently, the minimum level of litigation costs at which settlement is pareto-optimal will be lower than in a system where the losing side bears costs and so this model predicts a lower propensity for suits to go to trial under the American system of justice than under the British system. Otherwise, the results in the paper do not change qualitatively.
18

6. Conclusions
We examined the settlement vs. trial decision when both parties to the suit evaluate this decision using Cumulative Prospect Theory. Under CPT, both parties are willing to trade off litigation costs against the opportunity to minimize their losses by prevailing at trial. It was found that the two parties are more likely to favor trial when litigation costs are low. As well, the two parties are more likely to favor trial when they have high curvature in their utility functions and/or probability weighting functions. The settlement vs. trial decision is more sensitive to the curvature of the utility function than to the curvature of the probability weighting function.
Furthermore, this choice tends to be more sensitive to the curvature of the utility function when the plaintiff is likely to prevail at trial than when the defendant is likely to prevail. In contrast, the sensitivity of this decision to the curvature of the probability weighting function is not significantly affected by the probability of the plaintiff prevailing at trial. Loss aversion has no impact on the settlement vs. trial decision in cases that do not involve punitive damages. When punitive damages are possible, greater loss aversion implies increased odds of a settlement.
In the model, the lawsuit is more likely to proceed to trial when full (vs. partial) restoration of the plaintiff’s loss is expected if the defendant is found liable. However, the likelihood of the suit proceeding to trial is negatively related to the amount of punitive damages that may be awarded. Uncertainty in the potential court award is found to increase the likelihood of a trial in cases where no punitive damages will be awarded, decrease the likelihood of a trial in cases where punitive damages may or may not be awarded if the plaintiff prevails, and have little effect of the likelihood of the suit going to trial in cases where punitive damages are certain to be assessed if the defendant is found liable.
19

Finally, for suits that do not involve potential punitive damages, the model predicts that the likelihood of the case going to trial is greatest when the two parties have approximately the same likelihood of prevailing. When punitive damages may be awarded by the court, trial is most likely when the odds of the plaintiff prevailing are slightly unfavorable (somewhere in the range of 30% to 50%, depending on the amount of potential punitive damages).
The richness of the model’s predictions indicates the potential for applying behavioral economics to various legal issues. As regards the current model, further research could be conducted to determine the extent to which the above results continue to hold when the parties
CPT functions are stochastic rather than deterministic. It would also be useful to examine the extent to which alternative subjective utility models yield similar predictions.
20

References
Abdellaoui, M. (2000). Parameter-free elicitation of utilities and probability weighting functions.
Management Science, 46, 1497-1512.
Abdellaoui, M., Bleichrodt, H., & Paraschiv, C. (2007). Loss Aversion under Prospect Theory: A
Parameter-Free Measurement. Management Science, 53 , 1659-1674.
Baucells, M., & Villasis, A. (2006). Stability of risk preferences and the reflection effect of prospect theory. Working paper, IESE Business School.
Bebchuk, L. A. (1984). Litigation and settlement under imperfect information. RAND Journal of
Economics, 15, 404-415.
Benartzi, S. & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle.
Quarterly Journal of Economics, 110 , 73-92.
Bigus, J. (2006). Tort liability and probability weighting according to Prospect Theory. Working paper, University of Osnabrück.
Bleichrodt, H., & Pinto, J. L. (2000). A parameter-free elicitation of the probability weighting function in medical decision analysis. Management Science; 46 , 1485-1496.
Camerer, C. F., & Ho, T.-H. (1994). Violations of the betweenness axiom and nonlinearity in probability, Journal of Risk and Uncertainty, 8 , 167–196.
Eide, E. (2005). Accident liability with rank dependent expected utility. Working paper,
University of Oslo.
Fennema, H., & van Assen, M. (1998). Measuring the utility of losses by means of the trade-off method. Journal of Risk and Uncertainty, 17 , 277-295.
Fishburn, P. C., & Kochenberger, G. A. (1979). Two-piece von Neumann Morgenstern utility functions. Decision Sciences, 10 , 503-518.
Hay, B. L. (1995). Effort, information, settlement, trial. Journal of Legal Studies, 24, 29-62.
Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1991). The endowment effect, loss aversion, and status quo bias. Journal of Economic Perspectives, 5, 193-206.
21

Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk.
Econometrica, 47, 263-291.
Mehra, R., & Prescott, E. (1985). The equity premium: A puzzle. Journal of Monetary
Economics, 15, 145-161.
Nalebuff, B. (1987). Credible pretrial negotiation. RAND Journal of Economics, 18, 198-210.
Prelec, D. (1998). The probability weighting function. Econometrica, 66 , 497-527.
Reinganum, J. F., & Wilde, L. L. (1986). Settlement, litigation, and the allocation of litigation costs. RAND Journal of Economics, 17, 557–566.
Shavell, S. (1982). Suit, settlement, and trial: A theoretical analysis under alternative methods for the allocation of legal costs. Journal of Legal Studies, 11, 55-81.
Shavell, S. (1993). Suit versus settlement when parties seek nonmonetary judgments. Journal of
Legal Studies, 22, 1-13.
Stott, H. P. (2006). Cumulative prospect theory’s functional menagerie. Journal of Risk and
Uncertainty, 32 , 101–130.
Sunstein, C.R., Kahneman, D., & Schkade, D. (1998). Assessing punitive damages. Yale Law
Journal, 107 , 2071-2153
Teitelbaum, J. C. (2007). A unilateral accident model under ambiguity. Journal of Legal Studies,
36 , 431-477.
Tversky, A., & Kahneman, D. (1992). Advances in Prospect Theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5 , 297–323.
Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function, Management
Science, 42 , 1676–1690.
22

