1. When discussing negligent behavior, the article addresses both actions and omissions. It should be noted, however, that definition of omissions as causes is a matter of controversy in the literature on causation. See, e.g., Armstrong, David, The Open Door: Counterfactual Versus Singularist Theories of Causation, in Causation and Laws of Nature 175, 177 (Sankey, Howard ed., 1999)Google Scholar (maintaining that “[e]very causal situation develops as it does as a result of the presence of positive factors alone”); Moore, Michael, For What Must We Pay? Causation and Counterfactual Baselines, 40 San Diego L. Rev. 1181, 1222–1227 (2003)Google Scholar; Michel S. Moore, Causation and Responsibility (2009), at 55, 444–451 (asserting that omission liability is not cause-based liability since negative events cannot be considered as causes). For a different view, see, e.g., H.L.A. Hart & Tony Honoré, Causation in the Law (2nd ed. 1985), at 38Google Scholar (stating that in the law, omissions can be perceived as factual causes, since they are “ways of describing the world … a real state of affairs, not just nothing”).

2. See Restatement (Third) of Torts: Liability for Physical and Emotional Harm (2010), at §26 (stating that conduct “is a factual cause of harm when the harm would not have occurred absent the conduct”). Under prevailing tort law, in order to impose legal liability in tort, a court must find both factual and proximate causation. While the former is considered to be based on questions of pure fact, hinging upon the result of the but-for test, the latter is perceived to be a matter of legal policy, such that it may limit the defendant's responsibility for the damage caused. The focus of this article is on factual causation although, as is later explained at length, its theoretical framework associates both factual and policy considerations within the counterfactual inquiry.

3. Schaffer, Jonathan, Contrastive Causation, 114 Phil. Rev. 297, 297–299 (2005)CrossRefGoogle Scholar (observing that “causation is a quaternary, contrastive relation” rather than a binary relation) [hereinafter Schaffer, Contrastive Causation]. For different approaches to the application of the theory of contrastive causation in the law, see, for example, Schaffer, Jonathan, Contrastive Causation in the Law, 16 Legal Theory 259 (2010)CrossRefGoogle Scholar (observing that the law requires us to look for the specific alternate event for the actual cause, which is the hypothetical scenario in which the defendant acted lawfully instead of wrongfully) [hereinafter Schaffer, Contrastive Causation in the Law]; Broadbent, Alex, Fact and Law in the Causal Inquiry, 15 Legal Theory 173, 175–177 (2009)CrossRefGoogle Scholar (suggesting the contrastive account of causation as a theoretical framework that enables us to distinguish matters of fact from matters of law within the cause-in-fact inquiry).

4. The definition of “the cause” as “making a difference” has long been accepted by the scholarship. See, e.g., Hart & Honoré, supra note 1, at 29 (“[T]he cause, though not a literal intervention, is a difference from the normal course which accounts for the difference in the outcome.”); Lewis, David, Causation, in Causations and Conditionals 180, 181 (Sosa, Ernest ed., 1975)Google Scholar (observing that a cause is something that “makes a difference, and the difference it makes must be a difference from what would have happened without it”); Schaffer, Contrastive Causation in the Law, supra note 3, at 285 (stating that the idea of contrast takes the counterfactual reasoning that causing is making a difference literally).

5. See, e.g., Guido Calabresi, The Costs of Accidents (1970), at 24–34 (arguing that the goal of accident law is to reduce the aggregate costs of both accidents and their prevention).

6. See supra note 2.

7. For a review of the counterfactual approach to causation, see, e.g., Collins, John et al. , Counterfactuals and Causation: History, Problems, and Prospects, in Causation and Counterfactuals 1–57 (Collins, John et al. eds., 2004)CrossRefGoogle Scholar; L.A. Paul & Ned Hall, Causation: A User's Guide (2013), at 13–24.

8. See supra note 3.

9. See supra note 4.

10. As later explained, in civil law causal inferences are subject to the probabilistic requirement of the preponderance-of-the-evidence standard. Causation is thus only considered established when the probability of its occurrence exceeds 0.5. See infra notes 20–21 and accompanying text.

11. See, e.g., Watson v. Meltzer, 247 Ore. App. 558, 565–566 (Or. Ct. App. 2011) (observing that in legal malpractice cases, the plaintiff must prove that, but for the defendant's malpractice, he or she would have obtained a more favorable result); Chocktoot v. Smith, 280 Ore. 567, 570 (Or. 1977) (same).

