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« Check out wild & crazy "coherence based reasoning"! Are rules of evidence "impossible"?, part 2 (another report from Law & Cognition seminar)m | Main | My remote post-it notes for my HLS African-American teachers »

Report from "Law & Cognition" class: Are “rules of evidence impossible”? Part 1 

Well, I didn't do a good job of sharing the to & fro of this semester's Law & Cognition seminar w/ the 14 billion of you who signed up to take the coure on-line. I'm happy to refund your enrollment fees--I actually parleyed them into a sum 10^3 x as large by betting incredulous behavioral economists that P(H|HHH) < P(H) when sampling from finite sequences w/o replacement-- but stay tuned & I'll try to fill you in over time...

If you’re a Bayesian, you’ll easily get how the Federal Rules of Evidence work. 

But if you accept that “coherence based reasoning” characterizes juries’ assessments of facts (Simon, Pham, Quang & Holyoak 2001; Carlson & Russo 2001), you’ll likely conclude that administering the Rules of of Evidence is impossible.

Or so it seems to me.  I’ll explain but it will take some time—about 3 posts’ worth.

The "Rules of Evidence Impossibility Proof"--Paaaaaaart 1!

There are really only two major rules of evidence. There are a whole bunch of others but they are just variations on a theme.

The first is Rule 401, which states that evidence is “relevant” (and hence presumptively admissible under Rule 402) if it “has any tendency to make a fact  [of consequence to the litigation] more or less probable” in the assessment of a reasonable factfinder.

As Richard Lempert observed (1977) in his classic paper Modeling Relevance, Rule 401 bears a natural Bayesian interpretation.

The “likelihood ratio” rendering of Bayes’s Theorem—Posterior odds = Prior odds x Likelihood Ratio—says that one should update one’s existing or “prior” assessment of the probability of some hypothesis (expressed in odds) by a factor that reflects how much more consistent the new information is with that hypothesis than with some rival hypothesis.  If this factor—the likelihood ratio—is greater than one, the probability of the hypothesis increases; if it is less than one, it decreases.

Accordingly, by defining as “relevant” any evidence that gives us reason to treat a “fact of consequence” as “more or less probable,” Rule 401 indicates that evidence should be treated as relevant (and thus presumptively admissible) so long as it has a likelihood ratio different from 1—the factor by which one should revise one’s prior odds when new evidence is equally consistent with the hypothesis and with its negation.


Second is Rule 403, which states that “relevant evidence” should be excluded if its “probative value is substantially outweighed by . . . unfair prejudice.”  Evidence is understood to be “unfairly prejudicial” when (the Advisory Committee Notes tell us) it has a “tendency to suggest decision on an improper basis.” 

There’s a natural Bayesian rendering of this concept, too: because the proper basis for decision reflects the updating of one’s priors by a factor equal to the product of the likelihood ratios associated with all the (independent) items of proof, evidence is prejudicial when it induces the factfinder to weight items of proof inconsistent with their true likelihood ratios

Lempert crica 1977 (outside Studio 54, during break from forensic science investigation of then-still unsolved Son of Sam killing spree)An example would be evidence that excites a conscious intention—born perhaps of animus, or alternatively of sympathy—to reach a particular result regardless of the Bayesian import of the proof in the case.

More interestingly, a piece of evidence might be “unfairly prejudicial” if it triggers some unconscious bias that skews the assignment of the likelihood ratio to that or another piece of evidence (Gold 1982).

E.g., it is sometimes said (I think without much basis) that jurors “overvalue” evidence of character traits—that is, that they assign to a party’s disposition a likelihood ratio, or degree of weight, incommensurate with what it is actually due when assessing the probability that the party acted in a manner that reflected such a disposition on a particular occasion (see Fed. R. Evid. 404).

Or the “unfairly prejudicial effect” might consist in the tendency of evidence to excite cognitive dynamics that bias the weight assigned other pieces of evidence (or all of it).  Evidence that an accident occurred, e.g., might trigger  “hindsight bias,” causing the factfinder to assign more weight than is warranted to evidence that bears on how readily that accident could have been foreseen before its occurrence (Kaman & Rachlinski 1995).

By the same token, evidence that excites “identity-protective cognition” might unconsciously motivate a factfinder to selectively credit or dismiss (i.e., opportunistically adjust the likelihood ratio of) all the evidence in the case in a manner geared to reaching an outcome that affirms rather than denigrates the factfinder’s cultural identity (Kahan 2015).

Rule 403 directs the judge to weigh probity and prejudice.

