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Citation: 61 S. Cal. L. Rev. 137 1987-1988
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BAYESIAN FACT-FINDING AND
EFFICIENCY: TOWARD AN
ECONOMIC THEORY OF
LIABILITY UNDER
UNCERTAINTY
JASON S. JOHNSTON*
A basic assumption underlying the economic analysis of law is that
substantive legal rules affect the behavioral incentives of persons subject
to those rules. However, if an actor is truly sophisticated enough to
respond to the incentives set by substantive rules, then the actor surely
will not respond to the nominal rule, but to the rule as actually interpreted and enforced in the legal process. If the substantive legal rule is
fault based and assigns liability only if a jury or judge concludes that the
actor violated the nominal legal standard determining fault, then the economic incentives created by the nominal standard will depend upon the
process of fault determination.
Despite the crucial importance to economic incentives of the process
by which fault is determined, even those who have analyzed the impact
of an imperfect, error prone legal process on the efficiency of fault based
liability rules such as negligence, have failed to model the process of legal
decisionmaking with any degree of specificity.' In particular, the law
* Associate Professor of Law, Vermont Law School. A.B. 1978, Dartmouth College; J.D.
1981, Ph.D. 1984 The University of Michigan. This article is based on my doctoral dissertation, and
I give thanks to Lawrence Blume, James Krier, and especially Daniel Rubinfeld for their encouragement and support in this endeavor. Helpful comments on earlier versions of this article were made
by Richard Craswell, Daniel Farber, Mitchell Polinsky, George Priest, Steven Shavell, and by participants in the Yale Law School Civil Liability Workshop. I am of course responsible for any
remaining errors.
1. The effect of error on the incentives created by liability rules was first studied by Diamond,
Single Activity Accidents, 3 J. LEGAL STUD. 107, 123-40 (1974), and has been examined more
recently in C. GOETZ, CASES AND MATERIALS ON LAW AND ECONOMICS 299-303 (1984);
S. SHAVELL, ECONOMIC ANALYSIS OF AccIDENT LAW, ch. 4, part D and app. (1987); Calfee &
Craswell, Some Effects of Uncertainty on Compliance with Legal Standards, 70 VA. L. REv. 965
(1984); Craswell & Calfee, Deterrenceand Uncertain Legal Standards, 2 J. LAW, ECON. & ORG. 279
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and economics literature has failed to deal with the inherent imperfec-
tions of evidence as a monitor or signal of actual behavior. There is,
however, a substantial literature in the economics of information which
investigates how to structure contracts to create optimal incentives when
a principal can only imperfectly monitor an agent's effort.2 The problem
of structuring an optimal liability rule when the court system only has
evidence of care, rather than actual knowledge of care, bears great struc-
tural similarity to the generic principal-agent problem.'
This disparity between evidence and actual conduct has also been
recognized and thoroughly investigated in the contemporary evidence
literature. The use of statistical models, particularly Bayesian models,
has yielded significant new insights into the legal process and evidentiary
rules.4
(1986); Grady, A New Positive Economic Theory ofNegligence, 92 YALE L.J. 799 (1983); Haddock &
Curran, An Economic Theory of Comparative Negligence, 14 J. LEGAL STUD. 49, 63-66 (1985).
In a somewhat different context, Calabresi & Klevorick, Four Tests for Liability in Torts, 14 J.
LEGAL STUD. 585, 617-19, 621 (1985), argue that the choice between variants of negligence and
strict liability depends upon which combination of tests is most effective in reducing the more costly
of private decisionmaking errors and errors by the social decisionmaker. Their article is significant
also in observing the trade-off between shifting the substantive basis of liability and altering the
burden of proof. See id. at 592-93, 601. I analyze this trade-off in Part II, sections C and D.
2. The principal-agent literature is vast. The work most relevant to the present approach falls
into two groups. The first group develops the monotone likelihood ratio property which I use to
define a rational fact-finding process. See Milgrom, Good News andBad News: RepresentationTheorems and Applications, 12 BELL J. ECON. 380 (1981); Grossman & Hart, An Analysis of the PrincipalAgent Problem, 51 EONOMETRICA 7 (1983); Rogerson, The First-OrderApproach to Principal-Agent
Problems, 53 ECONOMETRICA 1357 (1985). These articles show how this property is necessary, but
not sufficient, for general reward schemes to be rational in the sense that the wage or reward (of a
firm manager, for example) is non-decreasing in the observed outcome (firm profit, for example).
The second group shows how even imperfect monitoring of the agent's effort or conduct will be
utilized in pareto-optimal contracts. See Harris & Raviv, OptimalIncentive Contractswith Imperfect
Information, 20 J. ECON. THEORY 231 (1979); see also Holmstrom, Moral Hazardand Observability,
10 BELL J. ECON. 74 (1979); Shavell, Risk Sharingand Incentives in the Principaland Agent Relationship, 10 BELL J. ECON. 55 (1979). For an excellent overview of the main results from this
literature, see 0. Hart & B. Holmstron, The Theory of Contracts (Working Paper No. 418 MIT
Dept. of Economics, March, 1986). The reader interested in the formal relationship between the
argument made here and the principal-agent literature should consult J. Johnston, Imperfect Decisionmaking and Optimal Civil Liability (1987) (unpublished manuscript), where I formally develop
the model and results presented in this Article.
3. See Arrow, The Economics ofAgency, in PRINCIPALS AND AGENTS: THE STRUCTURE OF
BUSINESS 37, 45-46 (J. Pratt and R. Zeckhouser eds., 1985) (interpreting the analysis by Shavell,
Holmstrom, and Harris & Raviv, see supra note 2, as implying that negligence, which involves monitoring of the agent's (defendant's) care, is efficient when the agent is risk averse, whereas strict
liability is efficient under risk neutrality).
4. For a comprehensive account of the development and current use of the Bayesian approach
in evidence scholarship, see the papers from the Boston University School of Law, Symposium on
Probability and Inference in the Law of Evidence, 66 B.U.L. REV. 377 (1986). Prominent applications of Bayesian decision theory to the analysis of evidentiary rules are found in Kaplan, Decision
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ECONOMIC THEORY OF LIABILITY
This Article draws from these related studies and attempts to further the economic analysis of liability rules by developing a relatively
formal model of how fault can be inferred from limited and imperfect
evidence. The model posits a legal decisionmaker who acts as a Bayesian
statistician asked to choose between the competing hypotheses of guilt
and innocence. This model is similar to those utilized in the evidence
literature and incorporates more institutional detail than does the typical
principal-agent model. The fundamental insight underlying this model
of the legal process is that errors are inevitable when the legal fact finder
must determine fault from the limited and imperfectly informative evidence presented at trial. These errors mean that there is an inherent separation between the announced legal rule, a nominal standard defining
unacceptable behavior, and the administered legal rule, a legal decisionmaker's statement about allowable inferences of fault based on the
evidence. Equivalently, and even more significantly for the incentives
created by the law, errors in the process of fault determination imply that
the reality of actual conduct is inherently distorted at trial, and that the
message sent by legal rules is blurred and uncertain.
Conclusions about how incentives are affected by this distortion
depend crucially on the underlying assumptions about the way the distortion takes place and about how much actors subject to the legal rule
know about the distorting mechanism. This Article posits a highly
sophisticated type of actor, who responds not to the announced legal
rule, but to the legal rule as administered. The incentives for compliance
by this kind of actor are determined not by a nominal legal standard
which says, for example, that negligence will be found if the defendant's
care level is below some required level, but by an evidentiary standard,
which tells the defendant that negligence will be found only if the evidence of care is in some sense "bad enough." Thus, this Article is concerned with how legal rules deter those actors who respond not to what
the law says they should do, but to what the law says is enough evidence
to escape punishment. 5
Theory and the FactfindingProcess, 20 STAN. L. REv. 1065 (1968) (analyzing the burden of proof);
Kaye, Probability Theory Meets Res Ipsa Loquitur, 77 MICH. L. REv. 1456 (1979); Kornstein, A
Bayesian Analysis of Harmless Error,5 J. LEGAL STUD. 121 (1976); Lempert, Modeling Relevance,
75 MicH. L. REv. 1021 (1977).
5. This focus on legally sophisticated actors is crucial to the results presented below. It distinguishes this Article, which takes an instrumental approach to the design of efficient legal rules,
from Professor Ronald Nesson's recent analysis of directed verdicts. See Nesson, The Evidence or
the Event? On JudicialProofand the Acceptability of Verdicts, 98 HARV. L. REv. 1357 (1985). For
although he too starts from the insight that inferences about reality drawn from trial evidence differ
inherently from reality itself, he concludes that this disparity implies that the standard for directed
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Part I of this Article develops a model of Bayesian fact-finding
which can be used to show how legal rules deter when they are viewed
merely as determining evidentiary requirements for liability. Although
Bayesian models in the evidence literature are now quite commonplace,
the model used here is novel in the economic analysis of liability rules,
and I therefore describe it in some detail.
Part II applies the model to analyze a number of issues raised by
uncertainty in fault determination. I demonstrate that the ordinary negligence rule-a rule imposing liability if the jury concludes that failure to
take reasonable care was more likely than compliance with this standard-is not efficient when errors are inevitable in fact-finding. In particular, this Article shows that although the preponderance of the evidence
civil burden of proof minimizes the probability of an erroneous decision
regarding fault, it leaves too high a risk of failing to punish the negligent
and of punishing the careful. The preponderance burden can induce too
little or too much investment in safety from the standpoint of minimizing
the sum of accident losses and safety costs.
Part II next applies the Bayesian fact-finding model to investigate
the economically optimal response to uncertainty. I first show that the
legal process is in a certain sense most random and most likely to overdeter when any violation of the legal standard, no matter how small, is
punished. This suggests that one way to eliminate over-deterrence is to
reduce the legal standard or require a more extreme departure for liability. Another method of eliminating false liability findings revealed by the
model is to increase the plaintiff's burden of proof. Although these liability restricting rule changes weaken incentives to take due care, this side
effect of eliminating the incentive to take too much care can be offset
with high punitive damages. The model thus suggests that suitably safeguarded punitive liability can restore optimal incentives in the world of
uncertain liability determination.
Perhaps even more significantly, the model also shows how overly
expansive interpretations of substantive liability standards-motivated
verdicts must be designed to make verdicts appear to the public as statements about the events
ostensibly being judged, rather than about the evidence. See id. at 1358, 1360-61. Professor Nesson
apparently wishes to disguise the qualified, uncertain nature of legal judgments both in order to
retain the appearance of ritual certainty and to ensure that legal judgments deter. See id. Insofar as
his "acceptability" thesis is justified as an instrument of deterrence, it shows the radical consequences of the underlying informational assumption made here. Because I assume that the actors
subject to legal rules are sophisticated enough to respond to the evidentiary implications of their
behavior, it is not necessary to make verdicts acceptable-they deter even when cast merely as statements about degrees of certainty of guilt achieved after observing the evidence.
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perhaps by noneconomic goals such as compensation and loss-shifting
and loss-spreading-may be offset and transformed into efficient standards by reducing the announced or nominal standard or requiring a
greater shortfall from the announced standard for liability. Increasing
the burden of proof will not alone suffice to eliminate over-deterrence due
to such expansions in substantive liability. On the other hand, the model
provides insight into polar opposite rule changes, such as res ipsa loquitur. The plaintiff's burden should be reduced or shifted to the defendant
when there is asymmetric access to the evidence, or, more specifically,
whenever defendants know that a strong case indicating compliance in
fact reflects the plaintiff's limited access to evidence and that jurors do
not take this limited access into account.
The specific questions analyzed in Part II are merely illustrative of
the range of issues which can be examined in this general model. The
model's larger contribution is in opening up the "black box" of legal
decisionmaking to allow systematic analysis of how richly described legal
rules consisting of a burden of proof and substantive standard affect economic incentives to choose between safety and risk. Underlying this formal development is the fundamental insight that uncertainty in the fault
litigation means nominal legal rules must differ from optimal rules of
conduct if they are to create incentives for legally sophisticated, deliberative actors to choose optimal conduct. Punitive liability is one instance
of this principle where a system which nominally punishes only extreme
departures from social norms in fact induces compliance with those
norms.
The Article concludes in Part III by discussing some caveats to the
results developed in Part II, and by presenting several issues that must be
addressed in order to fully access the practical desirability of the theoretically efficient liability policies developed here.
I. A MODEL OF RATIONAL FACT-FINDING
This section develops a simplified model of rational fact-finding.
The purpose of the model is primarily heuristic, to provide a reasonable,
yet rigorous description of the fact-finding process, a description which
helps to illuminate and facilitates the design of solutions to the problems
caused by uncertain fact-finding, and which formalizes the important
relationship between the defendant's actual conduct and the juror's belief
about the defendant's conduct, a belief which is formed on the basis of
the limited evidence presented at trial.
