Legal Theory Lexicon 122: False Positives and False Negatives

Introduction

Law students frequently encounter the idea of false positives and false negatives when discussing Blackstone’s ratio: “better that ten guilty persons escape than that one innocent suffer.” The conviction of an innocent person is what is called a “false positive,” whereas a guilty person escaping punishment is a “false negative.” This Lexicon entry analyzes these concepts and connects them to the related ideas of “Type I” and “Type II” errors used in statistics generally and empirical legal studies in particular. Along the way, we explore the relationship of false positives and negatives to standards of proof, which are best understood as devices for allocating the risk of error between the parties to civil litigation or criminal prosecutions. From there, we will glance at how the same framework illuminates other corners of the law, and we will note some complications. This entry in the Legal Theory Lexicon provides an introduction to false positives and false negatives for law students, especially first-year law students, with an interest in legal theory. As always, the Lexicon aims to introduce the basic ideas—the bibliography provides resources for readers who want to go deeper.

The Concepts: False Positives and False Negatives

Imagine a medical test for a serious disease. The test can fail in two different ways. It can tell a healthy patient that she has the disease—a false positive. Or it can tell a sick patient that she is disease-free—a false negative. These two errors are not just different in kind; they have different costs. A false positive means anxiety, follow-up testing, perhaps unnecessary treatment. A false negative means a disease that goes untreated. And here is the crucial point: the two error rates are connected. If we make the test more sensitive so that it catches more cases of the disease, it will also flag more healthy patients by mistake. If we make it more demanding so that it clears more healthy patients, it will miss more sick ones. Any test—indeed, any decision procedure that must sort under uncertainty—faces this trade-off. The law is full of such decision procedures, and the vocabulary of false positives and false negatives has become one of legal theory’s most useful tools for thinking about them.

Let us make the concepts more precise. Talk of false positives and false negatives presupposes three things. First, there must be a question with a true answer—the patient either has the disease or does not; the defendant either committed the crime or did not. Second, there must be a decision procedure that answers the question—a test, a trial, a screening algorithm—and the procedure’s output must be binary: positive or negative, yes or no. Third, the procedure must be fallible, so that its output can diverge from the truth. When these conditions hold, there are exactly four possibilities. The procedure can say “yes” when the true answer is yes—a true positive. It can say “no” when the true answer is no—a true negative. It can say “yes” when the true answer is no—a false positive. And it can say “no” when the true answer is yes—a false negative. The first two outcomes are successes; the last two are the two ways the procedure can fail. Notice that which answer counts as “positive” is a matter of framing: in a criminal trial, we call a conviction the positive outcome because the trial tests the prosecution’s accusation, and a conviction affirms it.

	Procedure says “yes” (positive)	Procedure says “no” (negative)
True answer: yes	True positive (guilty person convicted)	False negative (guilty person acquitted)
True answer: no	False positive (innocent person convicted)	True negative (innocent person acquitted)

The two kinds of error are connected. Every decision procedure has a threshold—a point at which the evidence is deemed sufficient for a “yes.” Move the threshold, and the two error rates move in opposite directions. Lower the threshold, and the procedure says “yes” more readily: false negatives decline (fewer guilty defendants acquitted, fewer diseases missed), but false positives rise (more innocent defendants convicted, more healthy patients flagged). Raise the threshold, and the pattern reverses. Holding the quality of the evidence constant, there is no way to reduce both error rates at once; the only question is how to distribute the inevitable errors between the two categories. This is why the choice of a threshold is never a merely technical matter. It is a normative judgment about which kind of error is worse—and by how much. Blackstone’s ratio is precisely such a judgment: it asserts that a false positive in a criminal trial (convicting the innocent) is at least ten times worse than a false negative (acquitting the guilty). One can, of course, improve on the trade-off itself by gathering better evidence—a more accurate test, a more thorough investigation—but at any given level of accuracy, the trade-off remains.

Type I and Type II Errors

Readers who venture into statistics or empirical legal studies will encounter the same distinction under different names: “Type I error” and “Type II error.” The terminology comes from the theory of statistical hypothesis testing developed by Jerzy Neyman and Egon Pearson in the early twentieth century. In hypothesis testing, the investigator starts with a “null hypothesis”—roughly, the default assumption that there is nothing there: the drug has no effect, the two variables are unrelated. A Type I error is rejecting the null hypothesis when it is actually true—finding an effect that does not exist. A Type II error is failing to reject the null hypothesis when it is actually false—missing an effect that does exist. The two types of error map directly onto false positives and false negatives: a Type I error is a false positive, and a Type II error is a false negative. If the criminal trial is recast in these terms, the null hypothesis is innocence—the presumption of innocence, in fact, is a legal expression of the statistician’s default—so convicting the innocent is a Type I error and acquitting the guilty is a Type II error. Almost no one can remember which type is which without a mnemonic, so here is one: the Type I error is the error of commission (the procedure affirmatively does something it should not), and it comes first, just as sins of commission traditionally come before sins of omission.