12. The contrastive language accompanying the text in the article carries theoretical importance in itself, as a medium in which causal thinking is embodied. For a broader discussion on the importance of language to causal analysis, see, for example, Edwards, Derek & Potter, Jonathan, Language and Causation: A Discursive Action Model of Description and Attribution, 100 Psychol. Rev. 23 (1993)CrossRefGoogle Scholar.

13. For a broader review of causal relativism, see, e.g., Hitchcock, Christopher Read, The Role of Contrast in Causal and Explanatory Claims, 107 Synthese 395, 399 (1996)CrossRefGoogle Scholar (proposing to take causation as an explanatory relevance relation); Menzies, Peter, Causation in Context, in Causation, Physics, and the Constitution of Reality: Russell's Republic Revisited 191, 192–193 (Price, Huw & Corry, Richard eds., 2007)Google Scholar (arguing that causal inference's truth-value “can vary from one context to another, depending on how a certain contextual parameter is set”).

14. See, e.g., Peter Lipton, Inference to the Best Explanation (2d ed. 2004), at 42Google Scholar (indicating the necessity of contrastive dimension to infer causation).

15. $\hat{A} = \lcub {A1,A2,A3.., Ai} \rcub $, whereas $\hat{A}$ is the set of all the possible alternate events to denote the constructive cause, A1 = water the plant once a day; A2 = water the plant once in three days; A3 = water the plant once a week; and so forth; and A*represents the event eventually chosen from set $\hat{A}$.

16. Since the but-for result is expressed by B − B*, whereby B is fixed, different B*s will always lead to different but-for results. However, as explained later, in light of evidential rules such as the preponderance-of-the-evidence standard, in the law, different alternate results (B1, B2, B3.., Bn ) are not necessarily also contradictory to one another, i.e., in the law, when B1 ≠ B2, it does not necessarily mean that B − B1 ≠ B − B2. See infra notes 20–21 and accompanying text.

17. Other possible results may, of course, be that the plant lost three-quarters of its vitality, half of it, and so forth.

18. Therefore B − B* = 0.

19. Since B − B*>0.

20. See, e.g., Dykes v. William Beaumont Hospital, 246 Mich. App. 471, 486–489 (2001) (where the Michigan Court of Appeal explicitly observed that the standard for causation is subject to the preponderance-of-the-evidence standard); Merrell Dow Pharm. v. Havner, 953 S.W.2d 707 (Tex. Sup. J. 1997) (where the Texas Supreme Court denied compensation in a mass tort case of children who suffered limb deformities since the plaintiffs failed to prove that the defendants increased the risk of such deformities by more than 50 percent); Dumas v. Cooney, 235 Cal. App. 3d 1593 (1991) (where the California Court of Appeal found the defendant's late diagnosis of lung cancer negligent, but denied compensation since the probability that the harm would have been avoided but for the negligence was lower than 50 percent).

21. See, e.g., Ariel Porat & Alex Stein, Tort Liability Under Uncertainty (2001), at 18.

22. As defined above, $\hat{A} = \lcub {A1{\rm \;}, \; A2{\rm \;}, \;.. \; Ai{\rm \;}} \rcub $, where A* denotes the alternate behavior eventually chosen from the set $\hat{A}$. See supra note 15.

23. Where Ai → Bi.

24. Section II discusses the few works dedicated to contrastive causation in the law that raise a similar concern. These works, however, investigate the problem of underdetermination in the law as an example of one prominent difficulty of the contrastive approach to causation, as demonstrated by the plant example below, rather than as a legal problem. They therefore miss the opportunity to develop a comprehensive discussion with regard to the source of causal underdetermination in the law in general, and in particular in negligence cases, and to provide useful tools to resolve it.

25. Overdetermination may also be referred to as duplicative or preemptive causation situations. For elaboration on situations of factual overdetermination and their suggested solutions both metaphysically and specifically in the law, see, for example, Note, Rethinking Actual Causation in Tort Law, 130 Harv. L. Rev. 2163 (2017), Hart & Honoré, supra note 1, at 122–128, 235–249; David Lewis, Causation as Influence, 7 J. Phil. 182 (2000); Wright, Richard W., Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts, 73 Iowa L. Rev. 1001, 1018–1023 (1988)Google Scholar.

26. I.e., it is established that both defendants deviated from the standard of care, imposing unreasonable risk on the plaintiff.

27. For further discussion regarding the “absence as causes” quandary, see supra note 1.

28. Hart & Honoré, supra note 1, at 122–123.

29. This example is based on the famous case in the matter of Summers v. Tice, 199 P.2d 1 (Cal. 1948), with some plot changes. In Summers, the two negligent shooters inflicted two different injuries. It was impossible to determine whose shot hit the plaintiff's right eye, and whose shot hit the plaintiff's upper lip. The illustration in the text presents a somewhat different scenario in which two shooters inflict one injury.

