The Hand Formula’s Unequal Inputs
abstract. Tort cases often hinge on whether the defendant behaved “unreasonably.” Tort theorists have long debated what makes behavior unreasonable, with many seeking answers in economic theory or Kantian philosophy. But whether a tort defendant’s conduct was unreasonable is typically a question for the jury, and we know little about whether lay jurors’ understandings of reasonableness align with tort theorists’ beliefs.
This Article addresses this gap in our knowledge, experimentally examining the extent to which economic and Kantian theories capture how laypeople, like jurors, judge reasonableness. The Article explicates and then tests competing economic and Kantian views about the relevance of the various inputs in the well-known Hand Formula (B < PL): the burden of taking additional precautions (B), the increased probability of harm occurring in the absence of those precautions (P), and the expected cost to society of the harm should it arise (L). Primarily, it tests the Kantian proposition that the significance of the risks associated with conduct (reflected by the PL side of the Hand Formula) has greater influence on reasonableness judgments than economic theory implies.
Across five experiments, 1,046 participants read simple tort cases that included full information about B, P, and L, in plain language, and then judged whether the defendant acted unreasonably. Participants found defendants’ conduct more unreasonable when B was less than PL, as one would expect if participants engaged in some degree of Hand-style, economic balancing of costs and benefits. But, critically, information about P and L had additional, Hand-independent effects on participants’ judgments: participants found defendants’ conduct more unreasonable as the value of PL—and particularly the value of P—increased, whether B was less than PL or not. A purely economic view of reasonableness cannot explain these findings. The Hand Formula, it seems, is misaligned with how laypeople think about reasonableness. Lay judgments may be influenced by cost justification to a degree, but they are also influenced by Kantian considerations of the significance of risks in ways the Hand Formula does not capture.
In short, the Hand Formula’s inputs do not have equal weight in lay decision-makers’ minds. P is most influential, though decision-makers may not be conscious of its outsized influence. These findings have theoretical and practical implications, including informing the ongoing normative debate as to how tort law should understand reasonableness, underscoring the importance of juries’ democratic role in negligence litigation, and highlighting types of evidence and arguments that may be particularly likely to persuade jurors.
author. Associate Professor of Law, Baylor Law School; J.D., Vanderbilt Law School; Ph.D. (Psychology), Vanderbilt University. I am grateful to Jessica Asbridge, Gilat Bachar, Edith Beerdsen, Joseph Blocher, Lauren Clatch, Neal Feigenson, Steve Gilles, Tonja Jacobi, Ted Jaeger, Rachel Kincaid, Heidi Liu, Jamie Macleod, Luke Meier, Jeff Rachlinski, Jennifer Robbennolt, Matthew A. Shapiro, Jay Silver, Ken Simons, Rod Sturdivant, Stephanie Tang, Jim Underwood, Richard Wright, and to participants in the Lay Understanding of Justice Concepts Session at Law and Society 2024, the Torts and Civil Procedure Session at the 2024 Southeastern Association of Law Schools Annual Meeting, the 2024 Association of American Law Schools (AALS) Jurisprudence Section’s Junior Works-in-Progress Workshop, the 2024 Central States Law Schools Association Conference, the 2024 Conference on Empirical Legal Studies, and colloquia at Baylor Law School and Emory Law School for helpful comments and conversations about this project. I am also grateful to Sammy Lutes, Jack Freese, and Justin Garber for excellent research assistance and to the editorial staff of the Yale Law Journal for exceptional comments and editorial work. I did not use any form of artificial intelligence in creating this work. This Article was named cowinner of the 2025 AALS Scholarly Papers Competition.
Introduction
Legal disputes, and tort negligence disputes in particular, often hinge on whether a defendant’s actions were “unreasonable.” But what does it mean for actions to be “unreasonable”? What criteria do legal decision-makers, often lay jurors, use to classify actions as reasonable or not?
Legal theorists have debated the criteria of reasonableness for decades,1 with the most active fault line in the debate situated between economic perspectives (grounded in utilitarianism) and Kantian perspectives (grounded in deontological ethics).2 Much of this debate has been normative, focused on how law should define reasonableness. But the debate has also been descriptive.3 Both economic and Kantian views aim to provide practical interpretations of tort law. Proponents of each perspective routinely cite specific cases that allegedly have been decided consistently with their preferred view.4 Proponents of each contend that fundamental features of negligence law demonstrate that it is animated by their preferred view.5 And proponents of each have argued that their view is superior because it is more intuitive and better aligns with how the relevant legal decision-makers—typically lay jurors—understand reasonableness.6 Indeed, the descriptive debate in many ways hinges on the open empirical question of how tort jurors apply the reasonableness standard.7
This Article addresses that open question, making both empirical and theoretical contributions. Empirically, this Article reports the first experiments investigating whether economic or Kantian theory better reflects how laypeople judge reasonableness. In laying the groundwork for the experiments, this Article carefully engages with both economic and Kantian theories to derive testable predictions as to the types of information that are relevant when judging reasonableness.
