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The Robustness Case for Proportional Liability

Alexander Stremitzer
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  • UCLA School of Law, 385 Charles E. Young Drive, East, 1242 Law Building, Los Angeles, CA 90095-1476, USA
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/ Avraham D. Tabbach
Published Online: 2014-01-11 | DOI: https://doi.org/10.1515/bejte-2012-0013


In important areas like medical malpractice and environmental torts, injurers are potentially insolvent and courts may make errors in determining liability (e.g. due to hindsight bias). We show that proportional liability, which holds a negligent injurer liable for harm discounted with the probability that the harm was caused by the injurer’s negligence, is less susceptible to these imperfections and therefore socially preferable to all other liability rules currently contemplated by courts. We also provide a result which might be useful to regulators when calculating minimum capital requirements or minimum mandatory insurance for different industries.

Keywords: compliance; uncertain causation; court error; judgment-proof problem; proportional liability

JEL Classification: K13


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About the article

Published Online: 2014-01-11

Published in Print: 2014-01-01

Kornhauser and Revesz (1990) point to the problem that the strict liability rule under the Comprehensive Environmental Response, Compensation, and Liability Act is likely to drive some injurers into bankruptcy.

Strictly speaking, the probability of causation can be calculated as just described if we rule out the possibility that harm is prevented because the injurer fell short of exercising due care. (See Schweizer 2009, for a rigorous treatment of the application of the causation requirement under uncertainty.) Given this assumption, the causation requirement is equivalent to the rule of proportional liability as proposed by Shavell (1985) and others. This rule exactly internalizes the consequences of deviating from the due care standard.

In Evers v. Dollinger, 95 N.J. 399 (1984), the Supreme Court held that, in the context of a claim of medical malpractice, when there is evidence that the defendant’s negligence increased the risk of harm to the plaintiff and that the harm was in fact sustained, it becomes a jury question whether or not the increased risk constituted a substantial factor in producing the injury. The Court determined that a less onerous burden of establishing causation should be applied. See also Hake v. Manchester Tp., 98 N.J. 302 (1985); Scafidi v. Seiler, 225 N.J. Super. 576 (App.Div.1988); Battista v. Olson, 213 N.J. Super. 137 (App.Div.1986); Gaido v. Weiser, 227 N.J. Super. 175 (App.Div.1988). Both Dubak v. Burdette Tomlin Memorial Hosp., 233 N.J. Super. 441, 450–452 (App.Div.1989) and Zuchowicz v. United States, 140 F.3d 381 (U.S. Court of Appeals for the Second Circuit, 1998) contain very insightful discussions of increased risk/substantial factor theory. In King v. Burlington Northern Santa Fe Ry. Co. 277 Neb. 203, 762 N.W.2d 24 Neb., 2009 the Court, suggests that any positive association that could reasonably support a causal inference could be sufficient to send a case to a jury. See also Grechenig and Stremitzer (2009) for a survey of court practice across jurisdictions.

To the same effect, the German Federal Court (BGH) shifts the burden of proof to the injurer, if it can be established that he acted with gross negligence. He then has to prove beyond a reasonable doubt that his negligence did not cause the harm, which will be impossible for him. See Stoll (1976, 145, 155ff) and Wagner (2004).

Kahan (1989) discusses the case of uncertain causation and considers an all-or-nothing rule in combination with a preponderance of the evidence standard of proof. We will not analyze such a rule since it does not achieve socially efficient behavior even if the standard of due care is set at the socially optimal care and injurers are solvent (see Kahan 1989, 440–1; Shavell 1987, Proposition 1, 52–3).

See, for example, Landes and Posner (1983), Rosenberg (1984), and Shavell (1985).

See, for example, Sindell v. Abbott Laboratories, 26 Cal.3d 588, 607 P.2d 924, 163 Cal.Rptr. 132 (1980).

This is the case where the harm – for example cancer – can be “caused” by a particular substance, but where it is impossible to pinpoint which particular person’s cancer would have occurred naturally and which would not have occurred but for exposure to the substance (see the famous case In Re “Agent OrangeProduct Liability Litigation, 597 F. Supp. 740 (E.D.N.Y. 1984).)

This is true if we rule out the pathological case that harm can be prevented precisely because the injurer was negligent, like in the case where an accident is prevented because he drove too fast.

This might be surprising, as one would expect that proportional liability performs better than full liability as the wealth constraint binds more often under full liability than under proportional liability. The reason this is not the case is that both rules cause injurers to pay more than is necessary to induce the efficient care level. As long as the wealth constraint just eats away the slack for deterrence purposes it does not matter. As soon as it starts to matter, it does so for both rules alike.

This is in the same vein as Ganuza and Gomez (2008) but a completely different effect than the one analyzed in their paper.

In a recent paper, Leshem and Miller (2009) compare full liability and proportional liability in a model of costly litigation. They recommend full liability on the ground that it leads to higher rates of compliance (conceding that it will also lead to higher rates of litigation and therefore to higher litigation cost). Yet, compliance is only unambiguously welfare increasing if it is assumed that courts set the standard of due care at the socially optimal level. Hence, they implicitly rule out the possibility of systematic court error. As they also assume solvent injurers, the two main ingredients of our model, court error and the judgment-proof problem, are absent from their analysis.

