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Two Theories of the
Civil Burden of Persuasion

Law, Probability, and Risk (2003), 2, 9-13

Two theories of the civil burden of persuasion

D. H. Kaye (1)

Center for the Study of Law, Science, and Technology, Arizona State University, College of Law, Tempe, AZ 85287-7906, USA

[Received on 21 October 2002; accepted on 31 October 2002]

Several judicial opinions and commentators have suggested that the more-probable-than-not burden of persuasion in civil cases reflects a policy of equalizing the rate or risk of factually erroneous verdicts as between plaintiffs and defendants. Concluding an exchange with Ronald Allen, this paper adheres to the view that the legal standard is better understood in terms of minimizing the expected losses due to such errors.

Keywords: Statistical decision theory, burden of persuasion.

Professor Ronald Allen's response to my discussion of "the error of equal error rates" (Kaye 2002), like all his writing, is immensely stimulating. His rejoinder has two themes. It defends one or another version of his textbook's description of error equalization as motivating the p>1/2 rule of most civil litigation, and it asserts that equalizing the incidence errors is a worthy goal that can explain the p>1/2 rule or justify departures from it. Although the discussion in the textbook remains flawed, (2) I shall not belabor that point. Instead, I want to focus on the underlying claim that the p>1/2 rule follows from the alleged goal of equalizing the actual incidence of erroneous verdicts as between plaintiffs as a class and defendants as a class. The standard theory is that the rule reflects the premise that deserving parties should prevail as often as possible. In contrast, the error-equalization theory insists that we should make mistakes for the sole purpose of ensuring that as many plaintiffs are misjudged as are defendants. Here, I respond specifically to arguments in Allen's latest defense of equalizing errors.

    There is no tension--superficial or otherwise--between the fact that the desire to equalize error rates does not work as either a positive or a normative explanation of the p>1/2 rule, while the desire to avoid errors does. If we knew that no deserving plaintiff will ever go to trial, then the optimal decision rule is trivial. A more subtle decision rule is required if there is doubt about whether the facts warrant recovery for plaintiff. In these cases, mathematical analysis reveals that the p>1/2 rule minimizes expected losses (as computed with the jurors' subjective probabilities).. If juries are well calibrated in assessing the probabilities in question, then the rule also minimizes expected actual losses. No further "empirical assumption" is required. (3) In contrast, the claim that the p>1/2 rule should be understood as a manifestation of the goal of equalizing actual errors requires, as explicated by Professor Allen and his coauthors, ad hoc and unspecified assumptions about unknown probability density functions. It would be 'curious' not to find the former theory more plausible than the latter.

    I objected to presenting my analysis as proving that the p>1/2 rule equalizes losses as between plaintiffs and defendants because it proved nothing of the kind. I certainly do not object to anyone's using my work to explore alternative explanations or justifications of the p>1/2 rule. But the notion that 'social perceptions of inequality among classes of various kinds' is such a justification seems far-fetched.

    Treating everyone with equal concern and respect suggests that just as proper names do not count in achieving distributional justice, neither do the labels of 'plaintiff' <---------- p. 11 ----------> and 'defendant'. Each and every litigant is entitled to prevail if the facts warrant recovery--as best determined by the judge or jury hearing the case (subject, of course, to the constraints and compromises reflected in the many rules of evidence and procedure). (3)

    This seems a more compelling interpretation of equality than am equal number of false verdicts for plaintiffs and defendants. The latter approach assumes that a mistake in favour of a plaintiff rectifies a mistake in favour of defendant. Unfortunately, such mistakes do not normally cancel each other out. Suppose that in a case in which Mr. A is injured by Ms. B, the jury fails to return a verdict for A even though B really was at fault, and A therefore loses an amount X in undisputed injury costs. Suppose further that a day later, in a similar case, another jury is charged with deciding whether another defendant, Mr. D should be ordered to pay X to another plaintiff, Ms. C, and that (whatever the state of the evidence) D was not really at fault. The prescription to make the 'same number of errors against deserving plaintiffs and defendants' leads to a verdict for the undeserving defendant, preventing C from the recovery that she deserves. Not only is this inefficient (resulting in an amount 2X instead of X going to the wrong people), but it does nothing to reduce the unfairness to A. Error equalization is not 'intuitively compelling'.

