The Cameron Todd Willingham test

There are problems with an adversarial system-- attorneys are rewarded for using weak but plausible arguments for their clients, and as stated above, there are also inequities in the quality of attorneys that different people can afford. Further, attorneys are so expensive that poorer people get an attorney supplied by the court who may not bother to try, or be so ill-paid that they can't afford to put a good case together.

There are also problems with an inquisitorial system. Iterated prisoner's dilemma implies that the investigator may be on the side of the court more than on the side of the accused. In theory, juries are supposed to prevent that, but US practice has been to give juries less and less information and to tell them that they have less and less freedom to use their whole minds.

I assume that a Bayesian court would permit-- possibly even encourage-- jurors to do additional research during the trial.

Some of the problems can be ameliorated by combining the systems-- three voices, speaking for the accused, the defense, and a third that's hopefully a neutral investigator.

Permitting the jurors to ask questions (afaik, a relatively recent addition to US practice and not universal here-- I don't know about other countries) is a significant contribution to getting more minds on the problem of getting all the relevant information and arguments on the table.

What do people think would be the ideal Bayesian structure for a trial. I think adversarial with a jury of peers is probably not the best choice. Some kind of inquisitorial panel makes sense but you have to deal with group think and career minded judges. The judges should be trained rationalists, I guess.

Frivolous link.

Now that you mention it directly, it's flabbergasting that no one's ever said what percentage level "beyond a reasonable doubt" corresponds to (legal eagles: correct me if I'm wrong). That's a pretty gaping huge deviation from a properly Bayesian legal system right there.

I wouldn't go that far. There are many cases where the legal system explicitly deviates from Bayesianism. Some examples:

• Despite the fact that Demographic Group X is more/less likely to have committed crime Y, neither side can introduce this as evidence, e.g. "Since my client is a woman, you should reduce the odds you assign to her having committed a murder by a factor of 4." (Obviously, the jury will notice the race/gender of the defendant, but you can't argue that this is informative about the odds of guilt.)

• Prohibition on many types of prejudicial evidence that is informative about the probability of guilt (like whether the defendant is a felon). (This can be justified on grounds of cognitive bias maybe, but not Bayesian grounds.)

• In the US, the Constitutional prohibition on using the defendant's silence as evidence, despite its informativeness, e.g., "If he's really innocent, why doesn't he just tell his side of the story? What's the big deal? Why did he wait hours before even saying what happened? Did he need to get his story straight first?" (Again, the jury will notice that the defendant didn't take the stand, but you can't draw their attention to this as the prosecution.)

• The exclusionary rule. The impact of illegally-collected physical evidence (i.e. not forced confessions but e.g. warrantless searches) has a small to non-existent impact on the evidence's strength. The policy on excluding illegally-obtained evidence may be justified on decision-theoretic grounds, but not on Bayesian grounds.

• Outside of trials, the fact that you have to wait years before you hear a judge's binding opinion on whether or not a law actually can be enforced (i.e. is Constitutional).

You give the legal system way too much credit.

Were defense attorneys left out by accident, or do you think it's not important that they be Bayesian?

What prior are you using for Knox? The pre-murder "chances a nice, pretty upper-middle class American girl would be involved in a murder in the next year" or the "chances the nice, pretty, upper-middle class American girl was involved in murder, given that her roommate was stabbed to death?

I've been kicking myself for months for not having done a better job of making the point that it shouldn't matter: so long as you take into account all of the relevant information, Bayes' theorem says nothing about the order in which you process the information.

What we label "prior probability" in everyday contexts like this is just an arbitrary matter of convenience: "priors" are in fact posteriors based on information not explicitly mentioned -- and that information is still there, whether we mention it or not.

Thus, for example, if you assign a high "prior" to Amanda Knox's guilt because of Meredith Kercher's death, you still have to lower the probability (to something around the "pretty middle-class female honor student" range) upon learning that Kercher's death was caused by Rudy Guede -- the screening off effect doesn't go away just because you decided to call that state of knowledge the "prior"; it just acquires the label of "evidence of innocence."

(Just to be clear, I'm not suggesting you don't realize this; I just think the point needs to be reinforced.)

I asked two questions that I wanted to see answers for. And the Bayesian justice question is a really hard question.

Every post does not have to be made with the specific goal of teaching rationality. There is a much larger set of possible purposes for posts.

This thread probably belongs in the meta thread.

I don't see what the harm is in more practice.

Yes, that is why I did not say that the prior probability was correct. I said it was a prior probability estimate.

If you can find demographic data that gives you a better prior probability than 13%, or would like to suggest an arbitrary constant to multiply by, go for it. I meant just to emphasize that the prior probability for Willingham's guilt is at least an order of magnitude higher than the prior probability of Knox's guilt.

I think you're conflating Bayesian justice with utilitarian justice.

There is still a whole bag of philosophical problems to be solved regarding punishment. Do you punish to prevent the same person from doing something again, do you punish as retribution for the victims (then it doesnt make sense to tax those to provide prisons), or do you want to set a sign against others for not doing crime. Atm there are many inconsistent terms put on various charges, which merit resolving. I read a few times that the legal system works because most people are aware of punishment, not because it punishes most punishworthy deeds, or because its particularly fair. In that case a bayesian system might have very little practical difference from the current (except for all those not guilty). A decent reform would include some liability for attorneys to withhold evidence, or threaten the accused and such. Maybe someone will put up a whole thought out concept.

The precedential value must be taken into account as these EV's. Someone who can convince you that they won't do it again who gets off will encourage others who are convincing to use their one-murder-free card. That's bad policy.

I agree with Jack. You are also conflating tax receipts, the "exchange value" of a citizen, with intrinsic worth, the "use value" of a citizen. In so far as it exists as a real phenomenon, society doesn't value citizens because they pay taxes; society values citizens because society is a construct set up by and for the benefit of citizens.

Also, much government spending is not fairly characterizable as mere redistribution; once you killed off, say, the bottom 40%, you would find that all citizens produced at least some net surplus, some of which would be confiscated to spend on public goods. Some remaining citizens would not contribute as much surplus as others, but an evil government that maximized total tax receipts (as opposed to average tax receipts, which is just a really weird goal) would not feel any urge to execute those citizens.

I think the certainty required should probably vary based on the length of the sentence (or the value of the penalty in civil cases, etc.).

"whatever percent of innocent convictions we're comfortable with." Isn't the right way to do it. You need to weigh the expected utilities and go with that.

For example, say we have someone suspected of murder, and you think its only 20% sure that he did it, but executing him given that he's the guilty saves an expected 10 lives, then you do it. If there was a second suspect (same p(guilt)) and you know only one of them is guilty, then you'd execute them both.

There are all sorts of disclaimers that could be added, but the point is that the threshold isn't arbitrary, and intuitions don't get close to the right answer.

Note that plea bargaining isn't even doable in many systems. Plea bargains are only really common in the US and a few other places. Many other locations require a full trial regardless. This is generally balanced with weaker rules of evidence and fewer restrictions on what prosecutors and police can get away with.

To try to answer the original question: I'm not sure plea bargaining ever makes sense in a purely Bayesian system because a plea bargain essentially shortcircuits an attempt to find out the truth.

The Beyler report looks very interesting - I will review it and Fire Chief McMullan's rebuttal thereof when I have time.