Notes
1.
Cf. Shavell (1982). This result only applies to civil suits involving monetary damages;
Shavell (1993) shows that it can be optimal for suits involving non-divisible real assets
(e.g., a dispute over child custody) to go to trial.
2.
Hay (1995) suggests that informational asymmetries can persist if one or both sides are unable to determine the amount of effort put into the case by the other side, thereby allowing the possibility of shirking on case preparation. However, such behavior is not consistent with a competitive market for legal counsel.
3.
Cf. Abdellaoui (2000), Fennema and van Assen (1998), Fishburn and Kochenberger,
(1979), Kahneman and Tversky (1979) and Tversky and Kahneman (1992). Though the evidence for convex utility over losses has been somewhat mixed, Baucells and Villasis
(2006) find that this can be primarily attributed to random noise in the stochastic utility function rather than risk-averse or risk-neutral behavior over the losses domain.
4.
Cf. Abdellaoui, Bleichrodt, and Paraschiv (2007), Kahneman and Tversky (1979), and
Tversky and Kahneman (1992).
5.
Tversky and Kahneman (1992) allow the utility function to have a different degree of curvature over the losses domain than over the gains domain. However, in their empirical analysis, they find that the curvature is identical over gains and losses. As well, if the utility function has more curvature over the losses domain than over the gains domain, the value function will not display loss aversion for large actuarially fair gambles, which goes against empirical evidence. For these reasons, the curvature of the utility function is usually assumed in practice to be the same over gains and losses.
6.
Cf. Bleichrodt and Pinto (2000), Camerer and Ho (1994), Kahneman and Tversky (1979),
Tversky and Kahneman (1992), and Wu and Gonzalez (1996).
7.
This implicitly assumes that s
≤ 1. Although the highest feasible award of damages by the court is a = 1, it is possible that the defendant may be willing to settle for more than this to save on litigation costs. However, this point is made moot by the fact that inequality (5), which describes the values of s under which plaintiff is willing to settle, includes all s > 1.
8.
All figures assume that

=0.6 and/or

=0.7, which are near the center of their range of observed empirical values. Similar qualitative results were found for alternative values of

and

and are available upon request.
23

9.
For purposes of succinctness, some figures that support confirmatory results have been omitted from the paper. These are available from the author upon request.
24

0
Amount of gain/loss
(a)
0.7
0.6
0.5
0.4
0.3
0.2
1
0.9
0.8
0.1
0
0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative probabilty
(b)
Figure 1.
A representative (a) utility function and (b) probability weighting function under
Cumulative Prospect Theory.
25

c min
0.5
0.4
0.3
0.2
0.1
0
0.2
p = .1 p = .3 p = .5
p = .7 p = .9
0.3
0.4
0.5
(a)
0.6
0.7
0.8

0.9
0.5
c min
0.4
0.3
0.2
0.1
p = .1 p = .3 p = .5 p = .7 p = .9
0
0.5
0.6
0.7
0.8
0.9

(b)
Figure 2.
Sensitivity of c min
, the minimum litigation costs for settlement to be pareto-optimal, to
(a)

, the curvature of the utility function, and (b)

, the curvature of the probability weighting function, when the potential court award is 50% of the plaintiff’s loss.

is set to 0.7 in (a) and
 is set to 0.6 in (b). p represents the probability of the plaintiff prevailing at trial.
26

c min
1
0.8
0.6
0.4
0.2
0
0.2
p = .1, p = .9 p = .3, p = .7 p = .5
0.3
0.4
0.5
0.6
(a)
0.7
0.8

0.9
1 c min
0.8
0.6
0.4
0.2
p = .1, p = .9 p = .3, p =.7 p = .5
0
0.5
0.6
0.7
0.8
0.9

(b)
Figure 3.
Sensitivity of c min
, the minimum litigation costs for settlement to be pareto-optimal, to
(a)

, the curvature of the utility function, and (b)

, the curvature of the probability weighting function, when the potential court award is 100% of the plaintiff’s loss.

is set to 0.7 in (a) and

is set to 0.6 in (b). p represents the probability of the plaintiff prevailing at trial.
27

1 c min
0.8
0.6
0.4
0.2
0
0 p = .1 p = .3 p = .5 p = .7 p = .9
50 100 150
(a)
200 250
Potential award as % of loss
300
1 c min
0.8
0.6
0.4
p = .1 p = .3 p = .5 p = .7 p = .9
0.2
0
0 50 100 150 200 250
Potential award as % of loss
300
(b)
Figure 4.
Sensitivity of c min
, the minimum litigation costs for settlement to be pareto-optimal, to the potential court award as a proportion of the plaintiff’s loss when 
= 0.6,

= 0.7, and the coefficient of loss aversion for the two parties is either (a)
λ
= 2.0 or (b)
λ
= 3.0. p represents the probability of the plaintiff prevailing at trial.
28

c min
0.5
0.4
0.3
0.2
0.1
0
0
1 c min
0.8
0.6
0.4
0.2
0
0
20 40 60 80 100
% uncertainty in potential court award
(a)
20 40 60 80 100
% uncertainty in potential court award
(b) p = .1 p = .3 p = .5 p = .7 p = .9 p = .1 p = .3 p = .5 p = .7 p = .9
29

1 c min
0.8
0.6
0.4
0.2
p = .1 p = .3 p = .5 p = .7 p = .9
0
0 20 40 60 80 100
% uncertainty in potential court award
(c)
Figure 5.
Sensitivity of c min
, the minimum litigation costs for settlement to be pareto-optimal, to the percentage uncertainty in the potential court award when

= 0.6,

= 0.7,
λ
= 2.5, and the amount of the potential court award is either (a) 50%, (b) 100%, or (c) 200% of the plaintiff’s loss.. p represents the probability of the plaintiff prevailing at trial.
30