CAUSATION AND FORSEEABILITY
Tel Aviv University
© Copyright 1997 Omri Ben-Shahar
This essay begins with a survey of the implicit role of causation in thewritings of the early, pathbreaking economic analysts of tort law. It thenclarifies the basic distinction between retrospective (ex post) causation andprospective (ex ante) causation, a distinction that forms the core of manysubsequent economic discussions of causation. Next, the explicit role ofcausation doctrines in inducing optimal care and activity levels is examinedunder the strict liability and the negligence regimes. The analysis is thenextended to cover several complications often plaguing the determination ofcausation: uncertainty over causation, joint actions among tortfeasors, andunforeseeability of harm.
JEL classification: K13
Keywords: Foreseeability, Retrospective and Prospective Causation, OptimalCare, Strict Liability, Joint Actions.
The contribution of economic analysis to the clearer understanding of thefunction of law is particularly evident in the law of causation. The vast juristicliterature deliberating the proper meaning of causation has left a trail of doubtand uncertainty. Prominent traditional tort scholars have conceded that "thereis perhaps nothing in the entire field of law which has called for moredisagreement, or upon which the opinions are in such a welter of confusion"( Keeton et al. (1984, p. 263) ), and that "...both courts and textbook writers still fallback when deciding issues in causal terminology" ( Hart and Honoré (1985, p. 1) ).Economic analysis helps distinguish the different problems that are involved andoffers a unified approach to their resolution.
The attempts of traditional tort scholarship to make sense of the law ofcausation have led to the classification of the debates into two separatedoctrines, cause-in-fact and proximate cause . The cause-in-fact doctrineincorporates the law's endeavor to define and to conceptualize the criteria thatwould determine when an act is part of a causal chain that ends with the injury.Here, the but-for test is the most common intuitive criterion for inferring such afactual causality relation. Of all the acts that pass any of the cause-in-fact tests,the law narrows down the responsibility to those satisfying additional, "legal"tests, which are mostly embodied in the proximate cause doctrine. Liability isimposed only upon a sub-set of the acts that are causally linked to the injury,those that survive the scrutiny of a variety of normative judgments regardingtheir proximity to the harmful event. As Cooter (1987) nicely labeled it, theproximity doctrine portrays causation as a "decaying transitive relation": as thechain of causal inference extends ("a caused b, b caused c, ..."), the relationshipbetween removed links weakens without being destroyed.
The economic analysis of the law of causation illuminates both thecause-in-fact and the proximate cause doctrines. Economic analysis appliespositive tools from decision theory and statistics to clarify the definition of acause-in-fact, and to resolve some of the confusion regarding the relativecontribution of a given factor to the harmful consequence. Under the normativeeconomic analysis, the proximate cause doctrine's designated role is to expandor shrink the scope of liability, in order to achieve efficient deterrence.
This essay is structured as follows: It begins with a survey of the implicitrole of causation in the writings of the early, pathbreaking economic analysts oftort law. It then clarifies the basic distinction between retrospective (ex post)causation and prospective (ex ante) causation, a distinction that forms the coreof many subsequent economic discussions of causation. Next, the explicit roleof causation doctrines in inducing optimal care and activity levels is examinedunder the strict liability and the negligence regimes. The analysis is thenextended to cover several complications often plaguing the determination ofcausation: uncertainty over causation, joint actions among tortfeasors, andunforeseeability of harm.
The original economic theory of tort law deliberately rejected an explicit role fora causation doctrine in determining liability. Coase's (1960) view was particularlyresolute in its exclusion of a formal causation element. Coase describes an injuryas a result of mutual and symmetric interaction among parties. Like particles thatrandomly collide with each other in space, actions of individuals may conflictand cause one-sided or mutual harm. Thus, the phrase "the injurer acted and,when coming across the victim, caused an injury" is interchangeable with thephrase "the victim acted and, when coming across the injurer, caused an injury".Both passive and active factors are equally necessary in making the harm occur.
Since liability cannot be placed solely on the basis of causation, as both theinjurer and the victim are necessary causes, it ought to be decided according toa cost-benefit analysis, which will determine the identity of the party that canalter its actions more cheaply and avoid the injury. As Calabresi (1970) explained,for instrumental reasons the least-cost avoider should be singled out as thecause of an injury. The forward looking social objective -- minimization ofaccidents' costs -- will be furthered if a party that can prevent an accident witha lower cost than the harm arising from the accident will be regarded as the solelegal cause of the accident and be held liable. Hence, under this view, causationis not a preliminary condition for evaluating liability, but it is the conclusion ofthe evaluation. (See Cooter (1987) ).
Posner and Landes (1983 , 1987, p. 228-255) have reinforced this view andargued explicitly that causation has no role in determining liability. Inasmuch asthe purpose of tort law is to promote economic efficiency, the injurer should beregarded as the cause of an injury when he is the lower-cost avoider of it, andnot otherwise. Therefore, they claimed, "the idea of causation can largely bedispensed with in an economic analysis of torts". When efficiency analysis isconducted to determine liability, it can be fully pursued without reference tocausation. Inefficient behavior is synonymous with causing an expected harm.
The symmetry among the roles of the injurer and the victim, as well as theabsence of any independent requirement of causation, became well evidentwhen Brown (1973) formulated his rigorous model of accidents. This model -- thebenchmark for subsequent economic analysis of tort law -- assigned symmetricroles to the injurer and the victim, by making the expected harm a function ofcare levels taken by both. A party's action can raise the probability of harm and,thus, can only be a cause of an expected harm .
Thus, in early economic analysis of tort law, cause is reduced to efficientprevention: the assignment of legal cause is dependent solely upon thejudgment about the economic efficiency of preventive measures. The inquiryinto causation carries no additional message once a cost-benefit analysis of thecare choices has been completed. This characterization of causation, whichprominent scholars have labeled 'causal minimalism' (see Hart and Honoré (1985,p. lxvii-lxxvii) ), has led authors to argue that causation serves goals other thanefficiency ( Epstein (1973 , 1979 , 1987 ); Borgo (1979) ; Cooter (1987) ) or that itmerely represents an older method of conducting efficiency analysis ( Grady(1989) ; Miceli (1996) ).