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By formalizing this relationship, the model of fact-finding developed
in this section enables us to see how changing the burden of proof
directly alters the evidence required to find guilt. If the defendant perceives trial evidence as a random sample of witness reports, documents,
and the like, the character of which depends on its actual choice of care,
then changing the evidentiary requirements for guilt changes the defendant's perceptions of the likelihood of guilt, given its actual care choice.
The likelihood of being found liable is a primary economic determinant
of the defendant's behavior, and thus the fact-finding model set out below
shows how changing the burden of proof changes the incentive effects of
a fault based liability rule. The model is used first to analyze why negligence liability is not generally efficient when there is uncertainty due to
errors in fact-finding, and then to explore optimal responses to
uncertainty.
Two types of errors are possible in a fault based liability system.
False negatives are erroneous decisions that the defendant was not at
fault. False positives are erroneous determinations that the defendant
was at fault and should be held liable. This Article considers two kinds
of uncertainty in the determination of fault which give rise to false positives and false negatives. The first kind of uncertainty is that which
arises from juror fact-finding errors. Even if the juror behaves as a
"rational" fact finder (in a sense to be made more concrete below), the
juror will inevitably make errors in inferring the defendant's actual care
level and in deciding what would have constituted reasonable care under
the circumstances. Second, the juror may err in setting the legal standard of care against which fault is measured, not because of fact-finding
difficulties, but because the juror's view of the standard differs from the
desired level.
These two kinds of uncertainty will be referred to as uncertainty in
fact-finding and uncertainty in standard setting, respectively. Because
they have somewhat different policy implications, each kind of uncertainty will be analyzed separately. 6 There are, however, some assumptions which will be maintained throughout Parts I, II, and III, regardless
of the type of uncertainty under consideration.
I assume that the defendant is a profit maximizing firm which
engages in an activity that runs a risk of causing harm to other individuals in society. The defendant firm is able to take steps to reduce the
likelihood or probability that harm occurs, but victims are passive in that
6.
Uncertainty in standard setting is analyzed infra Part II, section D.
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they can do nothing to affect either the probability or the gravity of the
injuries they suffer. The firm is sued by the victim whenever harm
occurs, and it is never sued when a victim's harm was inflicted by some
other cause. If sued, the firm is found liable if and only if it is found to
have been at fault in causing the harm, which means that it is found to
have taken less care to reduce the probability of harm than is required by
the legal standard. If the firm is found liable, it must pay money damages to the victim; otherwise it pays nothing. Suit is costless to society
and to the individual parties. Settlement before trial is ruled out, so that
whenever suit is brought, a trial to determine whether the firm was at
fault necessarily follows. The firm is risk neutral, and therefore is concerned only with its expected damages, rather than with a measure of the
cost of possible legal liability which also includes loss due to risk bearing.
These assumptions are made in order to focus solely on uncertainty in
liability determination due to the jury.
I also usually assume that the juror is the fact finder and the standard setter, and that the judge is the social policymaker. This latter
assumption ensures that society's goals are identical to the judge's goals,
and removes yet another source of uncertainty in the determination of
fault: varying judicial attitudes regarding the purposes of legal liability
and the meaning of fault.
Finally, I will continue to refer simply to the "juror" rather than the
"jury," since the behavior of the jury as a decisionmaking body composed of diverse individuals is beyond the scope of this Article.7
I assume that an essential characteristic of any rational fact-finding
process is that the evidence presented at trial reflects randomly (i.e.,
probabilistically), the reality it purports to portray.8 In a suit involving
the alleged negligence of a hospital in failing to provide adequate postsurgical care to a patient given large doses of morphine, testimony by
7. For theoretical models of how juries composed of several heterogeneous individuals deliberate and reach decisions, and how varying the size of the jury affects the accuracy and cost of jury
outcomes, see Klevorick & Rothschild, A Model of the Jury Decision Process, 8 J. LEGAL STUD. 141
(1979); Klevorick, Rothschild & Winship, Information Processingand Jury Decisionmaking, 23 J.
PUB. ECON. 245 (1984); see also Lempert, Uncovering 'Non-Discernible Differences'. Empirical
Research andJury Size Cases,73 MicH. L. REv. 643 (1975) (criticizing empirical results from mockjury experiments). For an interesting, related model of how increasing the number of judges on a
court can improve judicial accuracy, see Korhauser & Sager, Unpacking the Court, 96 YALE L.J.
82, 97-100 (1986).
8. "Random" is used here to mean a stochastic or non-deterministic process, not an unsystematic process in which the reality-the defendant's actual care level-has no bearing on the evidence presented at trial and hence on the likelihood of liability, as would be true, for example, if all
evidence types were equally likely regardless of the defendant's choice of care.
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nurses, family members, and other hospital employees, along with the
hospital's written records regarding the frequency with which nurses
checked in on the patient, must bear some relationship to the actual frequency with which such visits were made. Otherwise, such evidence is of
no use to the juror in inferring the actual frequency of such visits. On the
other hand, it is not necessary for the evidence to precisely indicate the
true state of affairs. The juror may form beliefs about what actually
occurred based on the evidence, but these beliefs may still fall short of
subjective certainty. Even if some nurses testify that visits were made
each quarter hour, the juror may still believe that it is nonetheless possible that visits were far less frequent.
Thus, the juror must perceive some relationship between evidence
and reality if reality is to be inferred from the evidence, but the relationship will generally be imprecise. Evidence is limited in quantity and only
imperfectly informative as to the true state of affairs it is adduced to
portray. One way of capturing these two features is to suppose that evidence is viewed as a random sample of reports regarding the behavior of
the defendant. 9 In the paradigmatic trial in a fault based liability system,
these reports would generally concern the actual level of care taken by
the defendant as well as the circumstances relevant to determining what
was required of the defendant under the general legal standard.10 To
simplify, I shall initially restrict attention to cases in which the level of
care required by the general legal standard is known to all actors, and the
only remaining factual issue for the juror is the defendant's actual level of
care.11 The evidence will then consist of a random sample of witness
9. Viewing the evidence as a random sample does not rule out strategic adversary behavior in
presenting evidence. Unlike, Bebohuk, Litigation and Settlement Under Imperfect Information, 15
RAND J. ECON. 404 (1984); P'ng, StrategicBehaviorin Suit, Settlement, and Trial, 14 BELL J. ECON.
539 (1983); or J. Sobel, An Analysis of Discovery Rules (1985) (University of California, San
Diego Department of Economics Working Paper 85-25), I do not model the strategic behavior of the
parties in this Article, but assume that the parties submit all the evidence they have which is
favorable to their contention so that I may focus on the care-evidence relationship. See infra notes
26, 33 and accompanying text. However, the random sample assumption itselfjust says that there is
some uncertainty, at least at the time the defendant chooses its care level, regarding the kind of
evidence of care that will be available later. Analysis of strategic choices regarding how much evidence to discover or disclose at trial can easily be based on the random sample model. Moreover,
intuition suggests that the parties often will choose to present all the favorable evidence they have
discovered if the cost of presentation is not too high, so that this assumption should be of minor
import.
10. See RESTATEMENT (SECOND) OF TORTS § 328C (1965); see also L. GREEN, JUDGE AND
JURY (1930).
11. Part II, section B briefly applies the model to situations where actual care is known and the
factual issue is instead what the legal standard required under the circumstances.
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reports and documents generated by the actual care level of the defendant. In the example of the allegedly negligent hospital, the evidence consists of testimony and documentary evidence on how frequently the
patient was visited while under morphine, and the actual frequency of
visits "generates" this sample in the sense that the average frequency
reported by the evidence, and perhaps also the dispersion of reported
frequencies, depends statistically on the actual frequency.
This model of evidence as a stochastic sample generated by, but only
imperfectly informative of, the defendant's actual conduct, suggests that
there are two key processes which determine the risks of guilt and innocence at trial: that by which conduct shapes the evidence, and that by
which the juror infers conduct from the evidence. The potential defendant choosing its care level with the administered legal rule in mind must
estimate both the kind of evidence likely to be presented at trial, and the
juror's response to that evidence.
The Bayesian approach to legal fact-finding and decisionmaking
provides a relatively simple, yet formal, framework for describing these
processes of evidence generation and conduct inference.12 The formalism
of this approach is justified by the insights it reveals. However, before
describing the model in more detail, a brief informal summary will be
offered for the reader bothered by statistical and diagrammatical
exposition.
As a model of evidence generation, the approach developed here is
very simple: I posit only that the defendant perceives that better care
generates better evidence in the sense that types of evidence favorable to
the defendant become more likely relative to unfavorable types, as the
defendant takes greater care. As a hospital actually increases the frequency with which the morphine-anesthetized patient is visited, the evidence will indicate a higher frequency, even though some witnesses may
still state a lower than actual frequency, and some documents may still
be incorrect or leave frequency unrecorded. This assumption will be
referred to as that of "monotone beliefs," and it supplies an intuitively
reasonable rule of evidentiary inference: better evidence leads the juror to
infer higher care.13
12.
For an excellent introductory account of the Bayesian approach to legal fact-finding, see R.
LEMPERT & D. SALTZBURG, EVIDENCE
157-62 (2d ed. 1982). For a summary description of the use
of Bayesian theory in the law of evidence, see I A. WIGMORE, EVIDENCE IN TRIALs AT COMMON
§ 37, 1011-13 (Tillers rev. 1983). See also supra note 4.
LAW,
13.
Technically, I assume that the juror's likelihood functions possess the (strict) monotone
likelihood ratio property, and that the evidence type is a sufficient statistic. These assumptions are
further discussed in J. Johnston, supra note 2; J. Johnston, Imperfect Information and the Legal
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As a model of how the juror is believed to infer the defendant's care
level from the evidence, the Bayesian approach here is somewhat more
complex because it relies on the basic statistical relationship known as
Bayes' Theorem, 4 but the essence of the model remains straightforward.
The defendant perceives a juror choosing between two competing contentions: the plaintiff's view that the defendant failed to comply with the
legal standard, and the defendant's assertion that it did comply. When
fact-finding is imperfect, the legal rule which tells the juror how to
choose between these contentions must generally allow for the possibility
that the juror will be uncertain in his choice. The general form of the
fault based decision rule is thus: "find the defendant liable if you are
convinced, to a level of certainty B, that the defendant took less care than
required by the standard." The required degree of subjective certainty of
noncompliance is given by B, which is customarily thought of as dictated
by the burden of proof.I5 This ranges from 1, absolute belief of guilt, to
0, absolute belief that the standard was not violated.
As applied here, Bayes' Theorem provides that, if the juror adjudicates fault with no particular pre-trial bias toward either compliance or
noncompliance, then the juror will only be convinced of noncompliance
to the degree of certainty required by the burden of proof, if the juror
believes that the evidence is sufficiently more likely to be observed given
noncompliance than compliance. In other words, in this model the juror
can conclude that noncompliance is sufficiently more likely than compliance, given the evidence, only if the evidence is more consistent with
noncompliance than compliance.
This is hardly surprising. However, this direct connection between
the juror's assessment of the likelihood of compliance and noncompliance and the juror's assessment of the consistency of the evidence with
compliance versus noncompliance, provides a link between the juror's ex
post inference of conduct and the defendant's ex ante prediction of the
probability of liability. If the defendant knows the burden of proof, and
knows how the juror will assess the consistency of the evidence with
compliance versus noncompliance, then the defendant will know how
unfavorable the evidence must be for the juror to find liability. Although
the defendant is not certain what the evidence introduced at trial will
actually look like, it can form its own subjective estimate of the
Process: Toward a General Economic Theory of Tort Liability, chs. 2-3 (1984) (unpublished Ph.D.
dissertation, University of Michigan) [hereinafter J. Johnston, Imperfect Information].
14. See infra note 17 and accompanying text (discussion of Bayes' Theorem).
15. As used throughout this Article, the burden of proof is equivalent to the burden of persuasion. See C. MCCORMICK, EVIDENCE § 336, at 947 (3d. ed. 1984).
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probability of different types of evidence, and hence can estimate the
probability that liability will be found. The probability that different
types of evidence will be introduced at trial varies with the actual care
level of the defendant, and, according to the monotone beliefs assumption made above, varies so that the higher the actual care level, the
greater the relative likelihood of evidence favorable to the defendant.
Hence, for a fixed burden of proof, the higher the care level, the lower the
probability of liability.