30. The court in Summers resolved the factual difficulty by imposing an alternative liability rule, according to which in such circumstances both shooters should be held liable. See id. at 13–14.

31. See infra notes 50–53 and accompanying text. See also Paul & Hall, supra note 7, at 257–258 (explicitly recognizing the special challenges derived from the relationship between causation and legal liability, including the idea of “multiple possible events”).

32. Malone, Wex S., Ruminations on Cause-In-Fact, 9 Stan. L. Rev. 60 (1956)CrossRefGoogle Scholar.

33. See, e.g., Sinclair v. Berlin, 758 N.E.2d 442 (Ill. App. 2001) (A case where the defendant physician negligently failed to examine the plaintiff's eyes despite her constant complaints of experiencing pain in her right eye. Subsequently, the plaintiff became blind in her right eye. Holding that the physician's negligence was the cause of her blindness, the Appellate Court of Illinois stated that to establish causation the plaintiff was not required to prove that had the physician acted reasonably instead of negligently the result for her eye would have been better.); Morris v. Mark IV Constr. Co., 203 A.D.2d 922, 923 (N.Y. App. Div. 4th Dep't 1994) (stating that the defendants' claims regarding the outcome that could have occurred for the plaintiff had the defendant offered any of the safety measures required by law “is not sufficient to raise a triable issue of fact”).

34. Accordingly, the lawful behaviors encompassing the reasonable ways the defendant did not follow is sometimes referred to by the term “theory of negligence.” See, e.g., Jones v. Alloy, 2015 N.J. Super. Unpub. LEXIS 290, 9–10, 13–14 (2015); Ykimoff v. W.A. Foote Mem'l Hosp., 285 Mich. App. 80, 87–88 (Mich. Ct. App. 2009); Posner v. Walker, 930 So. 2d 659, 667 (Fla. Dist. Ct. App. 3d Dist. 2006).

35. See, e.g., Shectman v. Bransfield, 959 A.2d 278 (N.J. Super. 2008) (Where a defendant's psychiatrist allegedly failed to monitor his patient and thus did not foresee his attempting to commit suicide. The Superior Court of New Jersey observed that, considering the circumstances, there were two possible medical approaches the psychiatrist could have followed; each of them was reasonable. Having followed one of them, the psychiatrist met the duty of care. Accordingly, the court absolved him of tort liability.). See also Saks v. NG, 890 A.2d 983 (N.J. Super. 2008) (A case in which a failed eye surgery resulted in blindness. The court held that there were two reasonable methods of anesthesia the physician could have chosen. Since the physician followed one of them, he was not held liable in tort.).

36. It should be noted that integrating normative considerations within the factual inquiry of causation is a matter of controversy among scholars in the field. See, e.g., Wright, Richard, Causation in Tort Law, 73 Cal. L. Rev. 1735, 1740, 1803 (1985)CrossRefGoogle Scholar (arguing that the causal inquiry in the law is a pure matter of factual and empirical inferences, almost always kept distinct from policy considerations). The contrastive account of causation embraced in this article presents a different view of factual causation in the law, which enables the imbrication of factual and normative elements within the counterfactual inquiry, on the one hand, and distinguishing facts from normativity, on the other hand. For a similar observation regarding the theory of contrastive causation in the law, see Broadbent, supra note 3.

37. Castro v. San Diego Gas & Elec. Co., 228 Cal. App. 4th 1280 (2010).

38. Id. at 7.

39. The exact phrase that the court used to describe the different reasonable behaviors not followed by the defendant was “theories of negligence.” See id. at 25. For additional examples of the use of this phrase, see supra note 34.

40. Castro, 228 Cal. App. at 25.

41. Id. (citing a former Court of Appeal decision in the matter of Jonkey v. Carignan Construction Co., 139 Cal. App. 4th 26 (2006), according to which “[a]s long as a single theory of negligence is lawfully rebutted on a lack of causation theory, it matters not that another theory of negligence is not so rebutted”).

42. Castro, 228 Cal. App. at 24–25.

43. For the observation that in the law, causal inference depends on the nature of the evidence available to prove what the outcome would have been had the defendant acted as she should have and on the factfinder's estimation of its weight, see, e.g., Rizzo, Mario J., Foreword – Fundamentals of Causation, 63 Chi.-Kent L. Rev. 397, 405 (1987)Google Scholar; Robertson, David W., Common Sense of Cause in Fact, 75 Tex. L. Rev. 1765, 1774 (1997)Google Scholar.