Again, there’s a Bayesian rendering: a court should exclude a “relevant” item of proof as “unfairly prejudicial” when the marginal distortion of accuracy associated with the incorrect likelihood ratio that admitting it will induce the factfinder to assign to that or any other items of proof is bigger than the marginal distortion of accuracy associated with constraining the factfinder to assign that item of proof a likelihood ratio of 1, which is the practical effect of excluding it (Kahan 2010).  

click me & behold what it looks like to do Bayesian analysis of evidence rules *after* emerging from a night of partying at Studio 54 circa 1977!If you work this out, you’ll see (perhaps counterintuitively, perhaps not!) that courts should be much more reluctant to exclude evidence on Rule 403 grounds in otherwise close cases. As cases become progressively closer, the risk of error associated with under-valuing (by failing to consider) relevant evidence increases faster than the risk of error associated with over-valuing that or other pieces of evidence: from the point of view of deciding a case, being “ovderconfident” is harmless so long as one gets the right result. Likewise the risk that admitting "prejudicial" evidence will result in error increases more rapidly as the remaining proof becomes weaker: that's the situation in which a facfinder is most likely to decide for a party that she wouldn't have but for her biased over-valuing of that item of proof or others (Kahan 2010).

For an alternative analysis, consider Friedman (2003). I think he's wrong but for sure maybe I am! You tell me!

The point is how cool it is-- how much structure & discipline it adds to the analysis-- to conceptualize Rules of Evidence as an instrument for closing the gap between what a normatively desirable Bayesian assessment of trial proof would yield and what a psycholigically realistic account of human information processing tells us to expect (someday, of coures, we'll replace human legal decisionmakers with AI evidence-rule robots! but we aren't quite there yet ...).

Let's call this approach to understanding/perfecing evidence law the "Bayesian Cognitive Correction Model" (BCCM).

But is BCCM itself psychologically realistic?  

Is it plausible to to think a court can reliably “maximize” the accuracy of adjudication by this sort of cognitive fine-tuning of the trial proof?

Not if you think that coherence-based reasoning  (CBR) is one of the reasoning deficiencies that a court needs to anticipate and offset by this strategy.

I’ll describe how CBR works in part 2 of this series—and then get to the “impossibility proof” in part 3!


Carlson, K.A. & Russo, J.E. Biased interpretation of evidence by mock jurors. Journal of Experimental Psychology: Applied 7, 91-103 (2001).

Friedman, R.D. Minimizing the Jury Over-valuation Concern. Mich. State L. Rev. 2003, 967-986 (2003).

Gold, V.J. Federal Rule of Evidence 403: Observations on the Nature of Unfairly Prejudicial Evidence. Wash. L. Rev. 58, 497 (1982).

Kahan, D.M. The Economics—Conventional, Behavioral, and Political—of "Subsequent Remedial Measures" Evidence. Columbia Law Rev 110, 1616-1653 (2010).

Kahan, D.M. Laws of cognition and the cognition of law. Cognition 135, 56-60 (2015).

Kamin, K.A. & Rachlinski, J.J. Ex Post ≠ Ex Ante - Determining Liability in Hindsight. Law Human Behav 19, 89-104 (1995).

Lempert, R.O. Modeling Relevance. Mich. L. Rev. 75, 1021-57 (1977).

Simon, D., Pham, L.B., E, Q.A. & Holyoak, K.J. The Emergence of Coherence over the Course of Decisionmaking. J. Experimental Psych. 27, 1250-1260 (2001).

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Reader Comments (5)

I'm confused by your plots, Dan. Are the x- and y- axis labels flipped? The color zones are defined by ranges of the x-axis, which are the perceived likelihoods of fault with proof, and yet the captions are arguing that the decision to admit or exclude should be made on the basis of perceived likelihood of fault without the proof. It seems like the figures argue for admitting and excluding evidence on the basis of perceived likelihood of fault with proof.

November 23, 2015 | Unregistered Commenterdypoon


yes, that's what happens after too much partying at Studio77... x & y axis labels inverted. Will fix. then tell me if makes sense


November 23, 2015 | Registered CommenterDan Kahan

Thanks for comfirming. Yes, the diagrams make sense now, and so does the argument, to me at least. The closer to the fence you already are, the more open you should be to new evidence of unreliable quality.

...Is your point going to be that administering the rule is inherently subjective because rational choice at this step requires assessment of the prior?

November 23, 2015 | Unregistered Commenterdypoon


well, it's not really that ... that's a very good point, though-- that BCCM requires the judge to form & rely on her own estimates of strength of all the proof in case.

Take a look at Old Chief v. United States, 519 U.S. 172 (1997)'s discussion of how to do Rule 403 balancing: basically marginal probative value compared to marginal prejudice. That actually does require, I think, the sort of judgment about strength of proof overall that this analysis presupposes.

I can see why one might doubt that that can be done properly.

But I am thinking of something much nastier...

November 23, 2015 | Registered CommenterDan Kahan


would say too that the lesson of doing "marginal probative value vs. marginal prejudice" weighing isn't that one becomes less willing to accept "unreliable" evidence or evidence of "unknown reliability" as case gets close. It's that the marginal value of whatever appropriate weight should be afforded the evidence by a rational factfinder increases, and whatever potential risk is posed by its being overvalued by an irrational factfinder decreases, as case gets closer. But obviously, this assumes that judge can ascertain that there *is* licit probative value in the evidence -- weight that a *rational factfinder* would give to it!

November 24, 2015 | Registered CommenterDan Kahan

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