Academics have never quite understood the standards of proof or, indeed, much about the theory of proof. Their formulations beget probabilistic musings, which beget all sorts of paradoxes, which in turn beget radical reconceptions and proposals for reform. The theoretical radicals argue that the law needs some basic reconception such as recognizing the aim of legal proof as not at all a search for truth but rather the production of an acceptable result, or that the law needs some shattering reform such as greatly heightening the civil standard of proof on each part of the case to ensure a more-likely-than-not overall result.

This Article refutes all those baroque rereadings. It shows that the standards of proof, properly understood on the law’s own terms without a probabilistic overlay, work just fine. The law tells factfinders to compare their degree of belief in the alleged fact to their degree of contradictory disbelief. Obeying that instruction resolves mathematically the paradoxes that traditional probability theory creates for itself. Most surprising, the burden of proof, by which the proponent must prove all the elements and the opponent need disprove only one, does not produce an asymmetry between the parties.

The law’s standards of proof need no drastic reconception or reform, because the law knew what it was doing all along. It deals with factual beliefs in a world that will remain uncertain, not with the odds of the facts becoming certain. And the well-established mathematics of beliefs are not the mathematics of odds.

### Introduction

Standards of proof are a simple concept, unless you stop to think about them. At the least, the law is quite clear in stating standards. Here is a pattern civil jury instruction:

Plaintiff has the burden in a civil action, such as this, to prove every essential element of plaintiff’s claim by a preponderance of the evidence. If plaintiff should fail to establish any essential element of plaintiff’s claim by a preponderance of the evidence, you should find for defendant as to that claim.^{1}3 KEVIN F. O’MALLEY, JAY E. GRENIG & WILLIAM C. LEE, FEDERAL JURY PRACTICE AND INSTRUCTIONS: CIVIL § 104.01 (6th ed. 2011). The pattern jury instruction also verbalizes the process imposed implicitly on the judge when acting as factfinder

Doing their job, academics have stopped to think about the standards of proof. What is a “preponderance”? The courts tell us it means more likely true than not, which to the academics means more probable than not, which thus calls for use of traditional probability theory.3 The routinely taught result appears below, showing the pull and haul of the plaintiff’s and defendant’s evidence, E, on a disputed issue, as plaintiff’s case in chief establishes the fact as more likely than not and then the case in defense pushes the probability back down: We are off and running—right off a cliff. The traditional probabilistic model^{2}By traditional probability, I am referring to the classical, frequentist, and subjective systems conforming to Kolmogorov’s axiomatization. See Alan Hajek, Interpretations of Probability, in STANFORD ENCYCLOPEDIA OF PHILOSOPHY § 1 (Edward N. Zalta ed., 2012), https://plato.stanford.edu/entries/probability-interpret/ [https://perma.cc/HAV8-QNFM] (listing the axioms of nonnegativity, normalization, and additivity). But the usual particularization of probability for discussing legal proof is subjective probability. See KEVIN M. CLERMONT, STANDARDS OF DECISION IN LAW: PSYCHOLOGICAL AND LOGICAL BASES FOR THE STANDARD OF PROOF, HERE AND ABROAD 120–21 (2013) (discussing probability theories); H´ajek, supra, § 3.3.1 (characterizing subjectivism, unfortunately, with the slogan of “Probability is degree of belief”). immediately introduces paradoxes, puzzles, and problems galore:

- Unrealistic factfinding. Probabilistic thinking induces one to speak in quantified terms, even as one simultaneously admits that probability percentages are not how people naturally think.5 Speaking in numerical terms can only mislead the factfinder.6 For example, it is silly to speak in terms of a razor’s edge at 50%. A human factfinder cannot tell 49% from 51%. Equipoise is a fuzzy zone in the factfinder’s mind.7
- Prior probability. The academics’ cure for a lack of realism is to speak in ever more sophisticated terms, urging Bayes’ theorem for discussions of factfinding in recent decades.8 Bayes tells us that we need to start with a prior probability, which the admitted evidence will alter. In the proper state of initial ignorance in a civil case, the plaintiff’s claim has a 50/50 chance. Consequently, even though it comports with neither the actual probabilities nor the law’s instructions, a popular starting point for the Bayesian factfinder is 50%.9 But among other difficulties,10 this prior probability would make the standard of proof ridiculously easy for the plaintiff to satisfy. Introducing a feather’s weight of evidence would arguably suffice to carry the burden of production, as well as the burden of persuasion over a silent defendant. We all know the law is otherwise:11 the rule on judgment as a matter of law requires plaintiff’s evidence to create at least a reasonable possibility.12
- Infinite alternatives. By contrast, the infinite range of possibilities alternative to the plaintiff’s allegations would seem to make the plaintiff’s burden nearly impossible to carry. Even if one invokes contextualism to pare down the range of plausible alternatives, one might still argue that almost no plaintiff could tell a story more than 50% true, given the theoretical difficulty of proving the truth by dissipating all the remaining alternatives.

### Multivalent Beliefs

One must begin by locating the topic of standards of proof within the subject of factfinding. As the very first step, “fact” can include anything that a court, other institution, or a person subjects to a proof process in order to establish what to treat as truth. The subject includes not only yes-or-no facts but also vague and normative terms like “fault” and many other applications of law to fact, as well as a variety of nonbinary opinions.24 Nonetheless, discussion remains easiest when fo

### Radical Models

Most, but not all,123 people who think seriously about this topic realize that traditional probability conflicts with the standards of proof.124 Accordingly, many have proposed a rethinking of the topic that would allow us to live with the accepted paradoxes, puzzles, and problems that accompany traditional probability.125 They try to circumvent the difficulties through heightened sophistication. Consequently, their competing models are radical reconceptions. Take the much-condemned conjunction paradox as an example again.126 Analysis of it has prompted some to abandon truth as an aim of trial and to embrace acceptability of result instead.127 Radical reconception calls for radical reform. For acceptability, it should not matter whether the plaintiff’s conjoined story is more likely than not, as long as the plaintiff’s story is more likely than any other single story.128 Others argue

### Plaintiff/Defendant Asymmetries

I cannot conclude that radical reconception and reform of the standards of proof are unnecessary simply because the multivalent-belief model avoids the difficulties of traditional probability theory in producing accurate results. Other theorists attack the law’s standards on the grounds of fundamental fairness as a process value. They argue that the playing field is not level. Plaintiffs have to prove a string of elements, while defendants can succeed by disproving only one, so creating an asymmetry. Even if criminal cases are supposed to be uneven contests, this asymmetry seems unfair in civil cases.164 The key to meeting this argument is to accept the justdeveloped idea that the multivalent-belief model requires that plaintiff’s best story be more likely than the defendant’s best story constructible out of the allegations and the evidence. From this vantage point, one can see that the plaintiff and the defendant are on a level playing field after all.

*To read. more, click here*: Staying Faithful to the Standards of Proof.

References

1. | ↑ | 3 KEVIN F. O’MALLEY, JAY E. GRENIG & WILLIAM C. LEE, FEDERAL JURY PRACTICE AND INSTRUCTIONS: CIVIL § 104.01 (6th ed. 2011). The pattern jury instruction also verbalizes the process imposed implicitly on the judge when acting as factfinder |

2. | ↑ | By traditional probability, I am referring to the classical, frequentist, and subjective systems conforming to Kolmogorov’s axiomatization. See Alan Hajek, Interpretations of Probability, in STANFORD ENCYCLOPEDIA OF PHILOSOPHY § 1 (Edward N. Zalta ed., 2012), https://plato.stanford.edu/entries/probability-interpret/ [https://perma.cc/HAV8-QNFM] (listing the axioms of nonnegativity, normalization, and additivity). But the usual particularization of probability for discussing legal proof is subjective probability. See KEVIN M. CLERMONT, STANDARDS OF DECISION IN LAW: PSYCHOLOGICAL AND LOGICAL BASES FOR THE STANDARD OF PROOF, HERE AND ABROAD 120–21 (2013) (discussing probability theories); H´ajek, supra, § 3.3.1 (characterizing subjectivism, unfortunately, with the slogan of “Probability is degree of belief”). |