Economic theorists have generally identified their reasonableness criteria more concretely than Kantians. On the leading economic view, the reasonableness of a behavior depends on aggregate cost-benefit analysis.8 People act unreasonably when their actions create risks that are not cost-justified. In the context of tort negligence cases, cost-benefit analysis is typically applied to the defendant’s failure to take some specific precaution.9 The failure to take the precaution is “unreasonable”—and the defendant may therefore be found liable for negligence—if “the reduction in expected accident costs [due to the precaution] would have been greater than the costs of the precaution.”10 This analysis is expressed through the well-known Hand Formula, which instructs that the failure to take a particular precaution is unreasonable when the burden of taking the precaution (B) is less than the increased probability of harm occurring in the absence of the precaution (P) multiplied by the expected cost to society of the harm should it arise (L)—that is, when B < PL—but reasonable where the burden is greater than that product—when B > PL.11
The most prominent alternatives to this economic account of reasonableness are Kantian.12 Kantian accounts focus on principles of justice rather than cost-benefit analysis.13 They proceed from the idea that all human beings are free and equal, to be treated as ends in themselves rather than means to others’ ends.14 Under Kantian accounts, an actor behaves unreasonably whenever the actor encroaches on others’ equal freedom by imposing “significant” (or “substantial”) risks on others without their consent.15
But how do Kantian accounts distinguish significant (and thus potentially actionable) risks from insignificant ones? Think of this issue in terms of the Hand Formula inputs of B, P, and L. While Kantian views are not generally concerned with Hand-style cost-benefit analysis, they are concerned with whether an actor imposes significant risks on others without consent.16 To impose risk on others is to impose some increased probability of harm on them—P. The Kantian concern with “significant” risks may imply that the severity of the harm being risked—L—is also relevant in evaluating whether the conduct that created the risk was reasonable.
The burden of taking a precaution, B, matters less to Kantians. On the strongest Kantian views, the burden is irrelevant: if the risks imposed by a defendant’s conduct are “significant” (based on a combination of P and L), it makes no difference how costly it would be for the defendant to mitigate them.17 Under any circumstances, imposing a significant, unaccepted risk on others encroaches on their equal freedom and is therefore unreasonable. Softer Kantian views, which allow some role for the extent of the burden, still assign B less importance than P and L.18 In sum, on Kantian views, a subset of Hand Formula inputs are particularly relevant to evaluating reasonableness: P and L (perhaps especially P)play a larger role in the calculus of negligence than the Hand Formula implies.19
Because the question of whether a negligence defendant acted reasonably is typically one for the jury, assessing whether the economic or Kantian view better describes the law of negligence turns in large part on lay jurors’ conceptions of reasonableness. The Hand Formula predicts that lay jurors weigh (or act as though they weigh) the burdens of taking precautions (B) against the risks of proceeding without them (PL); Kantian views predict they focus more, or perhaps exclusively, on the risks (PL). This Article tests these predictions, using experimental methods to probe the criteria lay decision-makers use to evaluate reasonableness.
Across five experiments, 1,046 participants assessed negligence cases that included full information about B, P, and L in plain language. Participants judged defendants more negligent in situations where B was less than PL than in situations where B was greater than PL, as one would expect if participants engaged in some degree of Hand-style cost-benefit analysis. But the Hand Formula did not capture the full effect of B, P, and L. Information about P and L—particularly P—influenced participants’ judgments above and beyond the weight accorded by the Hand Formula. This Kantian effect appeared whether the case involved risks of property damage or physical injury, whether those risks were concentrated on one identified person or spread across multiple unidentified people, and whether the defendant was an individual or a corporate entity. And it persisted even when participants were told exactly what cost-benefit analysis indicated the defendant should have done. In sum, my studies provide experimental evidence that B, P, and L do not factor into the calculus of negligence quite as the Hand Formula assumes: PL, and particularly P, plays an outsized, Kantian role.
In addition to informing important debates within the legal academy, these findings also speak to practicing tort lawyers. While more work is needed to build the bridge from vignette studies to legal practice, these findings suggest that lawyers trying tort cases might strategically emphasize evidence about the probability of harm over evidence about the severity of harm or costs of additional precautions. Further, a more refined sense of lay jurors’ concept of reasonableness can help lawyers better value cases for settlement.