Standards of Proof as Error-Allocation Devices

You may not hear about false positives and negatives in your classes directly, but every law student learns about burdens of proof (more precisely, burdens of production and persuasion). The three most important burdens of persuasion are: (1) preponderance of the evidence, (2) clear and convincing evidence, and (3) proof beyond a reasonable doubt. But what are these standards? The most illuminating answer is that a standard of proof is a threshold of the kind described above: it specifies how confident the factfinder must be before returning a “yes.” And because moving the threshold trades one kind of error for the other, the choice among standards is a choice about how to allocate the risk of error between the parties. A low threshold shifts the risk of error toward the defendant: more false positives, fewer false negatives. A high threshold shifts the risk toward the plaintiff or prosecution: fewer false positives, more false negatives. On this view, the standards of proof are not arcane verbal formulas; they are the legal system’s explicit answers to the questions, “which errors do we view as most costly?” and “what price are we willing to pay to avoid them?”

Burdens of proof can be decomposed into burdens of production (which party must raise an issue) and burdens of persuasion (what is the standard of proof on the issue, once it is raised). Burdens of production are important, because the failure to meet such a burden results in an automatic determination of the issue against the party that fails to meet its burden. But in the context of false positives and false negatives, burdens of persuasion do the important work.

Begin with the preponderance of the evidence standard, which governs most civil litigation. The traditional formulation—the plaintiff must show that her claim is “more likely than not” true—places the threshold at just above fifty percent. In error-allocation terms, this is the symmetric solution: it treats a false positive (holding a defendant liable when he should not be) and a false negative (denying recovery to a plaintiff who deserves it) as errors of roughly equal gravity. The implicit judgment is that civil litigants stand on equal footing before the law: a dollar wrongly taken from the defendant is neither better nor worse than a dollar wrongly denied to the plaintiff. If the two errors are equally costly, the sensible aim is simply to minimize total errors, and a just-over-fifty-percent threshold accomplishes that: in every case, the factfinder sides with the party whose position is more likely correct. Justice Harlan made this reasoning explicit in his influential concurrence in In re Winship: in civil litigation, he wrote, we view it as no worse for there to be an erroneous verdict in the defendant’s favor than an erroneous verdict in the plaintiff’s favor, and so the preponderance standard directs the factfinder simply to choose the more probable account.

Discussing burdens of persuasion in terms of probabilities is standard in the law, but there are deep questions lurking behind the idea that preponderance of the evidence should be understood as P > .5 (the probability of the fact to be proved is greater than 50%). This approach is Bayesian, but there is another approach to the interpretation of burdens of persuasion that focuses on the idea of inference to the best explanation. For a discussion of that idea, see Legal Theory Lexicon 089: Inference to the Best Explanation (Abduction) and the articles by Ron Allen and Michael Pardo in the bibliography.

Now consider proof beyond a reasonable doubt, the standard for criminal conviction. This standard aims to minimize false positives (erroneous convictions) at the expense of false negatives (erroneous exonerations). This asymmetry is justified on the assumption that the costs of convicting an innocent person are much greater than the costs of failing to convict someone who is guilty: a false positive means that the state has imprisoned—or in the extreme case, executed—an innocent person, stripping away liberty, reputation, and sometimes life itself; a false negative means that a guilty person goes free. Blackstone’s ratio is an attempt to quantify the asymmetry: better that ten guilty persons escape than that one innocent suffer. In theory, the beyond reasonable doubt standard minimizes false positives. In In re Winship (1970), the Supreme Court held that the reasonable doubt standard is constitutionally required in criminal cases as a matter of due process, and Justice Harlan’s concurrence explained why in exactly the terms of this Lexicon entry: because the disutility of convicting an innocent man is so much greater than the disutility of acquitting a guilty one, the margin of error must be allocated overwhelmingly to the defendant’s side.

Does the beyond reasonable doubt standard actually work to minimize false positives (wrongful convictions)? Answering that question would require an assessment of the way the criminal justice system functions. Given the practice of plea-bargaining, innocent defendants may plead guilty to avoid the costs of a criminal defense and the risks of conviction on a more serious offense or a lengthier sentence.

The clear and convincing evidence standard sits between preponderance of the evidence and beyond reasonable doubt. It governs proceedings in which the stakes are asymmetric but not as radically asymmetric as in a criminal prosecution—and the Supreme Court’s cases identify a recurring pattern: the standard applies when the state seeks to impose a serious deprivation that is nonetheless something less than criminal punishment. In Addington v. Texas (1979), the Court held that involuntary civil commitment requires clear and convincing evidence: erroneously committing a person who is not mentally ill is a grave loss of liberty, so the preponderance standard tilts too far against the individual, but commitment is not punishment, so the criminal standard would overshoot. In Santosky v. Kramer (1982), the Court applied the same logic to the termination of parental rights. Deportation, denaturalization, and civil fraud follow the same pattern in various bodies of law. The intermediate standard is, in effect, an intermediate answer to the error-allocation question: false positives are deemed substantially worse than false negatives, but not so much worse as to warrant the near-categorical protection of proof beyond a reasonable doubt. The three-standard architecture, viewed as a whole, illustrates the idea that the law calibrates its thresholds to its judgments about the relative costs of error.