As used here, then, Bayes' Theorem shows how a rule which tells
the juror to assign liability for faulty conduct can be reduced to a rule
which tells the juror to assign liability only when evidence of the defendant's care is "bad enough." I do not claim that jurors actually behave as
Bayesian hypothesis testers;' 6 the crucial insight of this model is that the
sophisticated defendant need predict only how bad the evidence must be
for liability and form beliefs about the probability that different types of
evidence will be observed in order to predict the probability of liability
generated by its actual conduct. The model thus says that the incentive
effects generated by legal rules depend on how the rules affect the evidentiary threshold for liability. The applications of the model presented
below demonstrate the enormous analytical power of this basic insight.
Before turning to these applications, which will further explain the
model informally, it is worthwhile to provide a slightly more formal
description of the approach, if only to further reveal its crucial underlying assumptions.
In Bayesian terminology, the decision rule tells the juror to assign
liability only when the juror's subjective post-trial or posterior
probability of guilt exceeds the level of subjective certainty required by
the burden of proof. By employing Bayes' Theorem, we can see how this
requirement for the juror's subjective post-trial probability of guilt can be
expressed equivalently as a statement about the likelihood of the evidence
and the juror's pre-trial beliefs. To use Bayes' Theorem, we must make
some formal definitions. Let e denote the type of evidence, which ranges
from 0, the worst from the defendant's point of view (no evidence shows
16. For bibliographies of the debate on the use of Bayes' Theorem and the Bayesian approach
in legal decisionmaking, see I A. WIGMORE, supra note 12, § 37; Fienberg & Schervish, The Relevance ofBayesian Inferencefor the PresentationofStatisticalEvidence andfor Legal Decisionmaking,
66 B.U.L. REv. 771 (1986); Nesson, supra note 5, at 1358 n.5. An excellent summary of the debate
among mathematicians over the Bayesian approach and the theoretical foundations of probability is
in J.
HARTIGAN, BAYES THEORY
ch.1 (1983), which is a comprehensive account of many of the
interesting mathematical issues in Bayesian statistical inference.
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any safety measures were taken), to 1 (all the evidence shows every possible safety measure was taken). Let the juror's perception of care be
denoted by y, which also ranges from 0 to 1, with 1 the highest possible
care and 0 no care at all. Let the legal standard of care be given by s.
Then where P(x) denotes the subjective probability of the event in parentheses, Bayes' Theorem states that P(y<s/e), the juror's post-trial
probability that the legal standard was violated, given evidence of type e,
is given by the following formula:
P(y <s/e) = P(y < s) P(e/y < s)
(1)
P(e)
where P(y <s) is the juror's pre-trial probability that the defendant violated the standard, P(e/y<s) is the juror's likelihood of observing evidence of type e, given that the standard was violated, and P(e) is the
likelihood of evidence type e. 17
According to this formula, the juror's subjective post-trial
probability that the defendant violated the standard will be proportional
to his subjective likelihood of observing the evidence, under the hypothesis that the defendant violated the standard. The degree of proportionality is determined by the ratio of the pre-trial probability that the standard
was violated to the likelihood of observing evidence type e. Intuitively,
the formula says that the post-trial probability of a violation will increase
if (1) the juror's pretrial probability of a violation increases; (2) the likelihood of evidence type e decreases; and (3) the probative value of evidence
type e increases.18 Observing unusual evidence which is strongly probative of guilt will lead the juror to place a higher probability on guilt, but
the juror biased toward innocence may still have a relatively weak belief
in guilt.
17. The supposition that people can form meaningful and consistent subjective probabilities
which obey Bayes' Theorem is fundamental to the Bayesian approach. A very readable introduction
to Bayesian statistics is S. SCHMITT, MEASURING UNCERTAINTY: AN ELEMENTARY INTRODUCTION To BAYESIAN STATISTICS (1969); intermediate texts include T. FERGUSON, MATHEMATICAL
STATISTICS: A DECISION THEORETIC APPROACH (1967), and M. DEGROOT, OPTIMAL STATISTICAL
DECISIONS (1970); an advanced source is J. HARTIGAN, supra note 16; and the classic statement of
Bayesian statistics is L. SAVAGE, THE FOUNDATIONS OF STATISTICS (1954). All of these develop
Bayes' Theorem, but perhaps the clearest presentation is found in R. LEMPERT & D. SALTZBURG,
supra note 12, at 157-62.
18. I thus refer to P(e/y<s) as a measure of probative value. For more detailed analyses of
probative value as measured by the likelihood ratio P(e/y<s) /P(e/y>s), see Tribe, Trialby Mathematics: Precision and Ritual in the Legal Process, 84 HARV. L. REV. 1329, 1352 n.75 (1971);
Lempert, supra note 4, at 1021.
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As the formula points out, post-trial beliefs about conduct are
affected by pre-trial beliefs about conduct and by beliefs about the evidence and its relationship to conduct. However, a fair trial process is
often assumed to depend upon the ability to weed out biased jurors,
allowing the plaintiff the benefit of a fact finder who is influenced only by
the evidence observed at trial.1 9 One way to formalize such freedom
from pre-trial predilections is to impose the assumption that the juror's
pre-trial beliefs are equally balanced between guilt and innocence.
Under this assumption, P(y<s) = 0.5 in equation
(1),2 0
and we can
express a legal decision rule phrased in terms of subjective probabilities
of guilt as a statement about the likelihood of observing the evidence
presented at trial. To do so, recall first that as defined earlier, the legal
decision rule tells the juror to find liability only if P(y <sle) > B, where
once again, B is the burden of proof. But if we define B = a/(a+b), then
this will only be true if
P(y < sle)
a
P(y>s/e)
b
(where P(y>s/e) is the post-trial probability of innocence), because
P(y<sle) + P(y>s/e) = 1.21 Using equation (1), and recalling the
assumption that P(y<s) P(y>_s) = 0.5, this rule is equivalent to the
following rule: find the defendant liable if and only if
P(e/y < s) > a
P(e/y_>s)
b
This says that the defendant will only be found liable if the subjective
odds of observing the evidence presented at trial, assuming that the
defendant did indeed violate the standard, exceed a/b, a number directly
determined by the burden of proof.
To see the intuition behind this, consider the preponderance of the
evidence burden of proof, which is usually thought of as requiring the
juror to believe that guilt is more likely than innocence before assigning
19. See, eg., Note, The Cross-Section Requirement and Jury Impartiality, 73 CALIF. L. REV.
1555 (1985). As one reader pointed out, pre-trial equipoise is not necessarily consistent with
"rational" juror behavior. If jurors form rational expectations, they will form prior probabilities
based on all available relevant information, and these priors would often rationally favor either guilt
or innocence.
20. That is, the pre-trial equipoise assumption is that P(y<s) = P(y>s). In Bayesian analysis,
probabilities sum to unity so that P(y<s) + P(y>s) = 1, which implies that P(y<s) = 0.5.
21. If B = a/(a+b), then P(y<s/e) > B if and only if P(y<s/e) > a/(a+b), or if bP(y<s/e)
> a [1-P(y<s/e)], or therefore if P(y<s/e)/P(y _s/e) > a/b.
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liability. 2 Under the preponderance test, B
= 0.5,23
[Vol. 61:137
which implies that
a = b. This in turn implies that liability is assigned only if P(y<s/e) >
P(y >s/e) (i.e., if the post-trial probability of guilt exceeds the post-trial
probability of innocence) or, equivalently by the argument above, if
P(e/y<s) > P(e/ys) (i.e., if evidence is more likely to be observed
given guilt than given innocence). This equivalence depends on the
assumption that the juror thinks guilt and innocence are equally likely
before trial. Under this assumption, the odds of guilt, given the evidence,
must mirror the odds of observing the evidence, if the defendant was
guilty, simply because the evidence is the only thing which influences the
juror's beliefs about guilt and innocence.
When the juror has monotone beliefs, this equivalence between odds
of guilt and innocence and odds of observing evidence can be reduced
further to a simple statement that liability is assigned only when the evidence toward the defendant is bad enough. This perspective on the legal
decision rule will be used repeatedly to analyze changes in the burden of
proof and standard of care. It is illustrated in Figure 1, where the juror's
beliefs about the likelihood of observing different types of evidence are
portrayed in somewhat more detail by the functionsfi(e) andf2 (e). These
give, respectively, the likelihood of observing different evidence types e
under the alternative hypotheses that the defendant took too little care
and disobeyed the legal standard or took enough care to comply with the
standard. The single-peaked and symmetric shape exhibited byfj andf 2
is of no general analytical significance. However, the fact that the ratio
is increasing in e is significant, because it is implied by the important
assumption of monotone beliefs.24
f2/fJ
22. See C. MCCORMICK, supra note 15, at § 339; James, Proofof the Breach in Negligence
Cases (IncludingRes Ipsa Loquitur), 37 VA. L. REV. 179, 180 (1951); McBaine, Burden of Proof:
Degrees of Belief, 32 CALIF. L. REV. 242, 261 (1944).
23. There is general agreement, at least among commentators who believe quantification is
possible, that the preponderance burden of proof is quantified at 0.5. See Cohen, Confidence in
Probability: Burdensof Persuasionin a World of Imperfect Knowledge, 60 N.Y.U. L. REV. 385, 394
n.61 (1985).
24. Formally, the (strict) monotone likelihood ratio assumption I have referred to as monotone
beliefs says that for x' > x, f(e/x9/f(e/x) is increasing in e. In particular, f2/fi = f(e/y._s)/
f(e/y<s) is increasing in e.
Monotone likelihood ratio, the mathematical implications of which are developed in Karlin &
Rubin, The Theory of Decision Procedures for Distributions with Monotone Likelihood Ratio, 27
ANNALS OF MATHEMATICAL STATISTICS 272 (1956), is extensively utilized in statistical decision
theory. See, eg., J. BERGER, STATISTICAL DECISION THEORY: FOUNDATIONS, CONCEPTS AND
METHODS (1980). Further, this ratio is an underlying assumption in many economic models of
information and incentives. See Milgrom, supra note 2; Grossman & Hart, supra note 2; Rogerson,
supra note 2. The monotone likelihood ratio assumption is the only assumption made here regarding
the shape and behavior of the juror's beliefs about evidence. It is a very unrestrictive assumption,
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FIG. 1
ECONOMIC THEORY OF LIABILITY
f
f2
e (.5)
e
Figure 1 can be used to show how each different level of the burden
of proof determines a minimal evidentiary "badness" necessary to find
liability. As was demonstrated above, each level of the burden of proof
fixes a value of the likelihood ratio f,/f, below which liability is found.
Since, as Figure 1 illustrates, f2lf, is increasing in e, a unique evidentiary
standard e(B), defined by the property that liability is found only if the
evidence is worse than e(B) corresponds to each level of B, the burden of
proof. By saying the burden of proof is B, the law says the evidence of
care must be worse than e(B) in order to find that the defendant took too
little care and violated the standard. Figure 1 displays e(5), the evidentiary standard corresponding to the preponderance of the evidence burden of proof.
The view of juror decisionmaking depicted in Figure 1 is that of a
Bayesian-rational hypothesis tester. The juror compares the likelihood of
two hypotheses, guilt and innocence, by comparing the likelihood of
observing the evidence presented in trial under these alternative hypotheses.2" Because of the perception that better care generates better evidence, the juror is able to conclude that the defendant is culpable to the
even though it characterizes a large number of probability distributions-including the exponential,
gamma, binomial, and normal-some of which have the single-peaked, symmetric shape depicted in
Figure 1. See J. BERGER, supra at 369-73.
I should also note that although the formulas in the text assume e is a discrete variable, these
ideas were originally developed in the case where e is continuous, see J. Johnston, Imperfect Information, supranote 13; J. Johnston, supra note 2, and the graphical exposition presumes also that e is
continuous. That is,f(ely<s)is the continuous analogue to P(e/y <s)andf(e/y>s) is analogous to
P(e/y _s).
25. The juror behaves as a Bayesian statistician asked to choose between two hypotheses-guilt
and innocence-by deciding on the basis of the evidence which hypothesis is more likely. This
model of decisionmaking is described in M. DEGROOT AND T. FERGUSON, supra note 17, and in
E. LEHMANN, TESTING STATISTICAL HYPOTHESES (2d ed. 1986). Under the assumption made
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degree of certainty called for by the burden of proof only if the subjective
odds of observing the evidence as to whether the defendant was guilty are
equally high, and this is true only if the evidence of care falls below a
certain point.
