“Statistical Evidence Paradox”: bogus

Here is a criminal law version of [a] problem. Defendants are both hunters. They recklessly fire bullets in a direction where they heard a rustle even though they have good grounds for fearing that the rustle might have been caused bya  person rather than an animal. Defendant One fires 95 shots; Defendant Two fires 5. In the end, it cannot be determined whose bullet killed the victim. Defendant One is prosecuted for manslaughter. The argument is made that the mere fact that he fired 95 of the 100 bullets that rained down in the vicinity of the victim proves by preponderance of the evidence that he is the killer. Again, courts would refuse to so interpret the evidence. But why?

That is a passage from Leo Katz’s book Ill-gotten Gains: Evasion, Blackmail, Fraud, and Kindred Puzzles of the Law. Katz argues that the courts, justifiably, would refuse to convict in this case because the evidence is “statistical,” and thus not a basis for the same type of knowledge that is required for a conviction. Katz draws the analogy (giving credit to another philosopher) to a person who believes that it is currently nine o’clock, based on the fact that his watch, which stopped exactly 12 hours ago (unbeknownst to the person), says nine o’clock. This person’s belief is correct, although it should not be said to constitute “knowledge,” since “there is an insufficient causal connection between [the] true, justified belief that it is nine o’clock and the fact that it is nine o’clock” — rather, the person’s belief is correct only by coincidence. Katz argues that, in the same way, although the belief that Defendant One killed the victim may be justified, it “would not be connected with the actual facts in the right kind of way to permit one to say that the court actually ‘knew’… that Defendant One killed the victim.”

(Katz’s argument is made entirely in the section called “The Statistical Evidence Paradox,” linked to above, which takes about 2 minutes to read. The part I’ve block quoted is from the 2nd paragraph of that section.)

This seems to be a completely bogus argument. Any evidence, if enough data is collected to quantify its usefulness, is “statistical evidence.” Suppose that Tom is on trial for murder based the following evidence: a) a videotape of him stabbing Scott in the chest at 12pm on Sunday, and b) the the medical examiner’s testimony that Scott died due to the fact that his heart stopped beating within minutes of being pierced by a sharp object around 12pm on Sunday. Suppose Tom’s defense lawyer calls to the stand a medical doctor who explains that the statistics suggest that a person with Scott’s cholesterol levels and body mass index has a 1 in 100 billion chance of dying due to heart attack within any 1 minute span, even if he is not being stabbed. Would Katz absurdly argue that this doctor’s testimony has rendered the evidence against Tom merely “statistical” and therefore not good enough for conviction? Of course, a 1 in 100 billion chance that Tom is innocent (i.e. that he stabbed Scott immediately after Scott had died naturally of a heart attack; assume for the purpose of the thought experiment that Tom, a psychopath, is just as likely to stab a dead person as a live person) is lower than the 5 in 100 chance that Defendant One (the hunter in Katz’s example) did not shoot the victim, but don’t be distracted by that: Katz admits that the 95% probability renders “justified” the belief that Defendant One is guilty. Katz is not quarreling with the magnitude of the probability itself, rather he is quarreling with the type of evidence used: “the connection… has the look of a coincidence.”

Katz suggests that there is a category of evidence which is epistemologically superior to mere “statistical evidence.” He is simply wrong: all evidence is statistical, if you bother to run the numbers.


Note: I previously posted on what I thought was a totally bogus argument made in this same book by Katz. Commenter (and friend) Julian defended Katz’s argument, and I admit I probably overstated the case when I called Katz’s argument “just utter nonsense,” partially due to my failure to fully understand his analogy. However I stand by my position that Katz’s argument is invalid, for the reason I explain in my last comment in that thread. In any case, I am comforted by Katz’s very clear blunder in the present case — and more confident that I was right about that previous argument, based on this new evidence that Katz,  at least sometimes, uses very sloppy arguments.

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One Response to “Statistical Evidence Paradox”: bogus

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