44. This assumption is discussed at length later in the article. See infra Section II.B.

45. 1 − (0.6 + 0.2)0.5 = 0.6.

46. The suggested aggregation of counterfactuals could be perceived as a specific implementation of the general idea of aggregation in the law. See Porat, Ariel & Posner, Eric, Aggregation and Law, 122 Yale L.J. 2 (2012)Google Scholar (suggesting that efficient deterrence could be achieved by the adoption of a general rule of aggregation of claims, instead of considering each claim separately).

47. See, e.g., Kaye, David, The Limits of the Preponderance of the Evidence Standard: Justifiable Naked Statistical Evidence and Multiple Causation, 1982 Am. B. Found. Res. J. 487, 494–503 (1982)Google Scholar (recommending the preponderance-of-the-evidence standard as the most appropriate mechanism unless it leads to systematic errors associated with long-run bias toward either the plaintiff or the defendant); Levmore, Saul, Probabilistic Recoveries, Restitution and Recurring Wrongs, 19 J. Legal Stud. 691, 693–696 (1990)Google Scholar (noting the problem of “recurring misses,” where there is constant bias due to which the but-for result constantly leads to the conclusion that there is a more than 0 percent but never more than 50 percent chance that a defendant in similar circumstances is the cause of an injury. In these cases, the tortfeasors are underdeterred).

48. 100K is the difference between the risk imposed on a patient by performing procedure A and the reasonable risk that would have been imposed on her had the physician performed either procedure A1 or A2. In terms of efficiency, to incentivize future physicians in similar situations to adopt an optimal level of care, they should be held liable only for the harm generated by their negligence. See, e.g., Porat, Ariel, Offsetting Risks, 106 Mich. L. Rev. 243 (2007)Google Scholar (offering that in order to align the defendant's liability in tort with the exact risk that her negligence imposed on the plaintiff, when a negligent defendant had to choose between two risky options, courts should offset damages by the risk that was not imposed on the plaintiff from the reasonable option).

49. The best known counterfactual approach to causation is Lewis's possible worlds view, inspired by the development of possible worlds semantics in modal logic. A very simplistic way to describe this view is that it holds a counterfactual true if and only if it is true in the closest possible world to the actual world. See Lewis, David, Causation, 70 J. Phil. 556, 556–567 (1973)CrossRefGoogle Scholar. For the position that the similarity relevance to decide which world is closer to the actual world is context related, see, e.g., Menzies, supra note 13, at 139, 139–142, 154, 172 (stating that “causal statements in different contexts require different similarity relations” and positing this view versus Lewis's view that for each claim of causal relation there is a unique kind of similarity that should determine the corresponding counterfactuals).

50. Schaffer, Contrastive Causation, supra note 3, at 315.

51. Stapleton, Jane, Choosing What We Mean by “Causation” in the Law, 73 Mo. L. Rev. 433, 451 (2008)Google Scholar.

52. Broadbent, supra note 3, at 189.

53. For further critiques on Broadbent's proposal, see Schaffer, Contrastive Causation in the Law, supra note 3, at 293–295.

54. A change of normative consideration may lead to a change in defining A* (which denotes the behavior the defendant should have followed), which in turn may lead to a change of but-for result. The exploration of differences in but-for outcomes resulting from defining A* in accordance with different normative perspectives is not within the purposes of this article.

55. According to Hand formula, if an injury could be avoided for less than it costs, then the individual should take the precautions, rather than allowing the injury to occur. Otherwise she will be considered negligent. The Hand formula was articulated by Judge Learned Hand in United States v. Carroll Towing Co., 159 F.2d 169 (1947), and was later endorsed by courts as well as the Restatement of Torts. See Restatement (Third) of Torts: Liability for Physical Harm (2010), at §3 cmt. e (suggesting that negligence can be asserted by a risk-benefit test identical to the Hand formula).

56. See, e.g., Calabresi, supra note 5.

57. 83 Cal. Rptr. 312 (Cal. Ct. App. 1970). The Court of Appeal decision was later reversed by the California Supreme Court. See Haft v. Lone Palm Hotel, 3 Cal. 3d 756 (Cal. Ct. Sup. 1970).

58. See Haft, 83 Cal. Rptr. at 316.

59. Id.

60. Id. at 321, 326.

61. Porat, Ariel & Stein, Alex, Liability for Uncertainty: Making Evidential Damage Actionable, 18 Cardozo L. Rev. 1891, 1908–1909 (1997)Google Scholar.

62. Unless it is the defendant's negligence that obscured the facts of the case and thus caused what is here termed normative uncertainty. See infra Section II.B.