The Bayesian model of fact-finding and liability determination
depicted by Figure 1 can be further understood by returning to the example of the allegedly negligent hospital considered earlier. In this example,
the trial issue is whether the hospital complied with the known standard
of post-surgical care due a patient given large doses of morphine. The
standard of care requires that nurses visit the patient sufficiently often,
and the evidence consists of testimony and written records regarding visit
frequency. The evidence may be conflicting and also imprecise, as witnesses testify, for example, that the visits were made at 10-20 minute
intervals, "often," "sometimes," and so forth. The Bayesian juror
believes that the more witnesses and documents indicating that visits
were made with sufficient frequency, the better the relative likelihood
that this evidence was generated by a reality of sufficiently frequent visits.
If the juror is asked whether the plaintiff has put in enough convincing
evidence showing infrequent visits to demonstrate that it is more likely
than not that visits were not made often enough, our hypothetical juror
determines how likely it is that he or she would view the total package of
evidence presented by the parties if the defendant hospital in fact had
visited as infrequently as the plaintiff asserts. If the juror came into trial
thinking it was as likely that the nurses visited as often as the standard
required as that they visited as rarely as the plaintiff alleges, then the
juror can decide that too much time elapsed between visits only if the
juror thinks the trial evidence showing this is more likely to exist if visits
were too rare than if they were sufficiently frequent.
The usefulness of this framework as a tool for analyzing changes in
the burden of proof and standard of care will become apparent in the
analysis of the incentive effects of uncertainty which begins in the next
Part. However, it is worth noting here how this model of fact-finding
provides some insights into the burden of proof which are not available
supra note 13, that the evidence type e is a sufficient statistic, the Bayesian juror's decision between
the hypotheses of guilt and innocence is equivalent to classical, non-Bayesian confidence regions of
the form e<e(B) and e>g(B). For this equivalence, see 1. BERGER, supra note 24, at ch. 8, and T.
FERGUSON, supra note 17, at ch. 5. The notion of a sufficient statistic, central to mathematical
statistics, both Bayesian and classical, is defined in H. BRUNK, AN INTRODUCTION To MATHEMATICAL STATISTICS, 178-80 (3d ed. 1975), and in T. FERGUSON, supra note 17, at 112-19. For a more
complete development of the formal framework underlying the exposition in the text, see J. Johnston, Imperfect Information, supra note 13, at chs. 2-3; Johnston, supra note 2.
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in less formal settings and yet remains consistent with basic intuition
about the operation of proof burdens.
First, the Bayesian fact-finding model confirms the idea that the
equivalence between the "preponderance of the evidence" and the "preponderance of the probabilities" is not between a quantity of evidence
and a subjective probability, for it is not true that the juror will be more
certain than not of fault merely because most of the evidence suggests
fault. This simplistic view of the "preponderance of the evidence"
neglects the importance of the juror's beliefs about how evidence reflects
reality. The juror will think fault more likely than freedom from fault
only if he or she thinks the evidence is more likely to be observed if the
defendant was at fault than if the defendant was faultless, and there is no
necessary connection between this belief and how much of the evidence
suggests fault and how much suggests faultlessness.
The intuitive sense of this model is reinforced by its implication that
if the juror is in equipoise before trial, and if each side in the trial submits
all the evidence it has which supports its position,2 6 then the burden of
proof can never be less than a preponderance of the evidence. To see
this, assume that the plaintiff has the burden of persuading a juror who
came into trial thinking that fault was as likely as freedom from fault.
If the plaintiff's task was merely to persuade the juror that fault was at
least 30% likely, then the plaintiff would have no reason to submit any
evidence, since the juror will find for the plaintiff at the outset. It is then
nonsensical to talk about the plaintiff bearing the burden. The natural
description of the burden in this case is to say that the defendant has the
burden of convincing the juror that freedom from fault is 70% likely.
For discussions of the burden of proof to conform to the logic of trial, the
plaintiff must have the burden of proof of convincing the "50-50" juror
that fault is more likely than freedom from fault, and the defendant must
26. This simplifying assumption is made because this Article focuses on the impact of uncertainty in the determination of fault on the defendant's incentives to make the correct choice of safety,
not on the incentives to produce and present evidence in an imperfect adversary system. This latter
topic is investigated in J. Sobel, supra note 9, and Sobel, Disclosureof Evidence and Resolution of
Disputev" Who Should Bear the Burden of Proofl, in GAME-THEORETIC MODELS OF BARGAINING
341 (A. Roth ed. 1985). Recent economic contributions to the study of the adversary system include
Milgrom & Roberts, Relying on the Information ofInterestedParties, 17 RAND J. ECON. 18 (1986)
(demonstrating circumstances under which even an unsophisticated decisionmaker who does not
take account of the parties strategic incentives in evidence presentation can reach a fully informed
decision in a competitive adversary system); Rubinfeld & Sappington, Efficient Awards and Standards ofProofin JudicialProceedings, 18 RAND J. ECON. 308 (1987) (analyzing the efficient level of
expenditures to inform the court and reduce losses from false positives and negatives shows that
increasing the random nature of the judicial process may improve efficiency if penalty is fixed by
reducing private expenditures on litigation).
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have the burden of showing the juror that freedom from fault is more
likely than fault, which implies that the burden of proof in either case
must exceed 50%, or the "preponderance of the evidence."
II.
A.
APPLICATIONS OF THE BAYESIAN
FACT-FINDING MODEL
FIRST APPLICATION:
WHY NEGLIGENCE RULES ARE NOT
NECESSARILY EFFICIENT
This Part uses the model of Bayesian fact-finding to show why ordinary negligence liability is not, in general, efficient (in a sense set out
immediately below) under factual uncertainty.
By ordinary negligence liability I mean that liability system which
assesses compensatory damages against the defendant if and only if the
plaintiff convinces the juror that it is more probable than not that the
defendant failed to take reasonable care; and where by "reasonable" care
the judge or policymaker means the "efficient" level of care under the
circumstances, or the total expected social cost minimizing level of care.
A liability rule is ex ante efficient if it causes actors subject to the rule to
act so that total expected social cost is minimized. If administrative costs
are assumed to be invariant with respect to the form of the liability rule,
and it is also assumed that potential victims are legally unsophisticated
and are not concerned with the impact of their behavior on their ability
to recover damages if harmed, the ex ante efficient liability rule is one
which induces the defendant injurer to choose that level of care which
minimizes the expected cost of accidents he may cause plus the costs of
27
care.
1. Perfect Liability Determination and the Efficiency of Negligence
It has been shown that when liability determination is perfect, the
negligence liability rule is ex ante efficient in this sense.2 8 It has also been
shown that when liability determination is generally imperfect, the negligence rule may either under-deter or over-deter-i.e., induce too little, or
27.
This simple efficiency criterion has been frequently employed in the economic analysis of
POLINSKY, AN INTRODUCTION To LAW AND ECONOMICS 37-49 (1983);
Brown, Toward An Economic Theory of Liability, 2 J. LEGAL STUD. 323, 325 (1973); Posner, A
Theory of Negligence, 1 J. LEGAL STUD. 29, 33 (1972).
28. See id. An important qualification to the efficiency result is that negligence will not create
the correct incentive for choosing the level of the activity, since the injuring party escapes liability
merely by choosing appropriate care when engaged in the activity. See Shavell, Strict Liability
Versus Negligence, 9 J. LEGAL STUD. 1, 2 (1980).
liability rules. See, e.g., A.
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too much care.2 9 The virtue of the Bayesian approach, however, is that it
allows us to see into the process of liability determination and better
understand why imperfect fact-finding and standard setting destroy the
optimality of negligence, and why the "preponderance of the evidence"
burden of proof minimizes the judge's ex post cost of error but fails to
optimize ex ante private incentives.
The efficiency of negligence under perfect liability determination can
be illustrated with a simple example. Suppose there are four levels of
care: low, medium, high, and highest. Suppose also that expected social
harm-the probability of harm multiplied by the amount of harm-falls
as more care is taken. Table 1 gives the magnitude of expected social
harm and the cost of care for each level of care and shows that medium
care minimizes social costs, the cost of care plus expected accidental
harm.
TABLE 1
The Social Cost of Accidents
Care
Level
Expected
Social Harm
Low
Medium
High
Highest
70
50
40
35
Total Social Cost
Cost of (Expected Harm
Care
Plus Cost of Care)
15
30
45
60
85
80
85
95
Under a perfect negligence rule, the actual damages assessed against
the defendant are equal to the magnitude of social harm; the defendant is
found liable if and only if the accident occurs and it has failed to take
optimal care; and the standard of due care is set equal to the optimal care
level. According to this rule, the defendant has expected damages of 70
in Table 2 if it takes low care, and expected damages of 0 for medium
care or any higher care level, because medium care is optimal and the
defendant is never liable if it takes at least optimal care. Hence, the
defendant has a more than adequate incentive to increase care from low
to medium, and no incentive to increase care above medium, as there
would not be a drop in expected damages. The perfect negligence rule
creates a sharp discontinuity in the defendant's marginal benefit of care
at the level of the legal standard, ensuring too much care will not be
29. See supra note 1.
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TABLE 2
Cost Internalization Under Perfect Negligence
Care
Level
Low
Medium
High
Highest
Expected
Social
Harm
70
50
40
35
Injurer's Cost
Expected of
Damages Care
70
0
0
0
15
30
45
60
Total Social Cost
(Expected Harm
Plus Cost of
Care)
Total Private
Cost (Expected
Damages Plus
Cost of Care)
85
80
85
95
85
30
45
60
taken, while at the same time, ensuring that enough care will be taken by
always imposing full damages on the defendant if too little care is
30
taken.
2.
The Ambiguity of Negligence When Fact-Findingis Imperfect
In the Bayesian model of fact-finding and liability determination,
the defendant's liability is not dependent on whether its actual care was
below or above the legal standard, but on the plaintiff's success or failure
in introducing enough evidence of low care to meet the evidentiary standard implied by the burden of proof. Thus, the defendant must forecast
how its actual care will be reflected in the evidence presented at trial if it
is to predict the probability of being found liable. The defendant's perception of the likelihood with which different evidence types are observed
at trial, given its actual care level, may differ systematically from the
juror's perception of this relationship, due, for instance, to the defendant's superior information regarding the strategic determinants of how
much and what sort of evidence is ultimately discovered and submitted
at trial. As a benchmark, however, I will initially assume that the
defendant and the juror perceive the same subjective, probabilistic relationship between care and evidence. The only difference is that the
defendant knows its actual care level and needs to predict the evidence to
30. Professor Robert Cooter has been prominent in recognizing and emphasizing the importance of the discontinuity in the private benefit of safety at the level of optimal safety created by
perfect liability determination. See Cooter, Unity in Tort, Contract and Property: The Model of
Precaution,73 CALIF. L. REv. 1, 7-11 (1985) [hereinafter The Model of Precaution];Cooter, Economic Analysis of PunitiveDamages, 56 S. CAL. L. REV. 79, 82-89 (1982) [hereinafter PunitiveDamages] (discussing fault rules and incentives to avoid injuries); Cooter, Prices and Sanctions, 84
COLUM. L. REV. 1523, 1526-30 (1984)(discussing the incentives individuals have to avoid sanctions
for the harms they cause).
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be presented in a future trial, while the juror, who does not observe the
actual care level, must infer past actual care from trial evidence.
To estimate its probability of liability, the defendant must predict
the likelihood that the evidence of low care generated by its actual care
level will be bad enough to meet the evidentiary standard. Observe that
under perfect liability determination, the defendant had to know the
standardof care in order to predict the trial outcome with certainty. Yet
under imperfect Bayesian liability, the defendant must know the standard of evidence in order to calculate the probability that the trial will
end in a liability finding. This suggests that the important question for
the defendant is not how good the legal command says its conduct
should be, but how good the evidence must be to convince the legal decisionmaker that its conduct was good enough. This is the question which
will be asked by a defendant whose conduct is determined not by a desire
to do as the law says it should do, but by the desire to avoid legal sanctions imposed when and only when the legal decisionmaker finds it violated the legal rule.3 1 Thus, the Bayesian model is general enough to
capture two kinds of "compliance" with legal norms: conforming actual
behavior to the norm, or influencing, editing, and even destroying evi-
dence in order to create a picture at trial of compliance, even though the
picture may be untrue.3 2
The focus for the present, however, is on the impact of inherent
factual uncertainty, and not on the effect of evidence manipulation and
31. Nesson, supra note 5, at 1367, also recognizes that there are some actors, for example,
"student[s] of the judicial process," who have a "complex and sophisticated understanding of the
meaning of a verdict" and do not accept verdicts as statements about what really happened but
rather as statements about the evidence. Nesson though, seems more concerned that we sufficiently
educate the less well informed mass public. Id at 1360, 1366-68, 1376-77. However, the uninformed public is unlikely to respond to legal rules in any form-as statements about conduct or
about evidence-and thus this class of actors is unresponsive to the threat of legal liability and is
irrelevant when considering efficiency and optimal deterrence.
