Uncertainty, Insurance and the Learned Hand Formula

Daniel H. Cole, Indiana University Maurer School of Law
Peter Z. Grossman, Butler University
Reed W. Cearley, Cearley & Thompson


Law and economics scholars have written extensively about how insurance markets affect the tort system. They have noted the beneficial cost-spreading function of insurance, as well as the detrimental incentive-distorting affects of insurance, stemming from the problems of adverse selection and moral hazard. Surprisingly, however, scholars have overlooked one of the most important salutary functions that insurance serves for the tort system: it provides much of the information that courts need to apply the marginal Learned Hand formula in negligence cases. The Learned Hand formula is an algebraic formula (B = PL), according to which liability turns on the relation between investment in precaution (B) and the product of the probability (P) and magnitude (L) of harm resulting from the accident. If PL exceeds B, then the defendant should be liable. If B equals or exceeds PL, then the defendant should not be held liable. This paper explains precisely how insurance markets collect and disseminate information about the expected values of all three variables in the Hand formula: the probability of accidents, the level of harm and the burden of precaution. This information is available to everyone, including those who choose not to purchase any insurance. Most importantly, in the absence of the information insurance markets provide, parties in many cases would have no way of cost-effectively determining, ex ante, the proper level of care to avoid liability/harm. Consequently, the Learned Hand formula could not effectively operate. This is not to say that the insurance markets provide complete information for making ex ante calculations of the expected value of accidents and avoidance measures. But in many (if not most) cases, insurance provides the best information available. Indeed, as a normative matter, judicial determinations of liability in accident cases might be improved by setting the burden of precaution using insurance market values as a baseline.