7/28/2019 Error IRLE

1/5

Internatronal Review of Law and Economics (1986), 6 (101-105)

NOTESOPTIMAL SUBSIDIES AND DAMAGES IN THE

PRESENCE OF JUDICIAL ERRORI. P. L. PNG*

Graduate School of Management, University of California, Los Angeles, CA 90024,USA

1. INTRODUCTIONAll men are liable to error (Locke, 1632-1704).

Many regulations and legal rules are framed in terms of standards of behaviour;regulators and courts are liable to make mistakes in enforcing such standards. Forinstance, some firms that did not emit more pollutants than the standard may befined while others that did violate the standard escape unpunished. Similarly, a courtmay find a defendant in breach of contract when in fact, he had performed, and, viceversa, find a defendant who had breached his contract not in breach.

The essential problem is that the standards are set in terms of behaviour that isdifficult for the regulator/court to observe. So errors will be made in enforcement.The question is then how to adjust for the likelihood of error. One method is toswitch to another instrument. Another is to vary the standard.* In this paper, I shallpresent a third alternative: it is to couple an adjustment to the sanction with anappropriate subsidy. The model will refer to judicial error, but is equally applicableto regulatory mistake.

In a trial, a court may err in favour of the defendant (Type-I error) or in favour ofthe plaintiff/prosecutor (Type-II error). These errors impose direct costs on theparties before the court. An example of such a direct cost is the cost of imprisonmentof a person mistakenly convicted of a criminal offence. Equally important, since thelegal system exists to influence individuals choices of activity and care, the prospectof court errors will give rise to indirect costs by affecting such choices.

The objective of this paper is to focus on the indirect costs and in particular, topropose methods to correct for both types of error so as to ensure that individuals willmake socially efficient choices of activity and care.3 The main results of this papermay be summarized as follows. First, to the extent that an individual who has notviolated the law will be made to pay damages, the cost of violating the law, relative tonot doing so, will be reduced. The result will be more violations of the law. Hence, toensure that the choice between violation and non-violation reflects the social cost, it*I am grateful to the Center for Economic Policy Research, Stanford University, and the AssociationInternationale pour 1Etude de IEconomie de IAssurance for financial support, and to S. A. Lippman,A. M. Polinsky, and the referees of the Revrew for their advice.014-G188/86/01 0101-05 $03.00 0 1986 Butterworth & Co (Pubhshers) Ltd

7/28/2019 Error IRLE

2/5

102 Optimal subsidi es and damages in the presence of udi cial erroris necessary that the sanction, when assessed, be higher than the social cost.Secondly, the probability that non-violators may be subject to the sanction, however,will have a chilling effect on participation in the activity that gives rise to the likeli-hood of being mistakenly assessed a sanction. Therefore, a subsidy is required toensure that the degree of participation in the activity is socially optimal.

II. MODEL OF OPTIMAL SUBSIDY AND DAMAGESFor concreteness, 1 shall refer to an example in torts: a motorist who drives along aroad will with some probability be involved in an accident and injure a pedestrian.The probability of accident and the harm caused to the pedestrian in the event ofaccident depend on the degree of care taken by the driver. For simplicity, assume thatthe motorist drives either with due care or does not.

Let the probability of accident be Q~ f the motorist takes due care and a, otherwise,where ~,

7/28/2019 Error IRLE

3/5

1. P. L. PNGa,[Pn(S+B,)+(l-Pn)(S+B,-D)l+(l-a,)B,

=B,+a, [S-(1 -p,)Dl.103

The social benefit less cost is B, - a,H,, hence for efficiency, it is necessary thatB,+a,[S-(1 -p,)D] = B,-a,H,,, which implies that a,[(1 -p,)D-Sl =a,H,. Butit was shown earlier that S=p,D- H,. Thus,

D = Hn - Hc1 - PC - Pn . (2)

Damages are paid only by those drivers whom the court deems not to have takendue care. The intuitive reason for the adjustment to damages is that for efficiency,the incremental expected damages faced by a driver who chooses less t han due care,(1 -pC -p,)D, must be equal to the i ncrement al harm caused, H , -H ,. The efficientquantum of damages is1. Increasing in the incremental harm caused when a person drives without due care

rather than with due care.2. Increasing in the probability that a driver who drives without due care will not

pay damages, that is, will get away with the offence (Type-I error).3. Increasing in the probability that a driver who drives without due care will not

pay damages, that is, will be wrongly punished (Type-II error).The Proposition shows that the optimal subsidy that must be paid to all driversinvolved in accidents is S = - H, +pCD. This formula consists of two terms. The first,

-H,, is negative: it internalizes the harm caused by a motorist who drives with duecare and is involved in an accident. The second term is positive and is an adjustmentto ameliorate the chilling effect of the possibility that a motorist who takes due careand meets with an accident will be required to pay damages.

Depending on the values of the parameters, S may be either a tax or a subsidy. Forinstance, if the courts have a zero probability of requiring motorists who have takendue care to pay damages, that is, if pC=O, then S= -H,.

III. APPLICATIONS TO SUBSTANTIVE LAWThe principle that the design of sanctions must take account of the probabilities ofboth types of error extends quite generally to other areas of law. It indicates, forinstance, that the theory of optimal criminal penalties advocated by Becker must bequalified. Becker argued that to elicit efficient choice, the sanction for an offenceshould be set equal to the harm caused, inflated by the probability of non-conviction.This prescription ignores the likelihood of mistaken conviction. The Becker formulais, however, a close approximation since one effect of the high standard of proof incriminal procedure is to hold down the likelihood of mistaken conviction.