32. A sampling of recent articles dealing with so-called "compliance" programs shows that as
a practical matter, the first response to threatened liability may be to change not the level of actual
care, but policies regarding document retention and evidence preservation. See, e.g., Oesterle,
A PrivateLitigant'sRemediesfor an Opponent'sInappropriateDestruction of Relevant Documents, 61
TEX. L. REV. 1185 (1983); see also G. EADS & P. REUTER, DESIGNING SAFER PRODUCTS: CORPORATE RESPONSES To PRODUCT LIABILITY LAW AND REGULATION, 107, 109 (1983) (manufacturing firms reduced product liability exposure by keeping names off component parts, producing
wasteful internal documentation); Fedders & Guttenplan, Document Retention and Destruction:
Practical,Legal and Ethical Considerations, 56 NOTRE DAME LAW. 5 (1980); Sugarman, Doing
Away With Tort Law, 73 CALIF. L. REV. 555 (1985) (tort liability acts as an "additional incentive for
cover-up"); Vogel & Delgado, To Tell the Truth: Physicians'Duty to Disclose Medical Mistakes, 28
UCLA L. REV. 52 (1980); Note, Legal Ethics and the Destruction of Evidence, 88 YALE L.J. 1665
(1979).
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destruction. In order to rule out evidence manipulation, assume that the
care-evidence relationship perceived by the defendant and the juror
reflects a process in which there is a known total quantity of evidence
available to each side in the dispute, each side presents all the evidence
favorable to its contention, and it is only the quality of the evidence
33
which is uncertain or random.
With the foregoing series of assumptions regarding the nature of the
relationship the defendant perceives between evidence and care, the operation of ordinary negligence liability when fact-finding is Bayesian imperfect can be depicted graphically. In Figure 2, the function f2 gives the
defendant's likelihood that various kinds of evidence will be presented at
trial when it takes the socially optimal level of care, medium care, which
is assumed to be the standard of care in the negligence system. Under
the assumption of 'identical juror and defendant beliefs, the function f2
also represents the juror's likelihood of observing various kinds of evidence under the assumption that the defendant took due care. The evidentiary standard implied by the preponderance of the evidence burden
of proof, e( 5), is that level of evidence at which f2 is just equal to fl,
where A is the juror's likelihood function under the hypothesis that the
defendant was negligent and took low care.
FIG. 2
f
f
f
e (.5)
As shown by Figure 2, the defendant perceives a positive probability
that the evidence will be unfavorable enough to satisfy the preponderance
of the evidence burden of proof even when it behaves non-negligently.
This probability is equal to the area under f to the left of e(5). On the
33. As discussed earlier, supra note 26, this assumption is made in order to focus on the effect
of uncertain liability decisions on the defendant's incentives to choose between safety and risk. For a
discussion regarding the incentives to produce and disclose evidence, see supra notes 9 & 26.
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1987]
other hand, there is a chance of escaping liability even when the defendant is negligent, as illustrated by the fact that there is a substantial area
underf' to the right of e(5). If the defendant thinks that better care will
produce better evidence, in the sense of increasing the ratio of f2 tof, as
in Figure 2, then it will receive a benefit in terms of a reduced probability
of liability from increasing the level of care from medium to high.34 This
final effect of uncertainty is illustrated by the function f2', which is the
defendant's likelihood function when it takes high care. As the figure
shows, the probability of liability, i.e., the area under the likelihood function to the left of e(5), is lower when high care is taken than when
medium care is taken. Uncertainty in fact-finding thus creates two
effects which generally characterize uncertain liability determination: a
chance of escaping liability, even if negligent, and a positive risk (which
falls as care is increased above the level required by the standard) of
being found liable even if non-negligent.
TABLE 3
Under-Deterrence Due to Imperfect Fact-Finding*
Care
Level
Low
Medium
High
Highest
Injurer
Probability
of Liability
Injurer
Expected
Damages
.4
.3
.2
.1
(.4)(70)=28
(.3)(50)= 15
(.2)(40)= 8
(.1)(35)= 3.5
Cost Total Private Cost
of (Expected Damages
Care Plus Cost of Care)
15
30
45
60
43
45
53
63.5
* As this example points out, it is a sufficient for the existence of an interior private
optimum that change in the marginal reduction in the probability of liability be non-
negative, provided the probability of harm function is convex. For a fuller explanation in the continuous case, see J. Johnston, supra note 2.
The chance of escaping liability, even if negligent, lessens the incentive to be non-negligent. This effect of uncertainty may so weaken the
defendant's incentives that, as in Table 3, the defendant will choose suboptimal care.
On the other hand, when fact-finding is imperfect and the risk of
being found liable falls as care increases, the defendant may be induced
to take too much care. In Table 4, for example, the probability of liability falls by so much when the defendant increases its care level from
34. For a formal proof that in the Bayesian model, the defendant's perceived probability of
liability falls as care increases, see J. Johnston, Imperfect Information, supra note 13, at 106-09.
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medium to high that the defendant's private gain-the reduction in its
expected damages-now exceeds the marginal cost of high care. This is
true even though the social marginal benefit of high care is outweighed
by its marginal cost (see Table 1. 31
TABLE 4
Over-Deterrence Due to Imperfect Fact-Finding
Care
Level
Low
Medium
High
Highest
Injurer
Probability
of Liability
Injurer
Expected
Damages
.6
.4
.1
0
(.6)(70)=42
(.4)(50)=20
(.1)(40)= 4
(0)(35) = 0
Cost Total Private Cost
of (Expected Damages
Care Plus Cost of Care)
15
30
45
60
57
50
49
60
Figure 2 and Tables 3 and 4 thus say that when fact-finding is Bayesian imperfect, ordinary negligence liability will not necessarily induce
the defendant to select the socially optimal level of care. But although
these examples demonstrate how errors in fact-finding destroy the certain
optimality of ordinary negligence liability, one may still question why it
is that the preponderance of the evidence burden of proof does not eliminate the adverse consequences of fact-finding errors. Intuitively, requiring the juror to be at least 50% certain of fault before assigning liability
might seem to imply that the two kinds of errors-false positives and
false negatives-will be equally likely and hence cancel each other out,
leaving the defendant's incentive to comply unchanged.
This intuitive argument fails because it does not account for the
effect of reductions in the probability of error caused by increasing care.
As argued above, reduction in error due to increased care is the reason
why the preponderance burden of proof/due care liability test under negligence can over-deter.
Referring to Figure 3, we can see that another reason why this intuitive hunch is untrue is because the preponderance of the evidence standard does not necessarily equalize the probability of the two kinds of
errors. The preponderance will equalize the error probability if the distributions of evidence types are symmetric, but this will not be true
when, as in Figure 3, the distributions are asymmetric. In the figure, the
35.
note 1;
More formal development of the effect of error can be found in Calfee & Craswell, supra
supra note 1; J. Johnston, supra note 2.
S. SHAVELL,
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probability of erroneously finding a non-negligent defendant liable-the
area underf 2 to the left of _(.5)-is less than the probability of erroneously acquitting a negligent defendant-the area underf, to the right of
g(.5). The preponderance of the evidence standard does not equalize the
probability of making the two kinds of errors, but instead minimizes the
total probability of error, and hence the total expected cost of error if the
cost of the two kinds of error is equal. This fact, long ago established in
the decision-theoretic literature examining the burden of proof,36 is also
36. Kaplan, supranote 4, at 1072, presented the first decision-theoretic analysis showing that a
quantified burden of 0.5 minimizes the total expected cost of ex post error when "costs" of the two
kinds of error are equal. Another early analysis of the burden of proof on expected error cost
grounds is Ball, The Moment of Truth:Probability Theory andStandardsof Proof,3 VAND. L. REV.
807 (1961). The error cost minimization goal was contrasted with the goal of equalizing plaintiffdefendant errors in M. FINKELsrEIN, QUANTITATIVE METHODS IN LAW 65-71 (1978), whose argument relied largely on numerical examples. Kaye, Naked StatisticalEvidence (Book Review), 89
YALE L.J. 601, 605 n.19 (1980) attacks the plausibility of error equalization as a meaningful policy
goal, and has the most general proof to date of the optimality of the preponderance of the evidence
rule. This argument is restated and summarized in Brook, InevitableErrors: The Preponderanceof
the Evidence Standard in Civil Litigation, 18 TULSA L.J. 79 (1982).
Using the model I have developed in this Article, it is easy to show that the preponderance of
the evidence rule minimizes the total expected error cost if errors are weighted equally. The result is
an immediate consequence of the Neyman-Pearson Lemma. Proofs of this lemma may be found in
M. DEGROOT, supra note 17 at 146-47; T. FERGUSON, supra note 17 at 198-206. See J. Johnston,
supra note 25, at 30-37. For judicial assimilation of this result, see Santosky v. Kramer, 455 U.S.
745, 755 (1982) (concluding that in civil disputes, the burden of proof is a mere preponderance
because the litigants should" 'share the risk of error in roughly equal fashion.' " (quoting Addington
v. Texas, 441 U.S. 418, 423 (1979), where the court stated that the "function of the legal process is to
minimize the risk of erroneous decisions," id. at 425, and contrasted the costs involved in civil
commitment with the "typical civil case involving a monetary dispute between private parties,"
where "society has a minimal concern with the outcome" and the plaintiff's burden of proof is a
preponderance, id. at 423)). For an analysis of Santosky, see Rizzo, The Economics of Termination
ofParentalRights: Santosky v. Kramer, 2 SuP. Cr. ECON. REV. 277 (1983). Contrary to the title,
however, this Article does not focus on the economic issue of ex ante incentives, but adapts the
decision-theoretic perspective and considers only ex post error cost.
The decision-theoretic approach defines the cost of error very narrowly, as the decisionmakers'
ex post cost of error. See, eg., Kaplan, supra note 4. The decision-theoretic goal of expected error
cost minimization, which goes to the "private transfer" between litigants, contrasts sharply with the
criterion of economic efficiency employed here, which involves the precedential, behavior-modifying
effects of the burden of proof. On this distinction, see Page, On the Meaning of the Preponderance
Test in Judicial Regulation of Chemical Hazard, 46 LAW & CONTEMP. PROBS. 267, 273 (1983).
While there have been economic analyses of the burden of proof concerned with the ex ante incentives created by different levels of the burden, these have dealt with the proper burden of proof on
the causation issue in mass exposure and toxic tort cases where there are multiple and background
causes. See Rosenberg, The CausalConnection in Mass Exposure Cases: A 'PublicLaw' Vision ofthe
Tort System, 97 HARV. L. REV. 851 (1984); Shavell, Uncertainty Over Causationand the Determination of CivilLiability,11 J. LAW & EON. 587 (1985). For the differences between criminal and civil
standards, see Keenan & Rubin, Criminal Violations and Civil Violations, 11 J. LEGAL STUD. 365
(1985); for a discussion of the burden of proof on incentives to commit resources to litigation, see
Rubinfeld & Sappington, supra note 26; cf Orloff & Stedinger, A Framework for Evaluating the
Preponderanceof the Evidence Standardin Civil Litigation, 131 U. PA. L. REv. 1159 (1983); Kaye,
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FIG. 3
f
[Vol. 61:137
f2
e' e(.5)
e
depicted in Figure 3. For example, a movement from the preponderance
standard toward, for example, a higher burden of proof, would decrease
the evidence threshold (require more evidence of low care). As shown by
the movement from e(5) to L in Figure 3, such a change increases the
probability of a false negative by more than it reduces the probability of a
false positive, and therefore increases the total error probability. Thus,
although the preponderance rule minimizes total ex post error cost, it
does not have the kind of "cancelling" effect which would ensure that
ordinary negligence liability will be ex ante efficient.3 7
To illustrate this point, suppose that a physician is considering
whether to perform an additional diagnostic procedure on a patient. The
physician realizes that the legal standard requires the procedure to be
performed if condition x exists, but not if condition x is absent. The
question for this physician is how much time and effort to expend in
investigating whether condition x exists. Under the traditional negligence test, the juror will find the physician liable for negligence if the
evidence is more likely to be observed given that insufficient effort was
spent determining the existence of the condition than if sufficient effort
was expended. The physician may quite reasonably assume that a very
strong case showing sufficient effort will be made by an attorney, even if
the actual effort was lower than required. The physician will also see
that even if the standard is complied with, the plaintiff's attorney may be
The Limits of the Preponderanceof the Evidence Standard:JustifiablyNaked StatisticalEvidence and
Multiple Causation, 1982 AM. B. FOUND. RES. J. 487 (adopting expost, decision-theoretic approach
to burden of proof in cases involving probabilistic causation).
