Relative plausibility or bayesian verdicts?

Note: This post (sorry for the delay), my tenth and final one on Ron Allen and Mike Pardo’s “relative plausibility” paper (available here, via SSRN), is based on my 2015 paper “Why don’t juries try range voting?,” which was published in the Criminal Law Bulletin.

Thus far, we have explored the pros and cons of Ron Allen and Mike Pardo’s relative plausibility theory of juridical proof, but as we say in academia, it takes a theory to beat a theory, so in place of plausible relativity, why not ask jurors to engage in full-fledged “Bayesian voting”? The type of Bayesian voting I am proposing here is “jury scoring” and is often called “range voting” in the literature on voting systems. (See Warren D. Smith, Range Voting, Paper No. 56 (2000), available at[tilde]wds/homepage/works.html; Claude Hillinger, “The Case for Utilitarian Voting,” 23 Homo Oeconomicus 295 (2005). See also chapter 14 of William Poundstone, Gaming the Vote (2008). For a glossary of different voting procedures, see Poundstone, at 287-89.)

In summary, my proposed Bayesian voting procedure by juries would work as follows. At the end of a jury trial, jurors would be instructed to rate or score on a scale of zero to ten, or some other specified scale, the evidence presented by the parties at trial. The jury’s verdict would then consist of a numerical value, either the average of each juror’s score or the sum or total of all the individual scores. There are thus two ways one could express the jury’s collective score or “range verdict”: one could calculate the average value of the jurors’ ratings (the average-value method), or in the alternative, one could simply sum or add up the jurors’ scores (the additive method). In either method, average-value or additive, Bayeisan voting by juries produces not a binary or qualitative verdict but a numerical or quantitative verdict consisting of an average score or total score. Also, since the jury’s verdict is a function of a range voting procedure, I shall refer to such a numerical verdict as a Bayesian verdict.

The Bayesian scoring system I propose is flexible and can take many different forms. At a minimum, jurors would have to score the evidence presented by the moving party in a case – the plaintiff in a civil case; the prosecutor in a criminal case. The plaintiff or prosecutor would prove his case as a matter of law only if the average value or sum total, as the case may be, of the jury’s collective score exceeded some critical threshold value. In the alternative, jurors also could be asked to score the evidence presented by the defendant. In this version of Bayesian voting by juries, the side with the highest average score or highest total score wins. (In criminal cases, where the moving party’s burden of proof (“proof beyond a reasonable doubt”) is much higher than in a civil case, one could require the moving party’s average or total score to exceed the defendant’s score by some specified margin.)

For my part, I prefer the simplest possible procedure in which jurors are only required to score the moving party’s case on a scale of one to ten. The moving party wins only if the jury’s average score exceeds some threshold, such as five in a civil case or a higher value in a criminal case. (See my sample scorecard below in which a juror is asked to rank the strength of the plaintiff’s claims. This sample scorecard assumes the plaintiff is asserting three separate legal claims, but the scorecard can be modified to include a greater or lesser number of claims, as the case may be.)

Under this approach, the judge or some other rule-making institution would have to establish the threshold or “cut-off” value for criminal convictions or for the imposition of civil liability. That is, to convict a defendant of a crime or to impose civil liability on a defendant, the sum total of the jurors’ scores under the additive method of voting–or the average value of all the jurors’ scores under the average-value method–would have to exceed some minimum threshold or cut-off value. Otherwise, when the jury’s collective score falls below this threshold value, the defendant would be immune from civil or criminal liability.

Consider, by way of example, a standard civil case, such as a personal injury or copyright infringement lawsuit. In a civil case, where the plaintiff’s standard of proof is based on the “preponderance of the evidence” or “more likely than not” standard, the threshold for imposing civil liability could be set at any value greater than five, if the average-value method were used, or at any value greater than 30 or 60, depending on the total number of jurors (six or twelve), if the additive approach were used.

Although my unconventional proposal may sound strange or exotic, Bayesian or range voting is actually very common in many areas of life, especially on the World Wide Web. For example, in the words of one commentator: “YouTube and Amazon allow users to rate videos and books on a five-point scale. The Internet Movie Database (IMDb) has ten-point ratings of movies.” (Poundstone, at 233; see also Claude Hillinger, Science and Ideology in Economic, Political and Social Thought (2006), available at If ordinary people are thus accustomed to Bayesian voting in their everyday activities, such as rating movies and restaurants, why not extend this method to juries? My proposal, in a nutshell, would do just that – extend range voting to juries.

Before concluding, it is also worth noting that range voting works best when the same group of people rates all the candidates or products. (See, e.g., Poundstone, at 233.) Bayesian voting is thus an especially appropriate method for juries, since this is precisely how the jury system works: the same group of people (the jury) must rate the strength of the evidence presented at trial. Moreover, in addition to its simplicity and user-friendly nature, my proposed method of Bayesian verdicts has another advantage (one that I explain more fully in my 2015 range voting paper): it allows stubborn jurors or “holdouts” to freely express their individual assessments of the case. In short, if we really care about accuracy and were willing to experiment with a new method of jury voting, Bayesian verdicts are the way to go …

Screen Shot 2018-06-18 at 9.39.43 PM

sample juror scorecard


About F. E. Guerra-Pujol

When I’m not blogging, I am a business law professor at the University of Central Florida.
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