Multiple empirical studies find that juries/courts take account of potential harm in the determination of punitive damages. The received view in economic theory, however, is that punitive damages should not depend on potential harm. The purpose of this note is to provide an efficiency rationale for the courts'' behavior. Our particular result is that when the punitive damage multiplier decreases as the actual harm increases, the optimal multiplier does depend on the potential harm.Compensatory damages, potential harm, punitive damages

Bharat Bhole

Jeffrey Wagner

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 2 
  
On the consideration of potential harm in the award of punitive damages 
  
 
 
Bharat Bhole  
Rochester Institute of Technology 
Jeffrey Wagner  
Rochester Institute of Technology
Abstract 
Multiple empirical studies find that juries/courts take account of potential harm in the determination of punitive 
damages. The received view in economic theory, however, is that punitive damages should not depend on potential 
harm. The purpose of this note is to provide an efficiency rationale for the courts'' behavior. Our particular result is 
that when the punitive damage multiplier decreases as the actual harm increases, the optimal multiplier does depend on 
the potential harm.
We would like to thank seminar participants at Binghamton University and session participants at the 2008 Southern Economic Association 
(particularly our discussant, Scott Wentland) for several helpful comments on our ideas for this paper. 
Citation: Bharat Bhole and Jeffrey Wagner, (2009) ''On the consideration of potential harm in the award of punitive damages'', Economics 
Bulletin, Vol. 29 no.2 pp. 1102-1106. 
Submitted: Jan 28 2009.   Published: May 22, 2009. 
 
       1 
1. Introduction 
 
This paper sheds light on the following puzzle: while multiple court opinions have found it ap-
propriate to use potential harm in the determination of punitive damage awards, the law-and-
economics literature suggests that only actual harm should typically be taken into account. For 
example, as noted by Polinsky and Shavell (1998, 914), “potential harm also served as a basis for 
the  trial  court's  upholding  the  $5 billion  punitive  damages  verdict  in  the  Exxon  Valdez  oil 
spill litigation; the court noted that, although 11 million gallons of oil spilled, another 45 million 
gallons in the Exxon Valdez could have spilled, making the potential harm much higher.”  Also, 
in State Farm v. Campbell (2003) the U.S. Supreme Court majority wrote “…ratios [of punitive 
to compensatory damages] greater than those which the Supreme Court has previously upheld 
may comport with due-process, where a particularly egregious act has resulted in only a small 
amount of economic damages.”  The law-and-economics literature in general, and Polinsky and 
Shavell (1998, 915) in particular, maintain that penalties assessed according to potential harm 
rather than actual harm are excessive, for the injurer would rationally take account of potential 
harm when computing the expected harm and therefore when computing the optimal amount of 
care to take.  We show below that the independence of the optimal punitive damages multiplier 
from the potential harm, as suggested in Polinsky and Shavell (1998), is desirable only if exactly 
the same multiplier is used across all damage levels.  If the multiplier when damages are high is 
lower than the penalty multiplier when damages are low, then the optimal value of the latter does 
depend on potential harm, and increases with potential harm.  Empirical evidence suggests that 
penalty multipliers on average do fall as compensatory damages increase (see, e.g., Eisenberg et 
al. (1997), Karpoff and Lott (1999), and Hersch and Viscusi (2004)).  These studies regress puni-
tive damages on compensatory damages and find that punitive damages increase with compensa-
tory damages at a decreasing rate, indicating that the ratio of punitive damages to compensatory 
damages falls as compensatory damages increase.  Since compensatory damages reflect the ac-
tual harm, this suggests that the use of potential harm in the determination of punitive damages, 
as courts have done, is desirable from an efficiency point of view. 
  We are not the first to  suggest that it may be efficient to take potential harm into account 
in the determination of punitive damages.  Hylton (1998), for example, examining the case of 
Jacque v. Steenberg Homes (1997, Supreme Court of Wisconsin)
1 notes that the Polinsky and 
Shavell paradigm would yield total damages equal to zero when one should perhaps also recog-
nize and deter the “secondary costs” of willful trespass.  However, Hylton (1998) refers to sec-
ondary costs that are not covered by compensatory damages under the current law, and therefore 
an injurer would not take these costs into account in the absence of punitive damages.  Polinsky 
and Shavell (1998), on the other hand, refer to potential harm as the highest harm that the injurer 
can directly cause the plaintiff and therefore is responsible for it in the form of compensatory 
damages, when such harm actually occurs.  We show below that punitive damages should be a 
function of potential harm even when it is defined as in Polinsky and Shavell (1998) and when 
secondary costs are zero. 
  Our note proceeds as follows.  We first describe the basic model in Section 2 and illus-
trate the Polinsky and Shavell (1998) perspective within that model.  Then in Section 3, we pre-
sent our result that the higher is the potential harm, the higher is the optimal deterrence punitive 
damages multiplier.  We conclude with a few brief comments.  
                                                 
1 In this case, the court awarded $1 compensatory damages and $100,000 punitive damages to Jacque when Steen-
berg Homes deliberately cut across Jacque’s private property to deliver a mobile home.   2 
 
2.  The Basic Model 
 
Suppose a potential injurer engages in an activity that yields social benefit B but may also result 
in an accident.  Let  denote the cost of care x and let p(x) denote the associated likelihood of 
an accident.  In the event of an accident, suppose damage can be either low, L, with probability π 
or high, H, with probability 1- π.  Let q denote the probability of escaping conviction.  Assume 
that: 
 
(A.1)    
(A.2)   . 
 