Building on the analytical framework of Calabresi (1970) and Brown (1973) ,subsequent treatments of causation distinguished among two concepts offactual linkage between acts and harms. Calabresi (1975) classified the empiricaltests of causality into two types, which he labeled causal link and but-forcause . Both describe effects of actions on outcomes. An act is a but-for causeif, without it, the injury would not have taken place. In contrast, an act has acausal link to an injury if it increases the probability of its occurrence. As Shavell(1980) later rephrased the distinction, causation can be either retrospective orprospective. Retrospective causation exists if, all else held fixed, but-for theaction the harmful consequence would not have occurred. Prospective causationexists when an action raises the probability of the harmful consequence. Thus,the distinguishing factor between the two types of causation is the tim e-perspective of the evaluation. Retrospective causation is backward-looking,answering the counter-factual inquiry of whether the action was a necessarycondition for the outcome. Prospective causation, in contrast, isforward-looking, answering the ex ante inquiry of whether the action increasedthe likelihood of injury (See also Rizzo (1981) ; Miceli (1996) ).
This distinction, and in particular the development of analytical tools tofocus on prospective-probabilistic causation, has helped the economic literatureadvance both in its normative and positive study of the law. In the normativedimension, probabilistic causation became a building block of economic modelsof tort law. As Shavell (1980, p. 475) has explicitly phrased it, "the first-best levelof care is determined by the cost of taking care and the degree to which lack ofcare is a cause of expected losses ". For an action ("low care") to raise theprobability of a consequence ("harm") relative to another action ("high care"),there must be states of the world in which harm occurs only if that action istaken, and not if the other action is taken.
The prospective causation concept has also advanced the positive analysisof tort law. Perhaps the sharpest example of the contrast between retrospectiveand prospective causation theories, and the clearest application of prospectivecausation analysis, arises within the family of "coincidental" accidents cases. Inthe famous case of Berry v. Borough of Sugar Notch , 43 A. 240 (1899) , anexcessively speeding streetcar happened to arrive at a point along its route justwhen a tree fell above that point, and struck it. A strict retrospective causationinquiry would have identified the action of speeding as a but-for cause, since theaccident would not have occurred had the streetcar travelled more slowly.Applying the traditional retrospective approach, the court sensed the illogic ofassigning liability for such an arbitrary episode, thus had to resort to elusiveconcepts such as "coincidental harm" or "abnormal risk" in order to screen suchresults and derive a general principle that will restrict the scope of liability. Incontrast, under prospective causation inquiry the action of speeding isrecognized to have not affected the likelihood of harm of the type that occurred.Ex ante, a tree can fall at any point along the route, and the speed at which thevehicle is moving does not increase its probability of being hit. The result thatthe court reached can be easily aligned with the logic of prospective causation.(See Honoré (1983, p. 50-55) for early applications of the prospective causationconcept.)
The causation requirement, although not an explicit element in the ordinaryeconomic model of tort law, can be isolated and characterized in economic terms.The basic proposition made by Shavell (1980 , 1987, p.105-126) , and reiterated by Rizzo (1981) , Landes and Posner (1983 , 1987) , and Cooter (1987) , claims that thedesirability of any precautionary action should be determined only withreference to states of the world in which failure to take the action would lead togreater expected losses. In determining the level of care that is optimal, thebenefits of care should be balanced against its costs. But whereas the costs ofcare accrue before the ensuing state of the world materializes and regardless ofthe actual state of the world that will materialize, the benefits of care arise onlyin those states in which taking care reduces harm. For example, in the case of City of Piqua v. Morris , 120 N.E. 300 (1918) the defendant failed to take sufficientmeasures against floods. However, a particularly severe flood occurred, one thateven appropriate precautions would not have withstood. Thus, in evaluating thedesirability of anti-flood measures, only the chance for moderate floods shouldbe counted.
The idea that care can be cost-justified only with reference to states of theworld in which it can reduce the harmful consequence was formulated by Shavell(1987, p. 118-121) in causation terminology. Shavell defined care (or lack thereof)to be a necessary cause of harm if, given some state of the world, a different levelof care would have led to a different level of expected harm. He then proceededto show that the socially optimal level of care depends only on states of theworld in which the injurer's care would be the necessary cause of any losses thatoccur.
In order to examine the extent to which liability rules can implement optimalcare, a causation restriction was formally introduced to the structure of liabilityrules. Shavell's (1980) concept of the scope of liability incorporates thecausation restriction. The scope of liability is defined as the set of states of theworld under which liability can be applied. The scope of liability is said to berestricted if, given a harmful consequence, there are some states of the world inwhich the injurer is not held liable. The scope of liability will be unrestricted if,anytime there is a harmful consequence, and no matter what state of the worldsurrounded it, the injurer will be held liable. The design of a liability regimeincludes, in addition to the determination of due care (in negligence) and themagnitude of liability (both in strict liability and in negligence), the determinationof the scope of liability. If an act is not a necessary cause of the injury, the injurymay be left outside the actor's scope of liability.
Adding the determination of a scope of liability into the analysis nicelyextends the early economic models, by capturing the effects of conditionsbeyond the control of the human actors. When the probability or magnitude ofinjuries depend upon external conditions, analyzing such conditions within theformal structure of liability rules is necessary.