37. Judge Richard Posner has intimated a belief in this cancelling of incentive cost errors
under the preponderance standard. See R. POSNER, ECONOMIC ANALYSIS OF LAW 520 (3d ed.
1986)(the preponderance of the evidence standard "implies that of cases decided erroneously, about
half will be lost by deserving defendants and about half lost by deserving plaintiffs. Whether this is
the efficient result depends on whether the costs of each type of error are about the same.").
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able to present a very strong case showing that too little care was taken.
The physician-defendant may realize that certain types of evidence showing compliance may not be admitted, while the credibility of the physician's own testimony is certain to be attacked.
The basic problem is that the preponderance of the evidence burden
of proof is both too difficult and too easy to satisfy. The noncomplying
physician will see that noncompliance, negligence, may go unpunished.
But compliance may not be fully reflected in the evidence either. If the
actual care level of the physician had nothing at all to do with the type of
evidence, then the physician would conclude on economic grounds that
no care need be taken. But when the evidence type can be made better,
in a rough average sense, by increasing care, there may be too great an
incentive to increase care to get better evidence and a lower chance of
liability.
This implies that if the policymaker desires to set the burden of
proof so as to award compensatory damages with minimum total
probability of error due to uncertain fact-finding, then the preponderance
of the evidence standard should be selected. But if the policymaker's
goal is to design a liability system which will induce efficient care-taking
by the defendant, then ordinary negligence liability would be a poor
choice. Theoretically, ordinary negligence liability is not an ideal compensatory mechanism because it often fails to compensate those who suffer harm, and it is inadequate as a regulatory mechanism because it errs
both in failing to punish when it should and punishing when it should
not. However, ordinary negligence liability is theoretically ideal from
the view of accurate arbitration of fault.38 Ordinary negligence liability
minimizes the total probability of error in resolving the litigants' dispute.
It minimizes the judge's expected cost of error where the judge is interested solely in resolving the dispute accurately, has equal concern over
the two kinds of errors, and ignores the ex ante incentive effects of
error.3 9 Ordinary negligence is not an efficient regulatory mechanism,
38. Here, I refer to "fault" in the broad sense as meaning "nothing more than a departure from
a standard of conduct required of a person by society." W. PROSSER & W. KEETON, THE LAW OF
TORTS 535 (5th ed. 1984).
39. In distinguishing between the regulation model of litigation, which focuses on the effect of
litigation on future ex ante incentives, and the arbitration model, which focuses on ex post judicial
concern over the interests of the parties to the instant dispute, I follow the terminology developed in
M. DAN-COHEN, RIGHTS, PERSONS AND ORGANIZATIONS 123-29 (1986). The regulation modelwhich is common to both the "public law" and law and economics approaches-is compared to the
arbitration or dispute resolution model in Scott, Two Models of the Civil Process, 27 STAN. L. REV.
937 (1975), and Chayes, The Role of the Judge in Public Law Litigation, 89 HARV. L. REV. 1281
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however, and as Part IIC shows below, may bear little resemblance to the
efficient fault based liability rule under imperfect fact-finding.
B.
SECOND APPLICATION: THE IMPORTANCE OF How VIOLATIONS
OF LEGAL STANDARDS ARE DEFINED
Before analyzing how to restore optimal incentives in the world of
imperfect fact-finding, it is worthwhile as a preparatory step to consider
an omission in the analysis thus far. Although I have assumed that the
juror forms beliefs about the distribution of evidence observed under two
alternative hypotheses, compliance with the legal standard, and noncompliance, I have not specified the level of supposed noncompliance. An
interesting implication of the Bayesian model is that if the evidence is
distributed symmetrically, then the civil preponderance of the evidence
burden of proof leads to a 50-50 chance of liability given compliance with
the legal standard only if any deviation from due care, no matter how
small, is treated as a violation of the standard.
FIG. 4
Evidence distribution
Evidence distribution
given care levels
2 and 3 (increasing but
still sub-optimal care)
Evidence distribution
given due care
given lowest care
"3
(Evidence thresholds under
care levels 2 and 3
threshold converging
to 6)
This is depicted in Figure 4. The evidence distributions are drawn
under the alternative care levels indicated, and the burden of proof is a
preponderance. As the plaintiff alleges that successively higher levels of
care were taken, the evidence threshold for liability increases; it becomes
(1976). See also Chayes, The Supreme Court 1981 Term-Forward:Public Law Litigation and the
Burger Court, 96 HARV. L. REV. 4 (1982).
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easier for the plaintiff to win, and more likely that the injurer taking due
care will be found liable. As shown in the diagram, the evidence threshold approaches , the average type of evidence given compliance, as the
alleged actual care level approaches the standard of care. When the
threshold equals , the risk of liability is precisely .5.4°
Figure 4 has an important implication for the structure of fault
based liability rules. If the burden of proof is a preponderance of the
evidence, then punishing even de minimus violations of the standard
maximizes the chance of over-deterring and makes the legal process
appear most arbitrary, by turning liability given compliance into a coin
flip.
To avoid this, the law should punish only discrete deviations from
due care. At the extreme, punishing only very large deviations can
ensure that compliance is not punished; false positives can in theory be
eliminated by punishing only very extreme departures from the desired
standard of conduct. This is illustrated in Figure 4, where the evidence
most damaging to the defendant who takes due care is designated by e.
If the juror was required to find a gross violation of due care, corresponding to "lowest care" in the Figure, then the defendant would be certain of
escaping liability given due care. This is because the best evidence given
lowest care, e, is still so bad that the defendant believes it will never be
observed if it takes due care. Assuming, as throughout, that the juror
and defendant have identical beliefs as represented by identical evidence
likelihood functions, the juror can only be persuaded that lowest care
was taken if the evidence is worse than e, whereas the defendant thinks
the evidence can never be worse than e* if it takes due care. Hence, the
defendant believes liability cannot be found if due care is taken.4 1
An application of Figure 4 of equal potential significance is to imagine that the trial concerns not the actual care level of the defendant in
comparison to a known standard, but the appropriate level of the standard, given known facts about actual care. In this case, the plaintiff tries
to show that the actual level of care was below the standard. Assuming
actual care is known, the evidence would consist, for example, of expert
40. If the distribution functions are single-peaked but asymmetric, then the evidence threshold
approaches the modal evidence type, and the probability of a false positive will be maximized but less
than (greater than) .5 if the distribution is skewed rightward (leftward).
41. The figure also shows how requiring too much of the plaintiff, for example-to show that
lowest care was taken-would cause underdeterrence, since there are evidence types which are both
too poor to be observed if due care is taken and too good to be observed if no care is taken. Since the
likelihood is zero under both alternatives, the plaintiff could not show the maximum violation of due
care, which is zero care, under any burden of proof.
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testimony about the proper standard, and a higher evidence index would
indicate a higher true standard. Then if the plaintiff is not required to
show that a discrete increase in care was required by consideration of the
benefits and costs of an increase, and can instead establish liability merely
by showing that any increase, however small, would have been desirable,
then there will be a 50% chance of rejecting the true standard if the
burden of proof is a preponderance of the evidence.
The Bayesian model thus shows that regardless of whether the disputed factual issue is the level of actual care or the level of the standard,
only if any violation of the standard is punished will uncertainty take the
form of equal odds of guilt and innocence given actual compliance.
When only discrete violations are punished, the chance of liability given
compliance will be less than 50% if the likelihood functions take the
shape depicted in Figure 4.42 Over-deterrence will be less likely, the
larger the deviation from the standard that must be shown to establish
fault.
C.
THIRD APPLICATION:
CREATING OPTIMAL INCENTIVES
UNDER UNCERTAINTY
The previous section not only sheds light on how the generic fault
based liability rule performs as a cost internalization mechanism, but
suggests a solution to the ambiguity of negligence.
To construct this alternative system, recall first that ordinary negligence liability is efficient under perfect liability determination only
because non-negligent defendants are never punished, thus eliminating
the possibility of over-deterrence. Meanwhile, negligent defendants are
always punished and must pay sufficiently high damages-at least equal
to the magnitude of social harm-so that it does not pay to take too little
care, thus eliminating the possibility of under-deterrence. Now, leaving
aside the problem of under-deterrence, this observation suggests that the
way to eliminate over-deterrence as a possibility when fact-finding is
uncertain is to manipulate the available legal rules to create a condition
under which the defendant thinks liability will never be found if optimal
care is taken. Ordinary negligence liability fails to do this, for as we have
seen, when the legal standard is set equal to the optimal level of care and
the burden of proof is a preponderance of the evidence, the defendant
42. Thus, the common assumption in recent work on uncertainty that the defendant sees a
50% chance of liability if he or she complies really assumes the special case where all violations are
punished. For examples, see Calfee & Craswell, supra note 1; Haddock & Curran, supra note I.
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the burden of proof is a preponderance of the evidence, the defendant
perceives a very significant chance of being held liable even if optimal
care is taken.
This difficulty with ordinary negligence liability was illustrated in
Figure 2, which is reproduced and supplemented in Figure 5 below.
f
FIG. 5
e
f2
e (.5)
e
Recalling thatf 2 gives the defendant's perception of the likelihood of seeing various kinds of evidence if it takes medium care, we see that the
defendant thinks the evidence may be worse than e(5) if it takes medium
care, which means that the defendant may be found liable even if it complies with the negligence standard. But observe that the defendant thinks
the evidence will never be worse than e* if it takes medium care, the
socially optimal care level. In other words, the defendant thinks the evidence cannot be worse than type e* if it is non-negligent. To again recall
the example of the allegedly negligent hospital, the hospital thinks that
the evidence could not consist entirely of reports that the patient was
never visited if in fact visits were made at the standard 10 minute interval. If the legal rules could be changed so that liability is found only if all
evidence shows visits were never made, then the hospital would have no
incentive to over-comply by visiting more frequently than the standard
10 minute interval, because it would think it could escape liability by just
barely complying; the evidence would never be bad enough for liability to
be assigned provided the actor complied.
It was earlier established that the higher the burden of proof, the
stronger the plaintiff's evidence must be to assign liability, or, equivalently, the worse the evidence type must be from the defendant's point of
view. Consistent with this general fact, we immediately observe that one
way to lower the evidentiary standard to e* is to raise the burden of proof
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This is becausef 2 =0 at e*, and thus the juror is certain that the defendant was not negligent only when the evidence is worse than e*. But then
we have a simple condition for eliminating over-deterrence: raise the
burden of proof to require certainty of fault.
As Figure 5 also demonstrates, however, the cost of eliminating
over-deterrence by raising the burden of proof to this level is that there is
now a much greater chance that a negligent defendant will escape punishment, which opens up the possibility of severe under-deterrence.
When the evidentiary standard is at e*, the area to the right of e* under
f, -the probability that the evidence will be good enough to escape liability even though the defendant is negligent and takes low care-has been
substantially increased relative to the similar probability of a false negative when the evidentiary standard was e(5). On the other hand, when
beliefs are monotone as in Figure 4, the defendant will perceive some
slight positive probability of being found liable if low care is taken. Only
if it takes medium care does the defendant think the probability is finally
zero.4 3 This means that the defendant perceives a positive marginal benefit of taking medium care. The probability of liability falls and hence so
do the defendant's expected damages when it moves from low to medium
care.
Although there will be a private benefit to taking optimal, medium
care even under the punitive burden of proof requiring certainty, this
high burden of proof drastically lowers this benefit. Since the probability
of liability given negligent low care is so low due to the high burden of
proof, the benefit of increasing care to the medium level is necessarily
very low. However, the defendant's marginal benefit of taking medium
care is equal to the fall in the probability of liability when care is
increased from low to medium, multiplied by the magnitude of damages.
If we consider the magnitude of damages to be a mere instrument serving
the goal of optimal deterrence, then it is clear that no matter how small
the probability of liability, if low care is taken the defendant's marginal
return from medium care can be increased by raising the amount of damages. If damages can be set above the level of actual harm, then the
incentive weakening effects of increasing the burden of proof can be offset
and optimal incentives assured, despite inherently imperfect fact-finding.
When the juror has monotone beliefs, it will generally be possible to
eliminate over-deterrence without increasing the burden of proof all the
way to the level of certainty. For any given burden of proof, lowering the
43.
If this were not so, then the monotone beliefs assumption would be contradicted.
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standard of care or, by the argument in Part IIB, requiring a bigger
shortfall from the standard, will also decrease the evidentiary standard
and reduce the probability of liability. Thus over-deterrence can be prevented by decreasing the standard of care to, say, some care, or requiring
gross negligence and increasing the burden of proof to require, say, clear
and convincing evidence. Part IIB illustrated how increasing the
required shortfall from the standard of care can eliminate false positives.