    In this passage, Allen abandons the equality rationale in favor of minimizing actual losses. This is a good move. The fundamental premise of my analysis of the burden of persuasion is that the goal of this device, operating in conjunction with all the other rules and procedures of civil litigation, is to minimize the losses (defined as the amount of damages withheld from deserving plaintiffs plus the amount paid by deserving defendants). I think that this outcome generally is most likely to be obtained by the p>1/2 rule together with procedures aimed (within certain limits) at the ascertainment of the true state of affairs, so that factfinders do not systematically make errors that can be prevented at reasonable cost. If there is a better way to minimize actual losses than by a rule that minimizes expected losses (as computed with subjective probabilities), then I would favor it. My criticism was directed at the notion that the p>1/2 rule plausibly follows from the putative goal of equalizing errors. <---------- p. 12 ---------->

    The argument here seems to be that jurors are expected to compute a subjective probability p(Ei) for the n elements Ei of a claim and to return a verdict for plaintiff if and only if p(Ei)>1/2 for all Ei instead of deciding for plaintiff if and only if p(Ei)>1./2. Suppose, contrary to what other commentators have found (Levmore 2001; Nance 1986, 2001), we accept this contested description of the law. Would it not be as much a problem for the equal-error theory as for the standard theory? That effort to explain the p>1/2 rule (or departures from it) seems to assume that the relevant probability also is p(Ei). The postulated goal appears to be attaining equal numbers of errors affecting awards for deserving plaintiffs and as for defendants rather than equalizing errors about each formal element of a cause of action. If "[t]he elemental structure of liability poses difficulties for all efforts to explain the proof rules," how can it be an argument for the thesis that the job of the p>1/2 rule is to equalize actual rates instead of minimizing expected losses? Or is it part of an as yet inchoate argument that some combination of the two objectives explains or justifies the alleged rule involving the "elemental structure"?

    In passing, Allen defines 'error administration' as 'equality of errors/reducing the total number or magnitude of errors'. While I share the view that we should be concerned with the impact of procedural and evidentiary rules on the latter form of 'error adminstration', I am less enamored of the former type of 'error administration.' I see no strong moral and political argument for demanding 'equality of errors' at the expense of error reduction. It is one thing to argue that we should depart, at least in principle, from the p>1/2 rule for subjective probabilities to improve accuracy, or that we should applaud Schechter v. Klanfer, 269 N.E.2d 812 (N.Y. 1971), in which the New York Court of Appeals concluded that an amnesiac plaintiff 'who lost his memory of the events causing his injury [should be held] to a lesser degree of proof than a plaintiff who could have testified to the events'. It is another to demand that plaintiffs or defendants suffer more mistakes so that they can suffer equally. The latter theory almost surely does not underlie the existing p>1/2 rule--the main point of my article--and I doubt that the rule should be superceded by a different rule that is more likely to achieve 'equality of errors'.

    For years, Professor Allen has been raising an oriflamme against "formalism" and "algorithms." If there were any formalists to attack, I might enroll in the campaign. But we clearly agree that to understand the rules of evidence and procedure, formal mathematical results are not enough. One must identify the appropriate goals of the rules and make some judgments about the world. We are both swimming in the same muddy waters. Of course the law of evidence is 'struggling to deal with errors'. The issue that separates us is whether the struggle is to equalize errors or instead to keep them to an efficient minimum. I continue to believe that increasing errors merely to promote a superficial form of equality neither explains nor justifies the usual civil burden of persuasion. The p>1/2 rule is better understood as part of an effort to reduce the total expected monetary loss to the parties using the factfinder's best estimates of the applicable probabilities.


I am grateful to Saul Levmore and Dale Nance for comments on a draft of this paper and to Richard Posner for related correspondence.


ALLEN, R. J. 2003 The error of expected loss minimization.  Law, Probability and Risk, 2, 1-7.

KAYE, D. H. 2002 The error of equal error rates, Law, Probability and Risk, 1, 3

KAYE, D. H. 1979 Probability theory meets res ipsa loquitor, Michigan Law Review, 77, 1456

NANCE, D. A. 2001, Naturalized epistemology and the critique of evidence theory, Virginia Law Review, 87, 1551

NANCE, D. A. 1986, A comment on the supposed paradoxes of a mathematical interpretation of the logic of trials, Boston University Law Review, 66, 947

LEVMORE, S. 2001 Conjunction and aggregation, Michigan Law Review, 99, 723


1. Of course, the presence of statistical and logical errors does not imply that the book cannot serve as an excellent vehicle for stimulating classroom thought and discussion.

2. The calibration requirement stated in the text is perhaps stronger than it needs to be. Expected-loss-minimization can motivate the p>1/2 standard even when jurors are not (yet) well calibrated. The idea here is that even if jurors do not (now) evaluate factual issues well, the legal system should strive to present evidence to jurors in a way that will lead them to do better. Of course, whether the rules for admitting and commenting on evidence achieve this objective when combined with the burden of persuasion is an empirical question.

3. Allen characterizes the resulting structure as a 'strange decision making process . . . crippled with weird cognitive constraints . . . ." This is not the place to examine the details of the many rules or of Allen's claims about evidentiary presumptions such as res ipsa loquitur, but my silence on these (or any other) matters should not be construed as assent. See, e.g., Kaye (1979) (clarifying the res ipsa doctrine within the framework of the p>1/2 rule).

updated 20 August 2003