Under strict liability, courts have to determine the magnitude of liability and itsscope. Assuming the magnitude of liability equals the victim's actual harm, whatremains to be determined is whether the accident is to be included within thescope of liability. Two principal propositions can be made regarding theincentive effects of the determination of the scope of liability:
(1) The Effect of the Scope of Liability on the Level of Care - The injurer willhave optimal incentives to take care as long as the scope of liability includes atleast all the states of the world in which the injurer's care is a necessary causeof the harm. If the scope of liability is too restricted, and does not include all thestates in which the injurer could alter the harmful consequence with its care, thenthe injurer will have insufficient incentives to take care. In this case, the injurerwill ignore some of the social benefits of its care -- the reduction in expectedharm occurring in states of the world outside the scope of liability -- and willunderinvest in care. If, in contrast, the scope of liability is optimally restricted,and includes only states of the world in which the injurer's care is a necessarycause, the injurer will bear only the increment in expected losses due to itsactions, and will have optimal incentives to take care. Similarly, if the scope ofliability is unrestricted, so that whenever harm occurs, and regardless of thestate of the world, the injurer is held liable, the injurer will engage in optimal care.Notice that an unrestricted scope of liability does not, in itself, distort theinjurer's incentives to take care. Even if the injurer is liable for harms which itscare could not have prevented, it will not exercise excessive care. Taking morecare will not prevent the harm in the states of the world in which care is not anecessary cause, and thus will not reduce its expected liability. Hence, theinjurer's incentives to take care can be distorted only by an overly-restrictedscope of liability, not by an unrestricted one. (See Shavell (1980 , 1987, p.105-110) ; Landes and Posner (1987, p. 236) .)
(2) The Effect of the Scope of Liability on the Level of Activity - If the scope ofliability is too restricted, and does not include all the states in which the injurer'scare is a necessary cause, it was already established above that underinvestmentin care will arise. This underinvestment can also lead to excessive incentives toengage in the activity, as the injurer will not bear the full "externality" of itsactivity. The cost of engaging in the activity is reduced by the incrementalreduction in the investment in care and by the incremental reduction in theexpected liability and, thus, an injurer may engage in an activity even when it isundesirable from a social point of view. Similarly, if the scope of liability is toobroad or unrestricted, it may discourage an injurer from engaging in a sociallydesirable activity. Although the injurer who faces an unrestricted scope ofliability will not take excessive care, the injurer will face an inflated expectedliability. As Shavell (1980 , 1987, p. 108) has termed it, the injurer may find theunrestricted scope of liability to be "crushing". An activity that is worthwhilemay be deterred by imposing upon the actor costs of losses that would havebeen occasioned regardless of this activity. For example, if a car manufacturer isheld liable for accidents arising from bad conditions of roads, such that cannotbe avoided by extra prevention devices in the car's design, it may be led toreduce the volume of production. Hence, for injurers to engage in optimal levelsof activity, courts have to restrict the scope of liability appropriately, which,according to some (e.g., Burrows (1984) ), may demand too much sophisticationfrom the legal system, and, according to others (e.g., Wright (1985) ) does notreflect prevalent causation doctrines.
Under the negligence rule, courts have to determine the level of due care, themagnitude of liability and the scope of liability. Assuming that the magnitude ofliability equals the victim's actual harm, what remains to be determined is whichharms should be factored into the determination of the standard of due care, andunder what states of the world the accident is to be included within the scopeof liability. Shavell (1980 , 1987, p. 105-121) has made the following propositionsconcerning the incentive effects of causal determinations:
(1) The Determination of the Optimal Standard of Care - The due level of careshould equal the optimal level of care, as determined by considering the effectof care only in circumstances in which care is a necessary cause -- that is, onlyin states of the world in which taking care would reduce harm. Care that has nobearing on the occurrence of harm should be excluded from the negligencestandard.
(2) The Effect of the Scope of Liability on the Actual Level of Care - Once astandard of due care is set, the scope of liability has only limited incentiveeffects. Whether the scope of liability is optimally restricted (to include onlystates of the world in which the injurer is the necessary cause), or whether thescope of liability is too broad or unrestricted, the injurer will take the due levelof care (assumed to be set optimally). Further, unlike the activity-crushing effectof strict liability, under the negligence rule an unrestricted scope of liability doesnot necessarily deter the injurer from engaging in the activity. The injurer isinduced to take due care and thereby avoid liability, and thus becomesindifferent as to the actual scope of liability ( Landes and Posner (1983 , 1987,p.236 )). As long as the exaggerated scope of liability does not boost the level ofdue care, it has no adverse incentive effects per se. In contrast, if the scope ofliability is too restricted, and does not include all the states in which the injurer'scare could have reduced harm, the injurer may (but not necessarily) be led totake too little care. The injurer will compare the cost of due care to the cost ofliability in its inefficiently restricted scope. If the cost of liability is smaller, theinjurer's incentives to take due care will be distorted.
(3) The Scope of Liability in an Imperfectly Operating Negligence System -Inasmuch as the application of the negligence rule is plagued with error anduncertainties, it contains an element of strict liability (the injurer may bearliability even if he were not negligent.) In this case, the unrestricted scope ofliability can have the crushing effect that is associated with the operation of astrict liability rule (Shavell (1980 , 1987, p. 108) , Landes and Posner (1983 , 1987,p. 236) ).
Even after Shavell's (1980) analysis of the optimal scope of liability, showingthat liability should be restricted only to accidents that would not have occurredhad the injurer employed due care, most economic models of negligence,including part of Shavell's (1987) book, continued to implicitly assume that thescope of liability is unrestricted, and that liability turns solely upon the injurer'snegligence. That is, if the injurer were negligent, no matter how slight itsdeviation from due care, it is liable for any accident that arises, includingaccidents that additional care would not have prevented. Grady (1983 , 1984 , 1989) , Kahan (1989) and Marks (1994) have shown that the analytical frameworkwhich assumes unrestricted scope of liability is not in line with either tortdoctrine or optimal incentive design. To adhere to Shavell's analysis and restrictthe scope of liability so that it includes only accidents that were caused by theinjurer's negligence, would imply that an injurer who takes less than due care isnot liable for every harm that arises, but only for those harms which would nothave arisen had the injurer taken due care. Thus, if the injurer takes slightly lessthan due care, the proper scope of its liability would include only the (slight)incremental harm that occurred due to this deviation, and will not include allharms that would have occurred anyway. In the ordinary case in which carereduces the probability of an accident but not its magnitude, if the accidentoccurs the negligent injurer will have to pay damages with a probability lessthan one.