Assumption (A.1) means that the cost of care increases at an increasing rate, while assumption 
(A.2) means that the likelihood of an accident falls at a decreasing rate with care level.  Given 
these assumptions, the social welfare from the potential injurer’s activity is: 
 
€ 
W(x) = B−c(x)− p(x) πL+ (1−π)H [ ].          (1) 
 
This implies that the first-best care level is: 
 
€ 
x
* = argmin
x c(x)+ p(x) πL+ (1−π)H [ ].          (2) 
 
In  the  absence  of  a  penalty  multiplier,  the  injurer  exercises  care  level 
 which is less than  .  As suggested in the literature,  the 
injurer can be motivated to take first-best care by imposing a penalty multiplier equal to (1/q), 
which is independent of the harm levels, L and H.  Based on this, Polinsky and Shavell (1998, 
914) maintain that damages should not depend upon the expected or potential harm, but should 
rather depend solely upon the probability of escaping conviction.  This, however, assumes that 
the same multiplier is imposed across all levels of harm.  We show below that if the size of mul-
tiplier is different for different levels of harm—in particular, if the multiplier is smaller for 
greater levels of harm—then the optimal multiplier when the actual harm is low turns out to be a 
function of the potential harm.   
   
3. Potential Harm and Punitive Damages 
 
Let m denote the multiplier when the harm is low (L) and   the multiplier when the harm is 
high (H), where  .  For any given m, the potential injurer will choose care x for which,  
 
          (3) 
 
To ensure that the actor exercises care  , we need: 
 
        (4) 
   3 
or, we need: 
   
              (5) 
 
Differentiating the RHS of (5) with respect to H gives 
€ 
∂m
∂H
=
1
q
(1−π)πL(1−α)
πL+ (1−π)αH [ ]
2 > 0.  That is, 
holding other things equal, the higher is H, the higher is the optimal m.  In other words, the size 
of the optimal multiplier when the actual harm turns out to be low (L) depends upon the potential 
harm, H, if the multiplier when the actual harm is high is smaller than the multiplier when the 
actual harm is low.  As shown by Eisenberg et al. (1997), Karpoff and Lott (1999), and Hersch 
and Viscusi (2004), the empirically-observed multiplier is indeed smaller when the actual harm 
is high than when it is low.  For example, Karpoff and Lott (1999, 541, Table 3) regress punitive 
damages P on compensatory awards C, compensatory awards squared (C
2 ) and some other vari-
ables, and find that the coefficient on C
2 is negative.  Letting β denote this coefficient and differ-
entiating the penalty multiplier with respect to C, we have: 
  
                (6) 
 
which implies that the penalty multiplier decreases as C increases.  Note that even if we increase 
H and decrease L such that expected harm and therefore optimal care remains unchanged, we 
still find m in equation (5) to be an increasing function of H.  That is, the increase in m referred 
to above is not because of an increase in the optimal level of care that needs to be induced when 
H increases.  We state this result in the following proposition. 
 
Proposition. If the penalty multiplier when the actual harm is low, L, is greater than the penalty 
multiplier when the actual harm is high, H, then the optimal size of the multiplier when harm 
turns out to be low is a function of potential harm. 
 
The intuition behind this proposition is the following.  A smaller multiplier   when 
harm is H, compared to the multiplier (m) when the harm is L, can be interpreted as using the 
same multiplier m for both harm levels but reducing the payment by  when the actual 
harm is H (since  ).  To ensure that sufficient incentive exists for the 
injurer to exercise optimal care, m has to be increased to make up for this reduction in expected 
payment.  The greater the reduction in expected payment, the greater has to be the amount by 
which m is increased.  Note that the reduction  is an increasing function of H, indicat-
ing that the higher is H the higher m has to be. 
  We  should  take  care  to  note  that  our  model  does  not  explain  why  the  empirically-
observed multiplier falls as the actual harm increases.  This could be motivated by factors such 
as caps on damages or judgment-proofness.  Or perhaps, as Karpoff and Lott (1999, 540) note, 
juries simply view compensatory and punitive damages as substitutes, and for this reason, they 
are negatively related.    4 
  Finally, note that our interpretation of a smaller multiplier when harm is H as reduction in 
damages when harm is H should not be confused with liability being smaller than the realized 
harm.  The liability imposed on the defendant can be greater than H, i.e.,   can be greater than 
one.  We are saying that even if the penalty when harm is H exceeds H, as long as  , it 
makes sense to make the multiplier when actual harm turns out to be low (L) dependent on H and 
an increasing function of H. 
 
4. Concluding Comments 
 
It is observed that courts take account of potential harm in the determination of punitive dam-
ages.  The received view in economic theory is that punitive damages should not depend on po-
tential harm.  The purpose of our paper is to provide an efficiency rationale for the courts’ behav-
ior.  We first observe that the empirical punitive damage multiplier decreases as the actual harm 
increases, and we show that when this is the case, the optimal multiplier does depend on the po-
tential harm.  Our model does not explain why the empirical multiplier falls as the actual harm 
increases; generalizing the model to endogenize this aspect is an important next step.   
 
References 
 
Eisenberg, T., J. Goerdt, B. Ostrom, D. Rottman, and M. T. Wells (1997) “The Predictability of 
Punitive Damages” Journal of Legal Studies 26, 623-661. 
 
Hersch, J., and W. K. Viscusi (2004) “Punitive Damages: How Judges and Juries Perform” 
Journal of Legal Studies 33, 1-36. 
 
Hylton, K. N. (1998) “Punitive Damages and the Economic Theory of Penalties” Georgetown 
Law Journal 87, 421-471. 
 
Karpoff, J. M., and J. Lott, Jr. (1999) “On the Determinants and Importance of Punitive Damage 
Awards” The Journal of Law and Economics 42, 527-573. 
 
Polinsky, A. M., and S. Shavell (1998) “Punitive Damages: An Economic Analysis” Harvard 
Law Review 111, 869-962. 

On the consideration of potential harm in the award of punitive damages

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