DNA and Guilt
the L.A. Times has an interesting article on partial DNA searches, prompting three posts by Patterico (so far) and others by Eugene Volokh and Radley Balko. In a nutshell, John Puckett was convicted in 2004 of raping and murdering Diana Sylvester in 1972, mostly on account of a partial DNA match. Like many of the older DNA cases, it wasn’t possible to run a full DNA match, which is essentially failsafe, but just a partial one, which has roughly a 1 in 1.1 million chance of matching the wrong person.
Sounds pretty damning, doesn’t it? I mean really, if the odds of a false match are really 1.1 million to one, what are the chances they matched the wrong guy? Pretty high, actually, if you searched 1.1 million times. Buy enough lottery tickets, and you will win. In Puckett’s case, they didn’t search 1.1 million records but did search 338,000, resulting in roughly one-in-three odds that someone would get falsely matched, or about 1 in 4 that exactly one person would. The actual odds are a bit lower than that once you control for the uncertain odds that the killer was in fact in that database; presumably, if he was, he certainly would have gotten a hit, while the odds are only 1 in 3 that a second person also would have. Only one person was matched, so we can be certain that either Puckett was matched because he was the killer, or he got unlucky based on 1 in 4 odds, times whatever the odds were that the killer was not in the database. Without knowing the odds of the killer being in the database it’s tough to say how serious that error was in Puckett’s case, but easy to say exactly how serious it is in any case like Puckett’s where we don’t know for a fact that the defendant was the only match (or the only match to a person who doesn’t have a 100% airtight alibi): 1 in 3.
Some would argue that a partial DNA match that shows 1 in 1.1 million odds against a previously identified suspect, but only 1 in 3 odds against a suspect for whom the DNA semi-match was itself the basis of the suspicion, should not be admissible in court. I disagree. Anything that says you’re twice as likely to be guilty as innocent is highly probative of the charge. It is crucial, however, that such evidence be presented for what it is: enough to make you think he likely did it, but without other, unrelated corroborating evidence, not nearly enough to extinguish reasonable doubt.
I should note that the same math problem, known as the “prosecutor’s fallacy,” likely occurs every day even with full DNA matches. There, the error is equally lame in theory but harmless in practice. Without knowing exactly how long the odds have to be in order to surpass reasonable doubt, I am pretty confident that that number is somewhere north of 3 but south of 1 million. So if a prosecutor tells you that the odds of a false full match are 1 in 1 quintillion, but neglects to tell you that he found the guy by combing through a database of 1 million individuals, all that means is that the odds have fallen “all the way down” to 1 in 1 trillion. No big whoop.