Using Kahan's (1989) illustration, suppose the proper height of a fencesurrounding a stadium is 10 feet, and the field owner erects a fence of 9 feet. Ifa ball flies over the fence and causes harm, the scope of liability should be (and,as a matter of common law, is) restricted to those accidents caused by ballsflying over the fence at heights between 9 and 10 feet. Only those accidents arecaused by the field owner's negligence. Making the field owner liable for allharms caused by flying balls, including those that fly at heights exceeding 10feet, would mean imposing an unrestricted scope of liability.
Until Kahan (1989) exposed it, most economic models managed to concealtheir incorrect characterization of the scope of liability. The reason these modelssuccessfully overlooked this restriction relates to the discussion above, whichsuggested that in the case of a perfectly operating negligence system anexaggerated scope of liability does not have a distorting effect. Since theperfect-information models of negligence find that the injurer will have theproper incentives to take optimal care under even the exaggerated scope ofliability regimes, and since there is no crushing of activity effect, they suppressthe significance of the exaggerated scope of liability. But, as Kahan clearlydemonstrated, an unrestricted scope of liability will have different incentiveeffects from an optimally restricted scope of liability in cases in which theapplication of the negligence rule is plagued with information imperfections.
Grady and Kahan's analyses also suggest that the proper characterizationof causation should eliminate what is otherwise considered a prominent featureof the negligence rule: the discontinuity of the injurer's cost function at the pointof due care. This feature of discontinuity plays an important role in modelsanalyzing injurers' behavior under uncertainty (see, e.g., Craswell and Calfee(1986) ; Shavell (1992) ; Ben-Shahar (1995) ). If the injurer' cost function iscontinuous, as Grady, Kahan, and Cooter (1989) have demonstrated it to be, theincentive to deliberately engage in excessive care, to ensure compliance with theuncertain legal standard, is significantly diminished.
7. Uncertainty over Causation
When an injury occurs, its origin may be ambiguous. Several reasons mayaccount for the uncertainty. First, it may be that separate factors created similarrisks simultaneously, and the actual injury cannot be clearly traced to any oneof them. Second, it may be that the injury manifested itself a long period after therisk was created or the accident occurred, in which case the cause is difficult toidentify. The principal question that needs to be addressed in the face of causaluncertainty is under what conditions should a party be liable for injuries thatare uncertain to have been caused by its actions ?
Two basic approaches to liability in the face of uncertainty over causationcan be proposed. The first approach applies an all-or-nothing criterion todetermining liability. An all-or-nothing criterion holds that either there is noliability or, if liability is imposed, then it equals the full losses of the victim. Themost common all-or-nothing criterion is the threshold probability rule, underwhich full liability is imposed upon the defendant if the probability that it causedthe accident exceeds a threshold level. Potentially, any threshold can be set,including one that would require proof of causation exceeding any reasonabledoubt. However, the prevalent doctrine applying the threshold probability ruleis the preponderance-of-the-evidence standard of many common lawjurisdictions, which incorporates a threshold probability of 50 percent. (In somecases the law reverses the burden of proof and presumes that the defendant isthe cause of the injury. Then, the defendant needs to satisfy the 50 percentthreshold in proving that he is not the cause of the injury.)
The second approach to resolving uncertainty over causation incorporatesa proportional liability criterion. Under this approach, whenever there is apositive probability that the defendant caused the injury, liability will beimposed, but its magnitude will be reduced proportionally to account for theuncertainty. The most common proportional rule, known as the "market share"approach, sets the defendant's liability equal to the actual harm multiplied by theprobability that the defendant caused the injury.
Traditionally, the law of torts has been governed by the first approach ofall-or-nothing. Full liability is assigned to a party whose acts are assessed to bea substantial factor in bringing about the harm. A "preponderance ofprobabilities" -- a threshold of 50 percent -- is required for imposition of liability,and without it no liability is inflicted. However, beginning in the 1980's, andcoming as a response to the onslaught of mass exposure or catastrophic injurytorts, American courts have been more willing to apply the second approach. Inthe case of Sindell v. Abbott Laboratories 607 P.2d 924 (1980) , which involvedthe mass disaster of the DES drug, the court determined each manufacturer to beliable for a fraction of every victim's harm, with liability determined in proportion
to the manufacturer's market share. The debate over the market share doctrinehas since occupied many branches of tort scholarship, including law andeconomics. The next two Sections examine the economic justifications for thetwo approaches.
The first systematic analysis applying economic methods to compare the twoliability approaches was presented by Kaye (1982) , who proposed to show thesuperiority of the 50 percent threshold probability rule over any other thresholdprobability rule as well as over the proportional approach. Kaye's argument isbased on the assumption that in situations of uncertainty over causation thesocial objective of tort adjudication is to minimize the ex post costs of erroneousliability decisions. Ignoring any ex ante incentive effects that the rules may have,and assuming that the two types of potential errors courts could make -- falsepositives and false negatives -- are just as costly, Kaye shows that the 50percent threshold rule is the error-minimizing one. To illustrate the essence ofKaye's argument, consider a case in which the harm is $100 and the probabilitythat the defendant caused it is 40 percent. Under thepreponderance-of-the-evidence rule, the defendant will not be liable, and theexpected error costs will equal $40 (there is a 40 percent chance that thedefendant is truly the tortfeasor, in which case it underpays by $100, for anexpected error cost of .4×$100 = $40). In contrast, if the court applies theproportional liability rule and sets the defendant's liability at $40, the expectederror costs will be $48 (there is a 40 percent chance that the defendant is truly thetortfeasor, in which case it underpays by $60, for an expected error cost of .4×$60= $24; and there is a 60 percent chance that the defendant is not the tortfeasor,in which case it overpays by $40, for an expected error cost of .6×$40 = $24; thesum of the expected costs of the two possible errors is $24 + $24 = $48).