Lowering the standard operates in essentially the same way." Subsequent sections will argue that it is generally necessary to both raise the
burden of proof and increase the required degree of fault (or, equivalently, lower the nominal standard).4 5 However, regardless of the particular configuration of the burden of proof/degree of fault, the basic idea
behind punitive liability remains the same: stiffen the plaintiff's proof
burden and/or relax the announced legal standard of care against which
fault is judged to make the defendant think liability will never be found if
optimal care is taken, and then apply punitive damages if the new liability test is met.46
The way in which punitive liability affects the defendant's incentives
is made more concrete in Tables 5 and 6. Table 5 shows that increasing
TABLE 5
The Effect of Ideal Punitive Safeguards
Care
Level
Low
Medium
High
Highest
Injurer
Probability
of Liability
Injurer
Expected
Damages
.2
0
0
0
(.2)(70)= 14
0
0
0
Cost Total Private Cost
of
(Column 3 Plus
Care
Column 4)
15
30
45
60
29
30
45
60
44. Changing the standard of care is not quite the same as changing the degree of fault when a
higher degree of fault is required. The fl distribution in Figure 5 shifts to the left but the f2 distribution is unchanged. But when the standard is lowered, both the fl and f2 curves shift to the left, and
the monotone likelihood ratio assumption does not by itself guarantee that the evidence threshold
will be lowered as a consequence. There is thus some ambiguity in the effect of lowering the standard. On the other hand, the potential problem with increasing the degree of fault is that if too much
fault is required, then there may be intermediate evidence levels which are both too bad to be
observed given compliance and too good to be observed given the required large shortfall from the
standard. Although these evidence levels are consistent with compliance, they would also be inconsistent with liability, so that marginal non-compliance would go unpunished.
45. See infra text accompanying notes 47-53.
46. See infra text accompanying notes 47-51.
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the burden of proof and/or lowering the standard of care eliminates false
positives, therefore creating a zero probability of liability if at least
medium care is taken. However, this also lowers the chance of being
found liable if only low care is taken by so much that low care would
minimize the defendant's expected total cost. In Table 6, punitive damages of $300-three times the magnitude of actual harm-are applied.
These increase the private benefit of compliance and make medium care
privately optimal, counteracting fully the incentive weakening effect in
Table 5.
TABLE 6
Optimal Punitive Liability
Care
Level
Low
Medium
High
Highest
Injurer
Probability
of Liability
Injurer
Expected
Damages
.2
0
0
0
(.2)(300)=60
0
0
0
Cost Total Private Cost
of
(Column 3 Plus
Care
Column 4)
15
30
45
60
75
30
45
60
The idea of punitive liability can be illustrated by referring again to
our example of the legally sophisticated, profit maximizing physician.
The economic goal is to provide an incentive for the physician to order
the optimal level of diagnostic tests, the level which minimizes the sum of
the cost of tests and the expected cost of misdiagnosis. In an illustrative
punitive liability system, the physician is found liable and made to pay
huge punitive damages if the juror concludes that clear and convincing
evidence shows an extreme departure from the norm of reasonable care
in diagnosing. The evidence consists primarily of expert testimony
regarding what level of testing would have been reasonable under the
circumstances. The model developed here says that the illustrative punitive liability system will, in theory, create an optimal incentive for the
physician if the physician: 1) thinks that the evidence will never be bad
enough for the juror to find clear and convincing evidence of an extreme
departure from the norm if the physician actually chooses the optimal
level of testing; and 2) perceives a small but clearly positive chance of
huge punitive liability if there is failure to perform the reasonable level of
testing. The physician will have no incentive to over-test, because legal
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sanctions are escaped merely by performing the reasonable level of testing, and yet will be deterred from negligence in testing by the threat of
punitive damages.
D.
FOURTH APPLICATION: ERRORS IN STANDARD SETTING
We have considered cases in which the unknown to be inferred from
the evidence is the defendant's actual level of care, as well as cases in
which the issue is the proper level of the standard under the circumstances. The latter case involves factual uncertainty over the level of the
legal standard. A different kind of uncertainty in legal standards is
uncertainty in the juror's interpretation of the standard. Even if the level
of the legal standard is not a contested issue, jurors may well differ in
how they view "reasonable" care, and may interpret the standard erroneously, in the sense that they interpret it in a way that the social policymaker did not intend. In the context of the model of decisionmaking
developed here, this kind of error in standard setting is important
because it implies that over-deterrence can be eliminated only by both
raising the burden of proof and requiring greater fault for liability.
Juror leniency in setting a very low standard of care can create the
potential for under-deterrence, by increasing the probability of failing to
find a negligent defendant liable. The severe juror, who sets a very high
standard and interprets "reasonable" care as requiring much more care
than the judge meant to require, raises the prospect of over-deterrence,
because now even if fact-finding were certain, the defendant would still
have to be concerned about the possibility that a harsh juror might find
that reasonable care was too little care. If the probability that a juror
will find the care level inadequate falls even as care is increased to due
care and beyond, then the defendant would perceive a positive marginal
benefit of taking care-the reduced probability of liability--even at due
care and beyond.47 Particularly when damages are uncertain and possibly supra-compensatory, the marginal benefit of care could exceed its
marginal cost well beyond the optimal care level.
When fact-finding is Bayesian imperfect, uncertainty in the juror's
interpretation of the standard may make it impossible to eliminate overdeterrence just by increasing the burden of proof. Even if certainty of
negligence is required, there still will be a chance of penalizing optimal
47. For a proof of this assertion, which assumes that the distribution of possible standards is
unbiased and symmetric about the correct level, see J. Johnston, Imperfect Information, supra note
13 at 143-44.
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care. The reason is that the juror who holds the defendant to an erroneously high standard of care may be certain the defendant is guilty even
when observing evidence levels which the defendant accurately perceives
as occurring even when optimal care is taken. Although this evidence
might be observed even if the defendant took the desired level of care, the
harsh juror thinks it would never be observed if the defendant took what
the juror considers to be reasonable care, a higher level than what is
economically optimal.
This effect is illustrated in Figure 6. The curvef* gives the distribution of evidence types if the defendant takes medium care, the efficient
f"
FIG. 6
e
f
e
e
level. The curvef' gives the distribution of evidence types if the defendant takes high care. The juror who thinks that "due care" is high care
will be certain that the defendant failed to take due care whenever the
evidence type is worse than e'. But the defendant perceives a positive
probability that the evidence will be worse than e' even if takes medium
care, the level the efficiency minded policymaker means by "due care."
Hence, even if the burden of proof was as high as possible and required
subjective certainty of noncompliance, the injurer would still perceive a
positive probability of being found liable even if socially optimal care was
taken.
The solution to the problem of false positives caused by harsh interpretations of the nominal standard must then be to either lower the nominal standard of care or increase the degree of negligence which must be
proven. If the harsh juror overinterprets the verbal standard by some
fixed degree, then there may be some lower standard, such as "some
care," which this kind of juror takes to mean optimal actual care.
(Indeed, if there is no announced standard which this type of juror thinks
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means medium care, then the juror must essentially be unresponsive to
the announced standard, in which case legal standards lose either symbolic or instrumental significance.) In terms of Figure 6, the idea is to get
the harsh juror to view "some care" as medium care and the evidence
distribution given compliance as given by f*. Then this juror, like the
defendant, would perceive no probability of observing an evidence type
worse than e* under the hypothesis of compliance with the standard, and
would be perceived by the defendant as never finding a complying
defendant liable.
Of course, some jurors may literally and accurately interpret a
relaxed announced standard and hence impose liability only when, for
example, lowest care or the most extreme failure to take care is shown;
and by assumption the goal was not to restrict liability by this much.
Jurors who literally interpret the new, more restricted liability standard
will often fail to find negligent defendants liable, and may never find liability for some slight violations of due care. However, the defendant will
still see a positive risk of liability from even marginal noncompliance provided that there are some jurors who do assign liability to such slight
violations. The hypothesized harsh juror who overly expands the substantive standard will do just this, since the standard has been set so that
this juror will find liability unless the defendant has actually complied.
While this analysis has assumed that the goal in fixing the burden of
proof and substantive standard is to eliminate the risk of false positives,
an aspect of the first-best liability system described in the previous Part,
it should be emphasized that the result established here is more general.
According to this model, however much the policymaker desires to lower
the risk of false positives, the possibility of erroneously expansive interpretations of the substantive standard necessitates relaxing the
announced standard as well as stiffening the burden of proof. When there
are two sources of error, fact-finding uncertainty and uncertain standard
setting, both the burden of proof and substantive standard must be
adjusted.
There are several reasons which account for overly expansive interpretations of substantive standards. Jurors may be hostile toward certain
types of corporate and institutional defendants, or may simply demand
supra-optimal safety when they are not actually made to pay the supraoptimal costs. On the other hand, the problem may lie not with juror
errors in interpreting the standard, but with overly expansive judicial
interpretations. Under some versions of the risk-utility test for products
liability, for example, the manufacturer is presumed to have known of
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the dangers posed by a product.4 8 To the extent that this test asks "given
what you, the juror, know now, could the defendant have modified the
product at lesser cost than the cost of the accident the modification
would have prevented?,"'4 9 it sets a supra-optimal standard. This is
because this test tells the defendant that some modifications, unjustified
in cost-benefit terms given reasonable expectations of harm at the time,
will be held necessary to avoid liability because they are justified given
the actual ex post realization of risk.
This interpretation of the risk-benefit test calls for supra-optimal
care. It can therefore over-deter. The theory outlined here says that a
legislature could offset this sort of expansive interpretation by requiring
that liability be found only if the product risks greatly outweigh the utility of the design, or if the cost of modification was far below the cost of
the accident it would have prevented. If the plaintiff could, by clear and
convincing evidence, prove this standard had been violated, then one
could be virtually certain that modification would have been cost-benefit
justified, not only vis-A-vis the realized risk reduction but also in light of
the ex ante foreseeable risk reduction. If substantial evidence shows that
an unusual, unforeseeable explosion could have been prevented at very
little or no cost, then the ability to have prevented a number of foreseeable explosions by making such a low cost modification, in addition to
negligence in failing to so modify the product, would undoubtedly be
established."
Thus, regardless of whether the cause of overly expansive liability is
juror error or judicial pursuit of compensation and loss shifting goals,
restricting the nominal liability standard may offset such errors from the
deterrence point of view, and restore optimal incentives."
48. See Fischer v. Johns-Manville Corp., 103 N.J. 643, 512 A.2d 466 (1986); cf
RESTATE-
MENT (SECOND) OF TORTS, § 402A (1965) (manufacturer of defective products strictly liable for
harm to consumer).
49. This is what Calabresi & Klevorick have called the "ex post Learned Hand Test." See
Calabresi & Klevorick, supra note 1, at 590-91.
50. Compare the examples showing how the ex post Learned Hand Test without an adjusted
nominal standard calls for supra-optimal safety presented in Calabresi & Klevorick, supra note 1, at
594-96.
51. An important distinction between this Article and articles by Calfee & Craswell is that,
while there is agreement that the defendant may either under-comply or over-comply with the ordinary negligence standard of due care when there is uncertainty in the interpretation of the standard,
Calfee & Craswell conclude that it is impossible to say whether the nominal standard should be set
above or below the optimal level of care to restore efficiency. See Calfee & Craswell, supra note 1, at
998; Craswell & Calfee, supra note 1, at 295 n.21, 298 n.26. The reason they fail to arrive at a
determinate policy prescription on the optimal level of the nominal standard is because their analysis
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FiFTH APPLICATION: ASYMMETRIC
ACCESS TO THE EVIDENCE
One potentially troubling aspect of the prescriptions against overdeterrence recommended thus far is the implicit assumption that the
plaintiff has access to a sufficient quantity of evidence to meet a very
difficult burden of proof in showing fault. This section relaxes this
assumption and analyzes situations where the plaintiff has very little evidence, and the defendant knows this, but the juror views the small
amount of evidence presented by the plaintiff as simply indicating a weak
plaintiff's case, rather than underlying problems with evidence availability. The Bayesian model shows how this problem with evidence availability can cause under-deterrence, and how it can be cured by lowering
the plaintiff's burden of proof or shifting the burden to the defendant.