63. See supra note 56 and accompanying text.

64. Id. See also Steven Shavell, Economic Analysis of Accident Law (1987), at 6–9.

65. For a similar observation, see Levmore, supra note 47, at 705–706 (explaining that applying the but-for test by comparing the actual result to the probable result of posting a warning sign may produce a causal link in 10 percent of similar cases).

66. For elaboration on the idea of aggregation in the law, see Porat & Posner, supra note 46.

67. See supra notes 44–46 and accompanying text.

68. As aforementioned, the behaviors encompassing the reasonable approaches the defendant did not follow is sometimes referred to by the term “theory of negligence.” See supra note 34.

69. This solution is based on the reasoning of David Kaye's suggested maximum-likelihood rule. See Kaye, supra note 47, at 508–513.

70. It should be noted that defining A* according to probabilistic data inferred from statistical evidence may be controversial. Some scholars believe that naked statistical evidence should not count as an indicator for proportional liability. See, e.g., Alex Stein, Foundations of Evidence Law (2005), at 238–241 (arguing that naked statistical evidence allocates the risk of error between the parties in an unequal fashion and thus violates the basic notion of equality in civil litigation); Sanchirico, Chris William, Character Evidence and the Object of Trial, 101 Colum. L. Rev. 1227, 1259–1263 (2001)CrossRefGoogle Scholar (arguing that leaning on data regarding statistical evidence, such as the defendant's prior criminal conduct, may create distorted incentives for efficient behavior ex ante).

71. Discussing the nature of causal law is not within the scope of this article.

72. There could be a distinction between the magnitude of proof regarding the existence of causation, based on the evidence, and the materialized belief regarding the existence of causation based on this estimation. Richard Wright, for example, argues that the latter belief is not a matter of degree but rather a binary decision as to the existence of causation. See Wright, Richard, Proving Causation: Probability versus Belief, in Perspectives on Causation 195, 205–212 (Goldberg, Richard ed., 2011)Google Scholar. The suggested analysis does not aim to contend against this observation. It is possible, for example, that the offered analysis would lead a factfinder to believe that there is a causal link between the physician's negligence and the patient's death as a matter of fact.

73. Be that as it may, the choice of liability regime is a matter of legal policy rather than causation.

74. This implementation expresses an all-or-nothing reasoning, according to which when the probability that the negligent defendant is the cause of the harm exceeds 0.5, the defendant should be held 100 percent liable for that harm.

75. For a related argument of a fifty-fifty split between the litigating parties, see, for example, Coons, John E., Approaches to Court Imposed Compromise: The Uses of Doubt and Reason, 58 Nw. U. L. Rev. 750, 759 (1963)Google Scholar (arguing that in some cases of factual uncertainty, courts should impose a compromise by dividing the sum claimed between the parties, assuming that the court assigns equal weight to every alternative); Parchomovsky, Gideon et al. , Of Equal Wrongs and Half Rights, 82 N.Y.U. L. Rev. 738 (2007)Google Scholar (suggesting that an equal division between litigating parties is justified in cases where other solutions may create windfall gains or losses).

76. According to the autopsy results, had the physician administered the surgery by A1 there is a 0.6 probability that the patient would have died anyway.

77. See Kaye, supra note 47, at 509.

78. B − B1 = 1 − 0.6 = 0.4; 0.4 × 1M.

79. Generally speaking, proportional liability determines recovery by multiplying the plaintiff's total damages by the percentage chance that the defendant caused the damages.

80. See, e.g., Delgado, Richard, Beyond Sindell: Relaxation of Cause-in-Fact Rules for Indeterminate Plaintiffs, 70 Calif. L. Rev. 881 (1982)CrossRefGoogle Scholar (suggesting relaxing the rules of causation in indeterminate plaintiffs tort cases and allowing distribution of damages based on allocation schemes of proportional recovery); Rosenberg, David, The Causal Connection in Mass Exposure Cases: A “Public Law” Vision of the Tort System, 97 Harv. L. Rev. 849 (1984)CrossRefGoogle Scholar (arguing that in mass exposure cases the court should award each potential victim compensation in proportion to the likelihood that her injury was caused by the defendant's wrongful exposure); Farber, Daniel A., Toxic Causation, 71 Minn. L. Rev. 1219 (1986)Google Scholar (same); Robinson, Glen. O., Probabilistic Causation and Compensation for Tortious Risk, 14 J. Legal Stud. 779, 779–780 (1985)CrossRefGoogle Scholar (observing that in many tort cases causation is inherently hard to prove, particularly when the injury is the result of a combination of several causes and isolating one of them as the cause is a difficult task).

81. Schaffer, Contrastive Causation, supra note 3, at 320.