Should you play poker with your lawyer?

Mark Kleiman thinks so?

Statistical decision theory teaches us, when we face a tradeoff between two opposite errors, to set the ratio of the marginal error probabilities as the inverse of the ratio of the damages caused by the two kinds of error. That is, if saying "no" incorrectly costs me a dollar, and saying "yes" incorrectly costs me $99, then I should say "no" unless the probability that "yes" is the right decision is greater than 99%. The standard of "beyond reasonable doubt" suggests to my mind a ratio at least that high: since I can reasonably fear an outcome that is only 1% probable, I wouldn't consider an outcome that is 99% probable "certain beyond reasonable doubt." Thus the "reasonable doubt" standard, if interpreted literally, would appear to be consistent with Benjamin Franklin's famous "Better that a hundred guilty persons should escape than that one innocent person should suffer."

But Sasha Volokh's playful article "n Guilty Men" reports that American lawyers -- due, no doubt, to the failure of law schools to teach decision analysis -- more conventionally set the ratio at ten-to-one, which implies that they are willing to treat an event as "certain beyond reasonable doubt" as long as its probability is greater than 91%. If that seems right to you, please get in touch with me; I want you in my poker game.

I wouldn't, however, want you on my jury, or as my judge. Given how horrible American prisons are, and how many people they house, the extent of the injustice resulting if even a few percent of them are actually innocent is, or ought to be, intolerable. Much better to be more generous about what sort of evidence is admissible at trial -- in particular, evidence of prior similar acts, even when those acts did not result in conviction -- than to send people away when their odds of being innocent are no worse than the odds of filling an inside straight.

Of course, the alternative explanation to the hypothesis that lawyers can't do statistical analysis is that they don't care very much about putting the odd innocent man away along with the guilty if by doing so they can get a higher percentage of the guilty incarcerated. I don't know which assumption is worse, really.