The all-or-nothing feature embodied in the threshold liability rule has anadditional potential advantage, suggested by Levmore (1990) , of reducing thedegree of uncertainty. If uncertainty is assumed to be endogenous, and to varyaccording to the incentives of the parties to bring evidence to court, then theliability approaches can be compared with respect to the degree of uncertaintythey generate. Here, Levmore claims, a high threshold probability will producethe most evidence and lead to the least uncertainty. When uncertainty is greatand tortfeasors are difficult to identify, plaintiffs face a complete denial ofrecovery under a threshold rule that sets a sufficiently high thresholdprobability. This will induce plaintiffs to invest more in developing evidence andidentifying the true injurers. In contrast, under a market share regime plaintiffsneed not invest in identifying the true injurers, since they are fully compensatedregardless of the degree of uncertainty. (Of course, if the defendant, rather thanthe plaintiff, were assumed to be the party that can develop superior evidence,then a market share rule will give the defendant the greatest incentives to bringevidence.) Again, ignoring the ex ante incentive effects of the rules and focusingon the ex post characteristics of the adjudicatory regime, a case is made for thethreshold probability rule.
Apart from minimizing uncertainty and the ex post costs of uncertainty, thethreshold probability approach may offer the additional advantage of reducingadministrative costs. As Shavell (1987: p. 117) suggests, there are three distinctreasons that the administrative costs will likely be higher under the proportionalliability approach. First, the volume of cases is likely to be higher under theproportional liability approach, because actions in which the probability ofcausation is less than the threshold could be brought. Second, more defendantscould be sued in a typical case under the proportional approach, raising thecosts of litigating the case. And thirdly, litigation under the proportionalapproach requires the added judicial determination of the precise probability ofthe defendant being the cause of the injury, whereas under the thresholdprobability approach the only thing that matters is whether the probability ofcausation exceeds the threshold. Some of these excess costs may be diminishedunder the enforcement regime that Rosenberg (1984) has proposed, whichborrows features from "public law", such as class actions, damage scheduling,and insurance fund judgments.
An economic analysis purporting to show the potential superiority of theproportional rule was presented by Shavell (1985 , 1987, p. 115-118, 123-126) .Shavell evaluated the effects of the two approaches with respect to a differentsocial objective from the ex post error-costs minimization criterion. Adopting anex ante focus, Shavell took the objective of liability regimes to create optimaldeterrence, i.e., the minimization of accident losses. In this perspective, legalerrors do not involve a welfare cost per se, and their minimization could perhapsbe taken as a measure of fairness but not as a proxy for optimal deterrence. (Seealso Kaplow (1994) ). Once embracing the social objective of optimal deterrence,Shavell has managed to demonstrate that the proportional liability approach isthe superior method of inducing socially desirable behavior.
The main propositions made by Shavell are as follows. First, the thresholdprobability criterion distorts the incentives of parties to take care. If theprobability of causation is systematically below the threshold probability, theparty will face too little liability and will take less than optimal care. This problemof underdeterrence under the conventional threshold probability rule waslabeled by Levmore (1990) and Farber (1990) as the problem of recurring misses .For example, if the probability of a party being the cause of a typical injury issystematically 40 percent (as in the case of a manufacturer holding a 40 percentshare of the market for a harm-causing product), the party will always escapeliability under the 50 percent threshold rule. The net of liability will miss thisparty repeatedly. Thus, the party will have no incentives to take care. Theunderinvestment result arises both under the negligence rule and under strictliability. (See also Landes and Posner (1987, p. 263-269) ; Robinson (1985) )
Similarly, if the probability of causation is systematically assessed above thethreshold, the injurer may have excessive incentives to take care. This distortionwill arise under a strict liability regime, since the injurer will pay for all losses,more than it actually causes. The injurer may take excessive care for a subtlereason. Since the injurer pays for all losses only if he is determined to by thelikely cause, the injurer will have the incentive to reduce the chance that thisdetermination would be made. By taking excessive care, the injurer may be ableto reduce the posterior probability that he will be designated as the likely causeof the injury. That is, extra care may shift the preponderance of probabilities, andclear the injurer from liability altogether. Notice that this overinvestment resultwill not arise under a negligence regime, since the injurer will take due care andwill avoid the excessive liability (unless, of course, the level of due care is ill
defined). This is another illustration of the general proposition discussed inSection 6 above, which claimed that an unrestricted scope of liability -- that is,liability for consequences that a party did not cause -- does not in itself lead todistorted incentives, and only enhances the motive to take due care under anegligence regime.
In contrast to the distorted outcome under the threshold probability rule, theproportional liability approach leads to socially optimal levels of care (see Delgado (1982) ; Rosenberg (1984) ; Shavell (1985 , 1987, p. 115-118) , Levmore(1990) ). The injurer faces expected liability equal to the expected loss associatedwith its behavior, and will behave as it would in the absence of uncertainty overcausation. For example, a manufacturer who causes 40 percent of the harms ofa particular type will pay for losses in every case, including the 60 percent of thecases which it did not cause. But in every case its liability will equal 40 percentof the individual harm, thus it ends up bearing liability of 40 percent of the totalharm, equal to the fraction it caused.
Another important proposition made by Shavell concerns the incentives ofparties to engage in the activity that produces the harm. Again, the thresholdprobability rule distorts ex ante incentives. When the probability of causationis systematically above the threshold, the injurer will be overdeterred fromengaging in activity under the strict liability regime. (Under the negligence rulethe injurer takes due care and escapes liability, thus engages in the same levelof excessive activity as it does in the absence of uncertainty over causation. See Shavell (1987, p. 21-32) .) Likewise, when the probability of causation issystematically below the threshold, the injurer escapes liability and, as a result,engages in excessive levels of activity, both under negligence and under strictliability. In contrast, under the proportional liability rule, the injurer's incentivesto engage in the activity are the same as they would be in the absence of anyuncertainty over causation.