In civil procedure, the standard of proof is typically that of preponderance of theevidence, which requires judgment for the plaintiff if, on balance, the evidencefavours the plaintiff.5 Under the preponderance standard, the probability of error infavour of the plaintiff need not be negligible. As shown in the Proposition, this errorwill affect individuals choices of whether to participate in the activity, and the degreeofcare that they take if they participate.

An important justification for the application of punitive damages in tort law has

7/28/2019 Error IRLE

4/5

104 Optimal subsidies and damages m the presence of judicial errorbeen the argument that insofar as tortfeasors do not pay damages with certainty,compensatory damages will leave violation under-deterred relative to the efficientlevel.j An implication of the present paper is that the argument in favour of punitivedamages is still stronger in those situations where there is a non-negligible probabilitythat non-violators must pay damages.

Farber made a parallel extension from the Becker theory to contract law. Henoted that in many contract settings, breach may be difficult to detect, as, forinstance, in contracts for the construction of large and complex buildings. Therefore,to ensure an efficient choice between breach and performance, super-compensatorydamages are necessary. Now just as breach may be difficult to detect, performancemay be hard to observe: it may be easy to see the cracks in the building, but are theydue to breach of contract? Where there is some probability that a contractor in per-formance may be made to pay damages, Farbers prescription will not be sufficient:damages must be adjusted still higher.

The second aspect of the Proposition was that a subsidy must be paid to all whomeet with accidents, regardless of the degree of care that they are deemed to havetaken. The parallel in the contract example is a subsidy to all contractors whosebuildings show cracks. Such a subsidy is necessary to induce an efficient amount ofdriving and of contracting for building construction. In practice, public support ofthe civil court system may be viewed as a means by which the required subsidy isprovided. Admittedly, this may be an imperfect method because only a smallproportion of all disputes are taken to trial, but it should be noted that the subsidyhas a wider impact than may seem at first because it does affect the disputantsdecision whether to go to court.

IV. CONCLUSIONThere is now considerable recognition that where there is some likelihood thatviolators will not pay damages, optimal deterrence requires that the damages, whenpaid, be inflated to take account of that likelihood.* The central point of this paper isthat equal attention is due to the probability that non-violators must pay damages.

In an important insight, Posner9 warned that the possibility of wrongful convictionwould undermine the deterrent value of criminal sanctions: punishing the innocent. . . increases the number of crimes. The logical corollary of this is that to ensurethat the choices of care are efficient, damages must be made larger. They must belarge enough that, in expectation, the increment in damages faced by a party whotakes less than due care is equal to the incremental harm caused.

It is crucial to notice too that the possibility of error in favour of the plaintiff willhave a chilling effect on the extent of participation in the activity. To the degree that aperson who takes due care and is involved in an accident must pay damages, the costof participation with due care is raised, and, at the margin, some will be deterredfrom participation altogether. To ensure that the decision whether to participate ornot is made efficiently, it is necessary that a subsidy be given to all who meet withaccidents, regardless of the degree of care that they are deemed to have taken.It has been assumed in this paper that individuals were risk-neutral. In a modelwith only error in favour of the defendant, Polinsky and Shavelli showed that ifindividuals were risk-averse, the optimal sanction would be less than the Beckerprescription. The reason is that the risk introduced by the prospect of less thancertain conviction itself has a deterrent effect. In the more general case with bothtypes of error, the implication of risk aversion for the optimal sanction is ambiguous.

7/28/2019 Error IRLE

5/5

I. P. L. PNG 105This is because with two types of error, both violation and non-violation give rise torisk. Hence, the appropriate adjustment of the risk-neutral prescription must dependon the difference between the two risk premia.

REFERENCES AND NOTES1. See, for instance, M. L. Weitzman, Prices vs. Quantities, (1974) 41 Rev. Econ. Stud. 477.2. See, for instance, J. E. Calfee and R. Craswell, Some Effects of Uncertainty on

Compliance with Legal Standards, (1984) 70 Virginia Law Rev. 965; and M. F. Grady,A New Positive Economic Theory of Negligence, (1983) 92 Yale Law J. 799.3. For studies that emphasize the direct costs of court error, see R. A. Posner. An EconomicApproach to Legal Procedure and Judicial Administration, (1973) 2 J. Legal Stud. 39;

D. Wittman, Two Views of Procedure, (1974) 3 J. Legal Stud. 249; D. Kaye, The Limitsof the Preponderance of the Evidence Standard: Justifiably Naked Statistical Evidenceand Multiple Causation, (1982) Am. Bar Foundation Res. J. 487; and especially, G.Tullock, Trml s on Tr i al : The Pure Theory of Legal Procedure, Columbia University Press(1980).

4. G. S. Becker, Crime and Punishment: An Economic Approach, (1968) 76 J. Polit. Econ.169.5. A stiffer standard that is less frequently applied in civil cases is that of clear and convincing

evidence. See Posner, supra, note 3.6. See, for instance, D. D. Ellis, Jr, Fairness and Efficiency in the Law of PunitiveDamages, (1982) 56 Southern California Law Rev. 1; and G. T. Schwartz, Deterrenceand Punishment in the Common Law of Punitive Damages: A Comment, (1982) 56Southern California Law Rev. 133.

7. D. A. Farber, Reassessing the Economic Efficiency of Compensatory Damages forBreach of Contract, (1980) 66 Virginia Law Rev. 1443.8. See, for instance, Report 98-355 of the House of Representatives Committee on Energy

and Commerce, 15 September 1983, pp. 7-8, where this argument was employed tosupport a provision for treble damages for insider trading violations.9. Supru, note 3, p. 411.10. A. M. Polinsky and S. Shavell, The Optimal Tradeoff Between the Probability and theMagnitude of Fines, (1979) 69 Am. Econ. Rev. 880.11. Supru, note 4.