If the amount of evidence available to the plaintiff falls from the
benchmark quantity presumed thus far, then it will be impossible for the
plaintiff to present the same high quantities of evidence indicating low
care that were formerly possible. Assume as before that the plaintiff
always presents all the evidence he or she possesses which is unfavorable
to the defendant-which equals the total amount minus the amount of
favorable evidence available-and that the parties know the total amount
of evidence available to the plaintiff but do not know the composition of
this evidence, which is randomly determined. Then, when the total
amount of evidence available to the plaintiff falls, the parties recognize
that some very unfavorable evidence presentations are now ruled out. If
the type of evidence which determines the juror's decision is fixed by the
relative quantities of evidence presented by the parties, then the parties
will now perceive a lower probability of very unfavorable types of evidence when the total quantity of evidence available to the plaintiff falls.52
Most importantly, the defendant's subjective distribution of evidence
types shifts toward more favorable types. From the defendant's point of
does not include a formal model of juror decisionmaking, and because they do not consider the
burden of proof, nominal standard and measure of damages simultaneously.
Ellis, Fairnessand Efficiency in Law of Punitive Damages, 56 S. CAL. L. REv. 1,34-37 (1982),
and Owen, Civil Punishment and Public Good, 56 S. CAL. L. REV. 103, 114-17 (1982), also argue
that uncertain or vague standards susceptible to fluctuating jury interpretations require restricting
punitive damages to "flagrant" or "extreme" violations of due care. However, the only other attempt
to explain the burden of proof/magnitude of damages combination typifying punitive liability on
economic grounds is Keenan & Rubin, supra note 36, who argue that damages and the burden of
proof should be higher in the criminal system than in the civil system if criminals are risk lovers.
52. Assuming that the evidence type determined by the relative quantities of evidence
presented by the adversaries is not restrictive, because quantities can be weighted, so that one very
credible witness testifying to a moderate care level may count as heavily in determining the "quantity" of the defendant's evidence as several less credible reports of high care.
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view, it is more likely that any particular amount of good evidence it
presents will correspond to a high evidence type, because some high
quantities of bad, pro-plaintiff evidence are now impossible because the
plaintiff has a smaller total quantity of evidence available.
It is reasonable to assume that the defendant knows the total quantity of evidence available to the plaintiff if the defendant in fact possesses
most of the evidence in the case. If the juror is normally not informed as
to which side has access to the evidence, and does not take the asymmetry in access into account in forming a subjective distribution of evidence
types, then the juror will not perceive the increased likelihood of observing favorable evidence types, while the defendant will.
The basic consequence of this disparity between the defendant's
accurate perception of the distribution of evidence types and the juror's
mistaken beliefs is that any given liability test consisting of a measure of
damages, burden of proof, and nominal liability standard will underdeter relative to the deterrence it would achieve if the disparity did not
exist. The juror will look upon some favorable evidence types as indicating compliance, when in fact these favorable evidence types indicate the
plaintiff's lack of access to the evidence. In extreme cases, a defendant
could be assured of escaping liability even when taking less than optimal
care, if the defendant knew that evidence consistent with liability, given
the burden of proof, would never be observed at trial.
FIG.7
f2
f' (defendant's
perception, given
It takes optimal
care)
*
e
I
e(.5) e
e
This problem is illustrated in Figure 7, which again depicts a liability system designed to eliminate false positives by lowering the evidence
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threshold to e* (even for the harshest juror). Because the amount of evidence available to the plaintiff is restricted, however, the defendant perceives that the evidence will never be worse than ' if it takes medium
care, where a' is by construction a much better type of evidence than e_.
From the maintained assumption that better care generates (strictly) better evidence, it follows that the defendant is certain of escaping liability if
it takes less than optimal care, so that no matter how high damages
might be, the system depicted in Figure 7 must under-deter.
Figure 7 shows that if the inequality is severe, it may be impossible
to offset the effect of unequal access to the evidence merely by reducing
the plaintiff's burden of proof. To restore optimality, the evidentiary
standard must be moved to level g', for then the defendant will be certain
of escaping liability only if it takes medium care. If e' is less than e(5),
then it falls in a region where the juror thinks guilt is more likely than
innocence, and there is some plaintiff's burden of proof consistent with
'. But if, as in Figure 7, e' is to the right of a (.5), then it will be necessary to shift the burden to the defendant. In Figure 7, the defendant
perceives so much more favorable a distribution of evidence given compliance than does the juror, that even the harsh juror thinks evidence
type ' is more likely given compliance than noncompliance (i.e., f, is less
than f2 at '). This is a very good evidence type from the juror's point of
view, even though it really reflects the plaintiff's limited access to the
evidence.
The burden of proof corresponding to e' instructs the juror to find
liability unless non-negligence appears more likely than negligence.
When the juror comes into trial thinking guilt as likely as innocence, the
defendant must bear the burden of convincing the juror that innocence is
more likely than guilt. Thus, when the plaintiff does not have access to
the normal amount of evidence and the defendant knows this but the
juror does not, any given liability system will be a weaker deterrent than
desired unless the burden of proof is relaxed or shifted to the defendant.
Once again, however, it should be pointed out that this model generalizes also to cases where the plaintiff has, unbeknownst to the juror,
exceptionally good access to the evidence. In such a case, the juror
might think that a particularly unfavorable evidence type was inconsistent with compliance. But if this evidence type was really the product of,
say, limited discovery by the defendant so that the defendant viewed it as
quite likely even given actual compliance, then there would be a positive
perceived probability of a false positive, contrary to the assumed goal of
the system, which required certainty of noncompliance for liability. The
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model's prescription for this problem is to decrease the substantive
standard.
This latter case, where the plaintiff has advantages in evidence
access of which the juror is unaware, might describe some criminal cases,
where the prosecution has access to the grand jury process. The situation where the plaintiff is at an evidentiary disadvantage is perhaps more
typical of tort lawsuits brought by individuals against institutional
defendants. The model may thus explain civil doctrines such as res ipsa
loquitur and strict products liability (insofar as it is justified by evidentiary considerations) as evidentiary devices designed to prevent underdeterrence due to defendant's superior, and otherwise unaccounted for,
access to evidence.5 3 A deterrence-oriented criminal system, conversely,
might be expected to employ difficult substantive standards justified in
part as safeguards against false positives.
III.
CONCLUSION: POLICY IMPLICATIONS AND ISSUES
The fact-finding model developed and used in this Article is admittedly abstract. However, it provides insights into the impact of uncertainty on the incentives created by fault based liability rules, which are
not available in a less formal setting. By describing a liability rule as a
configuration of damages, substantive standard of care or fault, and burden of proof, the model provides much more detail than has previously
been present in economic analyses of liability rules. Such a relatively
rich, albeit formal depiction of liability rules is crucial not only in analyzing the effect of uncertainty but in designing responses to uncertainty.
53. For the classic judicial statement of this rationale for res ipsa loquitur in medical malprac.
tice, see Ybarra v. Spangard, 25 Cal.2d 486, 154 P.2d 687 (1944), and in strict products liability, see
Escola v. Coca-Cola Bottling Co., 24 Cal.2d 453, 463, 150 P.2d 436, 441 (1944) (Traynor, J., concurring). A more recent judicial recognition of evidence access asymmetry in products liability is found
in Barker v. Lull Eng'g Co., 20 Cal.3d 413, 431, 573 P.2d 443, 455, 143 Cal. Rptr. 225, 237 (1978),
holding that:
Because most of the evidentiary matters which may be relevant to the determination of the
adequacy of a product's design under the "risk-benefit" standard . . . involve technical
matters peculiarly within the knowledge of the manufacturer, we conclude that once the
plaintiff makes a prima facie showing that the injury was proximately caused by the product's design, the burden should appropriately shift to the defendant to prove ... that the
product is not defective.
(quotedin Calabresi & Klevorick, Four Tests for Liability in Torts, 14 J. LEGAL STUD. 585, 593 n.21
(1985)).
Calabresi and Klevorick also observe that courts often shift the evidentiary burden to the
defendant at a response as an alternative to adopting a different substantive test for liability. Id. at
592-93. See also Note, ProductsLiability and the Problem of Proof 21 STAN. L. REV. 1777 (1969).
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The model shows why the paradigmatic negligence rule, which
assesses compensatory damages if a violation of due care is shown by a
mere preponderance, is not necessarily efficient. It also shows how false
positives and the consequent threat of over-deterrence can theoretically
be eliminated by requiring the plaintiff to meet a difficult burden in establishing gross fault. When combined with high punitive damages, an
appropriately adjusted burden of proof and heightened fault requirement
can restore optimal incentives. With perfect safeguards, the model says,
punitive damages will not only deter and punish, but they will optimally
deter. This is the first time that punitive liability has been defended on
efficiency grounds in such a general way.54
The particular application of the model to designing an efficient
punitive liability system obviously relies on the strong assumption that
perfect punitive safeguards are achievable. This assumption may be quite
implausible, and moreover, it runs counter to the general spirit of the
model presented here, which assumes that legal rules are blurry, and that
the innocent are not to be easily separated from the guilty. However, the
idea of punitive liability as an optimal deterrent has been presented here
merely to illustrate the general power of the model of fact-finding I have
developed.
Indeed, the applications of the model to incentive problems caused
by errors in standard setting and asymmetric access to the evidence are
of even greater importance, for these reveal the generality of the model.
Although I focused here on how uncertainty in the standard and disparate beliefs about evidence affect a liability system designed to eliminate
false positives, the model could be extended to examine the impact of
these factors on any liability system designed to achieve an arbitrary
probability of false positives.
The fundamental implication of this analysis is that announced legal
rules must differ systematically from the law's actual goals if the
announced rules are to optimally deter legally sophisticated actors who
perceive uncertainty in the adjudication of factual issues. An announced
substantive standard may say that only the very careless are punished,
but only in order to offset errors by jurors who interpret announced standards too harshly. And the location and level of the burden of proof are
54. For a comparison of this view with previous economic analyses of punitive damages, see
Johnston, Punitive Liability: Toward a New Paradigmof Efficiency in Tort Law 87 COLUM. L. REV.
(forthcoming 1987).
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determined not by the judge's concern over the two kinds of errors possible at trial, but by the need to assure defendants that noncompliance will
be provable while compliance cannot be wrongly cast as a violation.
These implications may well be disturbing. The stated goals of the
law are not its actual goals. The law either deceives or, if taken literally,
sends the wrong signal entirely. But there is difficulty in a disparity
between announced and actual goals only if it is assumed that there is but
a single audience toward whom legal commands are directed. Indeed,
one of the greatest failures of law and economics scholarship has been its
treatment of all persons as rational cost-benefit calculators who are
keenly aware of, and sensitive to, the implications of present behavior for
future liability. This Article, however, has explicitly had in mind only
the compliance incentives of the legally sophisticated defendant which
responds to the evidentiary implications of its behavior, not the mass
public. If we assume that there are two such separable audiences, then
the distortion between desired and announced conduct which this Article
argues is necessitated by uncertainty is not only not troublesome, but a
positive attribute. For then a liability system which ostensibly punishes
only severe departures from social norms, and then only when the jury is
very convinced by the evidence, will simultaneously optimally deter the
legally sophisticated and give the ex ante insensitive mass public a clear,
admonitory ex post message that extreme departures from social norms
will not be tolerated. Finally, the theory developed here suggests a way
to eliminate the adverse consequences of uncertainty while preserving the
institution of trial by jury, and reserving that institution for telling stories
of gross departures from norms, rather than borderline violations whose
punishment evokes as much popular sympathy as condemnation. 55
This rather radical prescription for an efficiency oriented civil liability is an implication of an admittedly abstract model. However, the
insights of this model suggest a number of issues that must be probed in
order to make a more realistic assessment of the proposed punitive system. How does punitive liability compare to negligence, and to strict
liability, when perfect exclusion of non-negligent defendants is not possible? How does it compare when efficiency is defined more broadly to
take account of risk, legal transaction costs, victim incentives, and the
possible presence of market forces supplementing legal sanctions as a
55. Cf M. DAN-COHEN, supra note 39; Dan-Cohen, Decision Rules and Conduct Rules: On
Acoustic Separation in CriminalLaw, 97 HARV. L. REv. 625 (1984); Nesson, supra note 5; (arguing
that because organizations often lack direct autonomy rights, a utilitarian or economic approach to
legal rules regulating organizations involves less conflict with notions of autonomy than does application of the economic approach to individuals).
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deterrent? Is punitive liability likely to create optimal incentives even
when additional institutional imperfections such as imperfect liability
insurance, solvency constraints, and defendant errors in choosing care
are considered? And what role should punitive liability play in a tort
system designed to promote not only optimal deterrence, but also fair
56
and speedy compensation?
These questions are beyond the scope of this Article, as are other
potentially interesting applications of the model presented here, such as
the explanation of differences between civil and criminal liability, and the
influence of alternative liability systems on the costs and incentives created by the adversary system. The results developed here, however, suggest that this model will provide insights into these and many other
issues raised by inherent uncertainty and error in the litigation of fault.
56.
For analysis of these issues, see Johnston, supra note 54.
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