The Article proceeds as follows. Part I discusses the role of the reasonableness standard in tort law. It explores economic and Kantian views of that standard, identifying what each view predicts about the role of B, P, and L information in reasonableness judgments. Part II reports five original experiments testing whether B, P, and L information influences lay reasonableness judgments in the ways that economic and Kantian views predict. Part III summarizes key experimental findings and discusses their implications, both for the scholarly debate about reasonableness and for the everyday practice of tort law. Part III also discusses promising directions for future research. Part IV concludes.
For scholarly discussion of the criteria for reasonableness, see generally, for example, Alan D. Miller & Ronen Perry, The Reasonable Person, 87 N.Y.U. L. Rev. 323 (2012); Benjamin C. Zipursky, Reasonableness in and out of Negligence Law, 163 U. Pa. L. Rev. 2131 (2015); Kevin P. Tobia, How People Judge What Is Reasonable, 70 Ala. L. Rev. 293 (2018); Kenneth W. Simons, The Hegemony of the Reasonable Person in Anglo-American Tort Law, in 1 Oxford Studies in Private Law Theory 45 (Paul B. Miller & John Oberdiek eds., 2020); and Mark D. Alicke & Stephanie H. Weigel, The Reasonable Person Standard: Psychological and Legal Perspectives, 17 Ann. Rev. L. & Soc. Sci. 123 (2021).
See, e.g., Cristina Carmody Tilley, Tort Law Inside Out, 126 Yale L.J. 1320, 1324-25 (2017) (“Broadly speaking, tort theory has split into two camps: economists view tort as a method of encouraging efficient private behavior, while philosophers and political scientists view it as a method of achieving a kind of moral justice.”); Miller & Perry, supra note 1, at 350 (“The Kantian definition of reasonableness is the strongest rival of the economic definition.”).
See, e.g., William M. Landes & Richard A. Posner, The Positive Economic Theory of Tort Law, 15 Ga. L. Rev. 851, 884-85, 892-903 (1981) (reviewing cases in support of the argument that the Hand Formula is descriptive); Stephen G. Gilles, The Invisible Hand Formula, 80 Va. L. Rev. 1015, 1016 n.4 (1994) (collecting judicial opinions endorsing the Hand Formula or similar formulations of negligence); Richard W. Wright, Hand, Posner, and the Myth of the ‘Hand Formula,’ 4 Theoretical Inquiries L. 145, 146-48, 211-23 (2003) (arguing that case law is better explained by Kantian “equal freedom” than by economic efficiency).
See, e.g., Richard A. Posner, A Theory of Negligence, 1 J. Legal Stud. 29, 52 (1972) (contending that “the basic formal structure of the negligence system broadly supports an economic theory of negligence”); Richard W. Wright, The Standards of Care in Negligence Law, in Philosophical Foundations of Tort Law 249, 256 (David G. Owen ed., 1995) (“It is the equal freedom conception of reasonableness . . . that is reflected in actual tort-law doctrines and decisions.”); Steven Hetcher, Non-Utilitarian Negligence Norms and the Reasonable Person Standard, 54 Vand. L. Rev. 863, 867 (2001) (noting broadly that advocates of Kantian and economic views have “each provide[d] a positive account of tort law that, as it happens, precisely dovetails with [their] prescribed normative account”).
See, e.g., Gilles, supra note 4, at 1020 (“Some proponents of Hand Formula negligence believe that jurors, if given only a reasonable person instruction, intuitively will arrive at results consistent with cost-benefit analysis at least as often as they would if given an explicit Hand Formula instruction. Proponents of ‘community values’ conceptions of negligence claim, to the contrary, that jurors will look to existing social practices and conventions to fill in the reasonable person standard.”); Brian Sheppard, The Reasonableness Machine, 62 B.C. L. Rev. 2259, 2296 (2021) (citing William M. Landes & Richard A. Posner, The Economic Structure of Tort Law 85-86 (1987)) (noting some scholars “have maintained that the Hand Test is the very best description of the [reasonable-person standard] in torts doctrine”); Arthur Ripstein, Reasonable Persons in Private Law, in Reasonableness and Law 255, 273 (Giorgio Bongiovanni, Giovanni Sartor & Valentini Chiara eds., 1st ed. 2009) (“A reasonable person[] would not think in the terms suggested by the Learned Hand test . . . [but] takes such care as is required by a like security and liberty for all.”); Richard W. Wright, Justice and Reasonable Care in Negligence Law, 47 Am. J. Juris. 143, 187-88 (2002) (“[I]t clearly is the disagreement of judges and jurors with the Hand-formula definition of reasonableness that explains both judges’ refusal to give Hand-formula instructions to jurors and the well-grounded expectation that jurors would often refuse to follow such instructions if they were given.”). While some scholars in both the economic and Kantian camps focus more on judges’ decisions than on juries’, reasonable care generally remains the province of juries. See Restatement (Third) of Torts: Liab. for Physical & Emotional Harm § 8(b) (A.L.I. 2010) (“When, in light of all the facts relating to the actor’s conduct, reasonable minds can differ as to whether the conduct lacks reasonable care, it is the function of the jury to make that determination.”). And even where judges take the reasonable-care issue from the jury, lay understanding likely highlights at least some conceptual underpinnings of judicial approaches. See Kevin P. Tobia, Law and the Cognitive Science of Ordinary Concepts, in Law and Mind: A Survey of Law and the Cognitive Sciences 86, 86 (2021) (“Laypeople’s common-sense understandings . . . are at the root of many important legal concepts . . . including . . . reasonableness . . . .”).
