# Only in Canada, eh?

“In essence, Bayes’s theory furnishes a mechanism for incrementally revising probability estimates in light of new information, thereby allowing a fact-finder to update continually an opinion about the relative likelihood of a fact.” Russell Brown, “The Possibility of ‘Inference Causation’: Inferring Cause-In-Fact And The Nature Of Legal Fact-Finding” (2010) 55 McGill L. J. 1 at 27-28 [Brown “Inference Causation”].

“Bayesian methodology suffers from several defects, however, making it incompatible with legal fact-finding.” Russell Brown, “Inference Causation” at 28.

Brown sets out the defects succinctly. I don’t propose to repeat them. Others hold different views. The literature is extensive. And easily found.

Bayes’ ~~Theory~~ Theorem is a method of handling statistics. There isn’t, to my knowledge, a reported decision in English from any Canadian court considering the question of whether a Bayesian analysis is, in any way, compatible or incompatible with evidence theory in law. I suspect there isn’t a recent French language decision, either, because a CanLII search produces only one case mentioning Bayes Theorem: a decision in English.

*Goodman v. Viljoen*, 2012 ONCA 896 affirming 2011 ONSC 821 is the first reported case that I know of, in Canada – I don’t know of any unreported cases – where an opinion on the probability of the connection between wrongful conduct and injury, based on a Bayesian methodology, has been accepted in a civil case. (I’m not aware of any where the argument was made – none have been reported, to my knowledge.)

I discuss aspects of the *Goodman* decision on Slaw, here. I’ll eventually repost that discussion here, perhaps with some comments on the merits. I’m inclined to wait until after leave to appeal to the SCC is sought, assuming it is, and I’ve read the applicant’s factum. And the defendant / appellant’s factum in the ONCA.

Some of you will understand the point of the title of this piece. It’ll become clearer (I hope) if you read the Slaw piece.

Once upon at time, as I was sitting outside a court room during a recess, I overheard two recently-called lawyers talking. I knew they were recently called because: (1) they were young and (2) it was the middle of summer, the air conditioning wasn’t working properly, the corridor was very hot, and both were still wearing all of their regalia – gown; closed vest; collar closed, and tabs.

Lawyer A said to lawyer B that a reason A had gone to law school was that A had trouble understanding mathematics. I don’t recall if the mathematics involved was statistics.

If you try to guess which gender they were, you’ll have 50% chance of being correct for each one but a 1/3 (not a 1/4) chance of getting them both right the first time. (My question doesn’t require you to decide which of the two was which gender.) There are 3 different combinations, not 4. F-M is the same as M-F. (M-M, F-F and F-M/M-F).

Thanks for the reference to a single example of Bayes Theorem usage in Canadian courts.

Also, thanks for the reference to Brown’s paper “Inference Causation”.

I may be three years out of date, but here’s my comment on Brown’s paper. His primary argument against Bayes Theorem is that one must carry the influence of a subjectively chosen prior through to the final posterior probability estimates is questionable, to say the least. The whole process can be conducted without ever selecting prior distributions. To do this, work instead with the likelihood ratio: Probability(guilty)/Probability(innocent), this ratio will either approach 1, indicating guilt, or 0, indicating innocence.

I don’t know about law, but I do know about stats.

I don’t know anything about the gender ratio of recent law graduates, nor do I know how many recent grads you’d be likely to see. So, I’ll make up some numbers.

Case 1. Suppose there are 100 recent grads that you might see, and that 50 are male and 50 are female. The probability you see two males is the same as the probability you see to females: (50×49)/(100×99) = 0.247474. The probability you see a male-female, (or female-male pair) is: (50x50x2)/(100×99) = 0.5050505. Pretty close to 1/4, 1/2, 1/4.

Case 2. Suppose there are 100 recent grads that you might see, and that 25 are male and 75 are female. The probability you see two males is: (25×24)/(100×99) = 0.060606. The probability you see two females is (75×74)/(100×99) = 0.56060606. The probability you see a male-female, (or female-male pair) is (25x75x2)/(100×99) = 0.3787878. Nowhere near 1/4, 1/2, 1/4.

nice blog,

alison