Several authors have argued that the market share approach may lead afree-rider problem which will cause underinvestment in care. Marino (1991)demonstrated that care practiced by one firm produces benefits to other firms.By reducing the probability of harm associated with its products, a firm producesa positive externality captured by the other firms in the form of reduced expectedliability. That is, each firm will underinvest in care because it bears the cost ofcare in full but can appropriate only a share of its benefits. The magnitude of thisunderinvestment will diminish as the firm's market share increases, and theunderinvestment problem will disappear if the firm is a monopoly. In similarspirit, other authors have argued that proportional liability will not generateoptimal incentives for safety research. Delgado (1982) and Rose-Ackerman(1990) have pointed out to the public good characteristics of safetyimprovements, and speculated that the infliction of full liability on an injurer whohas the greatest opportunity to conduct safety research may be superior to thedivision of liability according to proportional causation.
The dichotomy between the proportional liability approach and theall-or-nothing threshold probability approach reflects the tension between exante and ex post goals of the tort system. A framework that seeks to unite thetwo approaches has been offered recently by Porat and Stein (1997) . Under thisframework, a liability rule should be designed to give incentives to parties whoare the cheapest evidence providers , to reduce the ex post uncertainty inassessing liability. The ingenious mechanism these authors examine is titled"liability for uncertainty" -- imposing liability for an injury whose cause isuncertain on the party that created or had the best opportunity to prevent thatuncertainty. This will lead the parties to invest optimally in removinguncertainties, and when ex post uncertainty is eliminated, the ordinary liabilitymechanisms can operate to generate optimal incentives to reduce the primarydamage. Thus, for example, DES manufacturers can either eliminate theuncertainty over causation (thus avoid liability for uncertainty), in which casethe all-or-nothing approach will apply and will generate optimal care incentives,or the manufacturers can choose not to eliminate the uncertainty over causation,in which case they will be liable for the injuries based on their proportionalcontribution to the creation of uncertainty.
The market share approach is a doctrinal step away from the strict fundamentalsof causation. But it is not the most radical step. With the growth of massexposure torts, and due to the large degree of uncertainty over causation inthese torts, authors have advocated an even more unorthodox mechanism legalmechanism which will practically abandon any causality requirement betweenthe injurer's action and actual harm. The idea is to structure a liability regimebased solely on "probabilistic causation". Under this regime, liability isproportional not to the harm itself, but rather to the risk of harm which the actorproduces; it is applied regardless of whether this risk actually materializes. Forexample, an individual who uses a product and later discovers that she is undera particular risk, that may or may not develop into actual harm, may recoverdamages equal to her expected harm. Thus, liability is assigned strictly on thebasis of the creation of unreasonable risk, independent of any injury. Contraryto the dominant role that the causation requirement was given in other influentialtheories (as in Epstein (1973) ), here the causation element is essentiallyeliminated.
Robinson (1985) and Landes and Posner (1984 , 1987, p. 263-269) have arguedthat awarding its expected losses to each potential victim exposed to the risk ofharm will create the proper incentives for injurers to take care and to select thecorrect activity levels. In the context of mass exposure accidents, and in light ofthe severity of risk-spreading and bankruptcy concerns, this view has triggeredserious attention. (See, e.g., Roe (1984) ; Celli (1990) .)
Viewed ex post, this approach gives many potential victims a windfall, asthey are going to be compensated without actually bearing any risk; at the sametime, actual victims will be undercompensated. But viewed ex ante, this approachcan provide superior incentives for care relative to other approaches that haveto await the actual, oftentimes lagged, harm and, thus, dilute the deterrent forceof liability. Obviously, a troubling aspect of a risk-based liability regime is itsadministrative costs. Litigation need not be conditional on occurrence of harmand thus could be more frequent, let alone more complicated (see Celli (1990) ).At the same time, each victim is awarded only a fraction of the actual harm,which may reduce the incentives to take legal action and, consequently, will leadto underdeterrence.
A different approach to monitoring incentives in cases that pose inherentdifficulties in ascertaining causation is a centralized approach, relying onadministrative regulation to enforce optimal risk reduction. Several authors( Shavell (1984 , 1993) ; Cooter and Ulen (1989, p. 420) ) have examined theadvantages of relying on regulatory authorities to monitor and deter risk creationin the period before harm manifests itself. These authors have suggested thatregulation of safety may perform better than a risk-based liability system inpreventing mass torts. The main justifications for the superiority of a regulatoryregime are: (1) The government may be a better information-gatherer than theinjurer; (2) Injurers may be judgment proof in catastrophic harms, thus liabilitywill not generate sufficient deterrence; (3) Suits may not be brought in all cases,due to their costs and to victims' lack of information, thereby diluting thedeterrent effect of liability; (4) Administrative costs of decentralized liabilityregimes may be higher.
Uncertainty over causation may involve another dimension. Apart from thedifficulty of identifying the actual cause-in-fact -- the party whose act caused theparticular accident -- courts may face the difficulty of determining the relativecausal share of each of several tortfeasors. There may be information as to theprobabilistic contribution of each act -- what ex ante risk each act imposes -- andhow the risks change when acts occur simultaneously. However, when two actsoperate simultaneously to cause harm, the contribution of each act to thecombined risk has to be determined before courts can apply either the thresholdprobability approach or the proportional liability approach. This determinationinvolves a "disentanglement" of the harm-production process, a logical exercisewhich has proven to be problematic.
To illustrate the problem, imagine two fires that are set simultaneously andindependently and combine to destroy a field. It is estimated that, ex ante, thefirst fire alone had a 10% chance of destroying the field, the second fire alonehad a 20% chance, and together they had a 50% chance of destruction. That is,their joint operation creates a synergistic effect. If both fires were set and thedestruction occurred, how should liability be divided across the two "causes"?Or, suppose a particular illness can be contracted either by use of a product (1%)or, independently, by smoking (4%). However, if an individual both uses theproduct and smokes, the risk increases to 15%. Again, a significant synergisticeffect exists. What fraction of the harm can a smoker that has used the productrecover from the manufacturer? In both examples, how should the synergisticeffect arising from the multiple causes joined together be divided across thecausal contributors?