See, e.g., Posner, supra note 5, at 32-33 (framing Hand balancing in terms of “overall economic value” and what makes “society” better off); Kenneth W. Simons, Tort Negligence, Cost-Benefit Analysis, and Tradeoffs: A Closer Look at the Controversy, 41 Loy. L.A. L. Rev. 1171, 1172 (2008) (“For most utilitarians and adherents to law and economics . . . to say that people should not be negligent is to say that they should minimize the aggregate expected costs of their activities—specifically, they should minimize the sum of the costs of accidents and the costs of preventing accidents.”). For an alternative, nonaggregative approach to the Hand Formula, see generally Emad H. Atiq, The Disaggregated Hand Formula, 114 Calif. L. Rev. (forthcoming 2026), https://ssrn.com/abstract=5152136 [https://perma.cc/Z9PJ-8PMY].
See Mark F. Grady, Untaken Precautions, 18 J. Legal Stud. 139, 139 (1989) (“The key question that courts ask is what particular precautions the defendant could have taken but did not.”); Simons, supra note 8, at 1172-73 (noting the economic view that people should take a precaution only if the marginal costs of that precaution (in terms of tangible costs or lost benefits) are less than the marginal benefits (in terms of reduced risk of injury)). It is not clear that every negligence claim is premised on the failure to take a precaution. For more on this point, see generally Christopher Brett Jaeger, A Two-System Theory of Negligence, 93 U. Chi. L. Rev. (forthcoming 2026) (on file with author). This Article focuses on the large set of negligence cases that do.
There are, of course, many other accounts of reasonableness. Both social contractarianism and reciprocity-based views share some conceptual overlap with Kantian theory. See, e.g., Gregory C. Keating, Reasonableness and Rationality in Negligence Theory, 48 Stan. L. Rev. 311, 359-68 (1996) (discussing social-contract theory); T.M. Scanlon, What We Owe to Each Other 191-97 (1998) (same); George P. Fletcher, Fairness and Utility in Tort Theory, 85 Harv. L. Rev. 537, 569-73 (1972) (discussing reciprocity). For sources reviewing various perspectives on reasonableness, see supra note 1.
See, e.g., Ernest J. Weinrib, Toward a Moral Theory of Negligence Law, 2 Law & Phil. 37, 54 (1983) (“[O]n the Kantian interpretation the defendant’s failure to exercise due care is a failure to give equal consideration to the plaintiff and is thus a wrong directed against him.”); Wright, supra note 6, at 164 (working from the Kantian imperative to treat humanity “always as an end and never as a means only” (quoting Immanuel Kant, Foundations of the Metaphysics of Morals 47 (Lewis White Beck trans., Bobbs-Merrill Co. 1959) (1785)).
See, e.g., Ernest J. Weinrib, Correlativity, Personality, and the Emerging Consensus on Corrective Justice, 2 Theoretical Inquiries L. 107, 116 (2001) (“[T]he unreasonableness of the risk created by the defendant is seen in terms of the probability and the gravity of its effects on others . . . .”) [hereinafter Weinrib, Correlativity, Personality, and the Emerging Consensus on Corrective Justice]. Weinrib argues that English courts generally and correctly ignore B and “focus[] narrowly on the risk, consisting in the combination of P and L.” Ernest J. Weinrib, The Idea of Private Law 148 (1995) [hereinafter Weinrib, The Idea of Private Law]. To the extent English courts allow some role for B in cases where risks are not fantastical but remain too small to be considered significant, see Weinrib, Correlativity, Personality, and the Emerging Consensus on Corrective Justice, supra, at 116. Weinrib considers this a mistake. Weinrib, The Idea of Private Law, supra, at 150 n.9 (noting that “even the modest role the English approach assigns to Learned Hand’s B may be excessive”). See also Stephen G. Gilles, The Emergence of Cost-Benefit Balancing in English Negligence Law, 77 Chi.-Kent L. Rev. 489, 496 (2002) (describing the Kantian view that actors are negligent when they impose a substantial, foreseeable, unaccepted risk on others, “without regard to how difficult it would have been to guard against that risk”).