In the latter case, we assume the effort to take care has an opportunity cost of x. One could interpret non-monetary care as the cost of effort that can be evaluated in monetary terms but does not reduce the wealth constraint. Alternatively, one could think of non-monetary care as an investment that is made in an asset which is subsequently transferred to a limited liability company. The value of the asset would then determine the wealth constraint. The assumption that care is non-monetary is made in (Shavell 1986), the assumption that care is monetary is made in Beard (1990).

The second-order sufficient condition is satisfied by the convexity of the p(x).

The analysis can be easily extended to the case where care is partially monetary in nature, in which case . Strictly speaking the minimization problem here and in the rest of the paper is subject to the constraint . However, as will become evident in Footnote 16, this constraint never binds.

The first-order condition is necessary and sufficient as the probability function is decreasing and convex: .Note that the constraint is never binding as, for , marginal benefits from care are zero, while marginal costs are strictly positive.

In this paper, acting negligently means exercising less than “due care” as determined by whoever sets the standard, regardless of whether it is determined efficiently.

Unless .

It is important to note that under a negligence-based full liability regime (or indeed under all negligence regimes) the potential minimizers , , or need not be unique. For example, if is set above efficient care level, then there exists such a level for which . In such a case, both and are minimizers of the cost function. We will adopt the convention that in such cases, the injurer chooses the care level that is more efficient from a social perspective. This qualification applies to the other negligence-based liability rules.

See, for example, Ben-Shahar (1999, 651); Tabbach (2008). The probability of causation can be calculated as in expression [4] if we rule out the possibility that harm is prevented because the injurer fell short of exercising due care (see Footnote 2).

This is because if the injurer is not wealth-constrained expected costs under threshold liability differ from expected costs under strict liability only by a constant.

Again the first-order condition is sufficient because of the convexity of the expected cost function.

Threshold liability as formulated in this paper can be applied to situations of uncertain causation in the following way. Suppose that in the face of uncertainty over causation the courts or juries would toss an appropriate coin reflecting the probability of causation and the probability of non-causation and would find the injurer liable in the relevant case. We would like to thank Jacob Nussim for offering us this interpretation of threshold liability.

Rules in which the probability threshold required to impose liability is were analyzed, for example, by Shavell (1985) and shown to induce socially non-optimal care even in the absence of wealth constraints. We therefore do not analyze these rules in the present paper.

See Footnote 2.

In a previous working paper version of this paper we offer a full fledged analysis regarding the effects of insolvency and biased standards under the different negligence-based liability rules. The interested reader can find this analysis in Stremitzer and Tabbach (2009).

In so doing, we rule out the possibility that sophisticated courts would fine-tune the standard of due care depending on the liability rule they apply. Allowing for such fine-tuning would increase the range of implementable outcomes under different rules and would probably weaken the case for proportional liability. It is, for instance, a well-known result that full liability converges to strict liability if the standard of due care is set to a very high level, so that no potential injurer would ever adhere to it (see, for example, Landes and Posner 1987). In line with the literature, we rule out the possibility that sophisticated courts would “game” a particular liability rule in this way. We assume that courts aim for setting the due care standard to the level of socially optimal care, but sometimes fail to do so because of systematic biases.

Guido Calabresi and Jeffrey O. Cooper in the their 1995 Monsanto Lecture, published in the Valparaiso University Law Review, Vol. 30. No. 3, described the advent of splitting rules, replacing the dominance of all-or-nothing recovery rules, as one of the most important shifts in tort law over the past decades comparable only to the coming of insurance 80 years ago. Calabresi and Cooper deplored that while “splitting rules give us more options, we do not necessarily know whether they create a better package of incentives than existed before” (p. 883). They concluded that a much additional analysis is needed to answer this question. By showing that proportional liability as a prominent example of such a splitting rule has desirable welfare properties, our article contributes to the vast research program outlined in their article.

This last point is similar to Ganuza and Gomez (2008) who have argued that, in the presence of wealth constraints, setting due care below socially optimal care is desirable as a second best. Dari-Mattiacci (2004), however, argued, that this effect does not occur if the causation requirement is taken into account and the precaution technology is such that only the probability of the harm occurring can be affected. Our analysis suggests that the effect of Ganuza and Gomez (2008) also holds in a setting where care reduces the probability of harm if causation is uncertain and proportional liability is applied. The criticism by Dari-Mattiacci (2004) is only valid under threshold liability.

Note that the wealth constraint is less binding under proportional liability than under strict liability.

To illustrate, suppose that is set sufficiently high that no injurer abides by it. Then the superiority of proportional liability to threshold liability depends on whether excessive or insufficient care is induced by these rules. For non-monetary care, , implying that proportional liability is superior to threshold liability. For monetary care and certain wealth levels such as , . In this case, threshold liability is preferable to proportional liability.

This differs from the argument by Rose-Ackerman (1990) that individualized causal claims should be discouraged in market-share liability cases because they are worthless and therefore only waste resources. See also Kaplow (1994) for the general argument that the benefits of accuracy be weighed against the cost of achieving it.

Strictly speaking, to induce the socially optimal care, damages should be a little bit higher than , since otherwise the injurer is indifferent among all . We shall assume that damages are set in order to induce injurers to take due care.

For details see Stremitzer and Tabbach (2009).

With a minor correction for the monetary nature of care, a similar result holds for monetary care.

Citation Information: The B.E. Journal of Theoretical Economics, ISSN (Online) 1935-1704, ISSN (Print) 2194-6124, DOI: https://doi.org/10.1515/bejte-2012-0013.

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