The problem of allocating the shares of liability in accidents that havemultiple causes is said to have "generated a bewildering variety of legal rulesand nomenclature" ( Kaye and Aickan (1984) ), and have perplexed scholars whoexpressed "doubts that there exists a single factotum satisfactory formula fordividing damages" ( Kruskal (1986) ). The first systematic treatment of the causalapportionment problem was offered by Rizzo and Arnold (1980) (see also Rizzoand Arnold (1986) ). These authors proposed an apportionment scheme thatassigns to each act a share of liability that consists of two elements. The firstelement is proportional to the act's "marginal product", which Rizzo and Arnolddefined to be the probability of harm given this act operating alone. The secondelement is a fraction of the synergistic effect, which Rizzo and Arnold arbitrarilyselected to be one half.
In the literature that followed, Rizzo and Arnold's allocation scheme wasgenerally rejected. Kaye and Aickan (1984) found flaws with the statisticalframework applied by Rizzo and Arnold, as well as with the material justificationsfor the apportionment scheme. In particular, Kaye and Aickan suggested thatRizzo and Arnold's definition of an act's marginal product -- the increase in theprobability of harm, given this act operating alone -- is no more appropriate thanmany other possible definitions, such as the incremental increase in theprobability of harm, given that the other act is also operating. Kaye and Aickanargued also that there is no one logical way to divide the synergistic effectacross the acts, and thus logic alone cannot provide a guideline for resolving thecausal apportionment problem. Hence, any apportionment scheme should beevaluated mainly according to the incentive effects it generates.
Further criticism of Rizzo and Arnold was voiced by Kruskal (1986) , Kelman(1987) and Rose-Ackerman (1990) , who again claimed that there is no oneprincipled way to apportion damages that will not be arbitrary and that will makeeconomic sense. An alternative to the Rizzo and Arnold method of defining anact's marginal product can be derived from the cooperative game-theory conceptof the Shapley value. This method offers a more structured way to define an act'smarginal product, based on its expected marginal contribution to the probabilityof harm, averaged over all possible combinations of acts (see Ben-Shahar(1996) .) While this approach enjoys some intuitive appeal that the previousmethod did not have, it has the similar shortcoming in its reluctance to considerthe ex ante effects of the apportionment rule on the incentives for care amongmultiple tortfeasors.
When multiparties are responsible for an injury, there may not exist anapportionment rule that leads to efficient incentives and keeps total liabilityequal to harm. To provide the right incentives to all parties, damages exceedingfull harm may need to be assigned. For example, Landes and Posner (1980 , 1987,p. 193-201) have focused on the effects of liability apportionment on incentivesfor care under the negligence regime. They have argued that joint tortfeasors canbe led to take due care under a no-contribution rule -- that is, a rule that makeseach party liable for the entire damage and allows the victim to determine eachtortfeasor's liability share. If the total cost of care is less than the expected harm,at least one of the injurers will have the incentives to take due care (his cost ofcare is less than half the expected harm), thereby placing the entire liability onthe other and leading the other to take due care as well. (See also Wittman (1981) for a related argument in a joint but sequential care setting.) Thus, in thecelebrated case of Summers v. Tice , 199 P.2d 1 (1948) , where two huntersindependently and simultaneously fired in the direction of a victim but only one-- unidentified -- hit, joint liability with no contribution will lead both to takeoptimal care. Notice that a doctrinal justification for making each hunter fullyliable can be obtained through Porat and Stein's (1997) idea of liability foruncertainty. Each hunter is liable since, but for his action, the apportionmentdifficulty would not have existed: either the fatal bullet was shot by him, inwhich case but for his action there would have been no injury, or the fatal bulletwas shot by the other, in which case but for his action there would have beenno uncertainty.
The problem with the negligence-based no contribution rule is that it maylead injurers to engage in excessive levels of activity. Miceli and Segerson (1991) study a different apportionment rule, one that would potentially lead jointtortfeasors to take efficient care and make efficient activity decisions. Theypropose a "decoupled" strict liability regime, under which each tortfeasor paysa sum equal to the difference between actual damages and the damages thatwould have resulted were he inactive. That is, all tortfeasors are held strictlyliable simultaneously , but each receives a "credit" for the expected damages thatwould have occurred in his absence. Since this rule may lead to paymentexceeding actual harm, the excess can be paid as a fine to the state.
Whether the objective probability of an accident is low or high should not initself affect its inclusion or exclusion from the scope of liability. As Shavell(1980) explained, even if the probability of the harmful consequence is verysmall, the act that is the cause of the increase in probability should carry liability.The effects on incentives to take care and on the level of activity will becorrespondingly small, as they ought to be. In addition, the added expectedadministrative costs of adjudicating a low-probability event are small, sincethese costs will be incurred only with a small probability. Thus, the benchmarkclaim is that whenever an act is a necessary cause of the harm, liability shouldfollow (see also Rizzo (1981) ).
However, to determine the incentive effects that any scope of liabilitygenerates, it is not the objective probability of harm that matters, but thesubjective probability -- the ex ante assessment of the possible consequencesas it is made by the injurer. Calabresi (1975) was the first to state explicitly thatthere is no sense in trying to deter an act which is a necessary cause of theinjury by threatening to impose liability on an injurer who assigns a subjectiveprobability of zero to the injury. An injurer who does not foresee a harmfulconsequence cannot be meaningfully labeled the least-cost avoider. As Shavell(1980) clarified and generalized, whenever the subjective probability is very lowin absolute terms, and lower than the objective probability in relative terms,liability will not produce sufficient ex ante behavioral effects to justify theincrease in the costs of dispute resolutions. Thus, under the doctrine ofunforeseeability, accidents whose probabilities are likely to be underestimatedby injurers should be excluded from the scope of liability. (But see Rizzo (1981) for an alternative view, advocating the use of objective probabilities indetermining the abnormality of events.)