Error Costs Across the Law

The concept of error costs associated with false positives and negatives is pervasive in the law. Drug regulation: when the FDA decides whether to approve a new drug, a false positive (approving a drug that is unsafe or ineffective) harms the patients who take it, while a false negative (rejecting or delaying a beneficial drug) harms the patients who go without it—and critics have long argued that the agency’s incentives skew toward avoiding the visible first error at the cost of the invisible second. Antitrust: in a series of influential articles and opinions, judges and scholars in the Chicago School tradition argued that the costs of false positives (condemning procompetitive conduct) exceed the costs of false negatives (missing anticompetitive conduct), because market forces eventually erode monopoly power but judicial errors persist as precedent—an argument, associated with Frank Easterbrook’s The Limits of Antitrust, that has shaped doctrine and drawn sharp criticism in the current era of antitrust revival. Free speech: the overbreadth doctrine permits facial challenges to statutes that sweep in protected expression, reflecting a judgment that false positives (suppressing protected speech, with its chilling effects) are systematically worse than false negatives (allowing some unprotected speech to slip through). Preliminary injunctions: the familiar balancing of likelihood of success against irreparable harm is, at bottom, an attempt to minimize the expected cost of error when a court must act before it can know the merits. In each domain, the analytical move is the same: identify the two errors, ask which is more costly, and design the decision procedure accordingly.

Complications and Critiques

The error-cost framework is illuminating, but it is not uncontroversial. One line of objection challenges the framework’s consequentialist premise: talk of “weighing” the cost of convicting the innocent against the cost of acquitting the guilty assumes the two harms are commensurable, and theorists in the deontological tradition deny this—on their view, convicting the innocent is not merely a costlier outcome but a wrong done by the state, which no quantity of avoided false negatives can offset. A second line of objection accepts the framework but questions the law’s traditional answer within it. In The Consequences of Error in Criminal Justice, Daniel Epps argues that the Blackstone ratio looks less obviously correct once we attend to its systemic effects: a regime that strongly protects against false convictions may increase the total amount of crime and punishment, erode the stigma of conviction less than we suppose, and distribute its benefits and burdens in surprising ways—so that even those concerned primarily with protecting the innocent might prefer a less skewed allocation than the tradition assumes. Whether or not one is persuaded, the debate illustrates a general point: the choice of an error ratio is a substantive question of political morality, and the answers we inherit are not beyond question. Deep waters! But we must leave these questions for another day.

Conclusion

The distinction between false positives and false negatives is one of the simplest ideas in legal theory, and one of the most powerful. Any procedure that must answer yes-or-no questions under uncertainty will make both kinds of error, and reducing one kind means accepting more of the other. Once the trade-off is in view, familiar features of the legal landscape snap into focus: the standards of proof are error-allocation devices; Blackstone’s ratio is a normative judgment about relative error costs; the presumption of innocence is the law’s version of the statistician’s null hypothesis; and doctrines from overbreadth to the preliminary injunction standard are calibrations of the same dial. The framework does not answer the hard questions—how much worse one error is than the other, and whether the harms can be weighed on a common scale at all—but it tells you what the hard questions are. That is what a good conceptual tool does. I hope this entry has given you a sense of the concepts and their power. As always, the Lexicon provides an introduction—the bibliography that follows will take you deeper.

Related Lexicon Entries

Bibliography

Ronald J. Allen & Michael S. Pardo, Relative Plausibility and Its Critics, 23 International Journal of Evidence & Proof 5 (2019).

William Blackstone, Commentaries on the Laws of England, Book IV, Chapter 27 (1769).

Frank H. Easterbrook, The Limits of Antitrust, 63 Texas Law Review 1 (1984).

Daniel Epps, The Consequences of Error in Criminal Justice, 128 Harvard Law Review 1065 (2015).

John Kaplan, Decision Theory and the Factfinding Process, 20 Stanford Law Review 1065 (1968).

Larry Laudan, Truth, Error, and Criminal Law: An Essay in Legal Epistemology (2006).

Jerzy Neyman & Egon S. Pearson, On the Problem of the Most Efficient Tests of Statistical Hypotheses, 231 Philosophical Transactions of the Royal Society of London, Series A 289 (1933).

Michael S. Pardo, The Paradoxes of Legal Proof: A Critical Guide, 99 Boston University Law Review 233 (2019).

Alexander Volokh, n Guilty Men, 146 University of Pennsylvania Law Review 173 (1997).

This entry was first published on July 25, 2026.

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Legal Theory Lexicon 122: False Positives and False Negatives

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