It may be that an injurer does not foresee some specific low-probabilityconsequences that subsequently materialize. However, the same injurer may stillbe in a position to associate an activity with unforeseen risks. The injurer mayrecognize a large variance of outcomes even if it does not recognize the natureof each outcome in the distribution. In this case, assigning liability forunforeseen harms will have the desirable effect of reducing the level of anactivity that is known, ex ante, to cluster many unforeseen risks (see Shavell(1980) , Landes and Posner (1987, p. 250) ). For example, handing a loaded gun toa child leads to many unforeseeable risks (apart from the obvious ones), and canbe deterred by imposing liability on this action. Of course, when injurerssystematically fail to recognize the unforeseeable consequences of their actions,other forms of deterrence may be required, such as criminalizing the actions (see Calabresi (1975) ).
The scope of liability for low probability events has another important effect,in determining the incentives of potential injurers to investigate and contemplatethe potential consequences of their actions. That is, the amount of informationindividuals have regarding risk and risk avoidance can be thought of asendogenous, influenced in part by liability rules. The effects of liability rules onthe incentives to acquire accurate information ex ante have been studied in moregeneral contexts by several authors (see, e.g., Kaplow and Shavell (1992 , 1996) , Shavell (1992) , Ben-Shahar (1995) ). Specifically, as the scope of liability forlow-probability harms expands, individuals will have greater incentives to learnand anticipate these harms, and to take proper measures to avoid them (orliability for them). Thus, the unforeseeability doctrine should be replaced by adoctrine of "expensive foreseeability": only risks that are too costly to anticipateand foresee will be excluded from the scope of liability. Therefore, in operatingthe hand formula to determine whether lack of care should be considerednegligent, courts have to account not only for the direct costs of care, but alsofor the costs of foresight ( Calabresi (1975) ; Grady (1984) ; Landes and Posner(1987, p. 239-247) ).
The concept of unforeseeability in tort law differs from the concept ofunforeseeable damage in contract law. The tort doctrine excludes only "freak"accidents from the scope of liability and serves to avoid unnecessary disputeresolution costs. The contract doctrine serves only to limit damages to theaverage, reasonable, level. However, in economic terms, both tort and contractdoctrines can be justified by their effects on ex ante information acquisition. Thelimited scope of liability in tort should apply only when the risk is too costly forthe injurer to anticipate, thus it creates incentives to foresee. The limited scopeof liability in contract has the important effect of inducing high-risk contractualparties to reveal their idiosyncratic traits ex ante, so as to secure fullcompensation and to reduce the chance of breach (See Bebchuk and Shavell(1991) ).
Two prominent tort doctrines can further illustrate the role of foreseeabilityin monitoring incentives. The first doctrine distinguishes between categories ofharms and can be illustrated by the well-known case of Palsgraff v. Long IslandR.R. (162 N.E. 99 (1928)) . In that case, as the result of a railroad employee'snegligence, a parcel containing fireworks fell from the train, exploded and causedthe crowd to panic and to knock down scales that were standing on the otherplatform, in a manner that injured a passenger. Since the employees did not knowof the parcel's content, the court found the harm to be unforeseeable and outsidethe scope of negligence. This result is found by most economic writers to bejustified (see Calabresi (1975) ; Shavell (1980) ; Landes and Posner (1983 , 1987, p.246-247) ). Since the injurer discounted the probability of that type of accident ,liability would not have generated better incentives and would not have led toprevention of the accident. The injurer may be the least-cost avoider withrespect to losses from injuries to passengers and, at the same time, not theleast-cost avoider with respect to non-passengers. Making the railroad liable forinjuries to non-passengers from acts that were negligent due to the risk theyposed to passengers will either have no effect in reducing risks tonon-passengers, or may lead the railroad to engage in socially excessiveinvestments to identify freak accidents.
Another well-known tort law doctrine is the eggshell skull doctrine,according to which courts impose liability for bodily harm equal to the fullseverity of the injury, even if the extent of the injury was unforeseeable due toa pre-existing condition of the victim. This may seem to contradict the basiceconomic insight, which established that when the probability of a high loss issystematically underestimated, holding the injurer liable for the total loss doesnot increase the incentive to take care ( Shavell (1980) ). However, as Landes andPosner (1983 , 1987, p. 249-250) have explained, there is economic sense inholding liability for an unforeseeable extent of injury. First, allowing onlyaverage damages could potentially generate optimal care incentives, but only ifcarried out in all cases, including in cases in which victims have "thick skulls"(that is, awarding these victims average damages despite the fact such damagesare known to overcompensate them). Put differently, if at the high end of thedistribution of harms liability is capped, but at the low end of the distributionliability equals actual harm, average liability will fall short of average harm andthe incentives for care will be diluted. As long as victims with low-harms gettheir actual damages, victims with egg-shell skulls should also get their fulldamages, to maintain the correct level of average liability ex ante (see also Kaplow (1994) ; Kaplow and Shavell (1996) ). In addition, liability for an unlimitedextent of injury may have a desirable activity-reducing effect, resulting frominjurer's de-facto strict liability.
The restriction on the scope of liability that the causation requirement embodieshas, in itself, an ambiguous effect on the administrative costs of the legalsystem. A restricted scope leads to a lower volume of suits that are filed, savingthe litigation costs in cases that are clearly outside the scope of liability. On theother hand, if the scope is unrestricted there may be less harms (through areduction in the level of activity) and thus less suits, and each suit that is filedmay be less costly to litigate, as there is no causation issue to resolve. (See Shavell (1980 , 1987, p. 109) ; Landes and Posner (1983) .)
Informational imperfections and their legal treatment have important effectson the costs of resolving disputes. When courts are uncertain about causation,a significant portion of the trial effort may be devoted to disentangling thecausation process. Applying simple standards such as thepreponderance-of-the-evidence rule may reduce administrative costs,sufficiently so to overshadow its inferior incentive effects. Similarly, when thecourt's ex post assessment of the probability of harm exceeds the injurer's ex anteassessment, administrative costs of determining liability may tip the scaletowards categorizing the harm as unforeseeable. Lastly, when causation isdifficult to verify ex post, but probabilitic linkage is known to exist ex ante, thecosts of decentralized dispute resolutions may exceed the costs of a centralizedregulatory scheme, outlining the proper bounds of the civil liability system.
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