Xeni Jardin reports that the press covering the final arguments yesterday at the ‘trial’ (i.e., which is the name that the Obama administration gives to the farcical proceedings presided over by a military judge who has been clearly hostile to Bradley Manning) are being intimidated by heavily-armed military police looking over their shoulders as they type, forbidding the use of Twitter, shutting down internet service, forbidding the use of the internet when it is up, etc.

The trial comes to an end today with the defense lawyer David Coombs making his final case. The verdict could come within the next few days.

I am not hopeful. I think the judge will give the maximum sentence. I feel sorry for Manning.

Marcus Ranum says

I think the judge will give the maximum sentence.I notice nobody is holding out any hope for a verdict of innocent.

Well, kangaroo courts work both ways. I’m sure none of the establishment will complain about injustice to the tricoteuses when it’s their turn.

slc1 says

Just for the record, it is my information that Manning chose to have only 1 judge, rather then a panel of judges which is usually the case in a court martial. I haven’t followed the gory details of the trial but I must wonder what the rational of Manning and his lawyer were.

Jared A says

This is just a shot in the dark, but it could be playing statistics. Let’s say you think 80% of judges will be hostile, then you have a 20% chance of lucking out with one judge. If there are 3 judges, then you have less than 15% chance of having majority non-hostile. (I think, my statistics skills aren’t great.)

Leo Buzalsky says

Well…you’d have a 1/125 chance (< 1%) that all three would be non-hostile… so it would have to be somewhere in between that and 20. What? That doesn't help much. Yeah, my statistics abilities are not pulling through for me today.

Unfortunately, you have me intrigued into figuring out the answer (given your hypothetical). I suppose what we have to do is take that result above and add it to the probability of getting

exactlytwo non-hostile judges and one hostile judge. Wouldn’t that be 1/5 * 1/5 * 4/5? Or 4/125? So that would add up to be 5/125, which simplifies to 1/25, which is 4%. That’s just a bit worse than you thought.Mano Singham says

The reasoning is good, the final number is slightly off. With your probabilities, there is a 10.4% chance that he will have

at mostone judge who is sympathetic to his case. (0.2^{3}+0.2^{2}*0.8*3=0.104)Marcus Ranum says

(0.23+0.22*0.8*3=0.104)How does that compare with a snowball’s chance in hell?

Jared A says

Thanks! I had eventually calculated the 10.4 % value, but I wasn’t confident enough that I did it right to go back and correct myself.

But isn’t that the probability that he will have at most one judge that is

unsympathetic?slc1 says

This is accurate if only a majority vote is required. If a unanimous vote is required, then the more judges on the panel, the greater the likelihood of at least one who might vote to acquit, at least on some of the more serious charges. I don’t know whether a unanimous vote is required in a court martial.

Corvus illustris says

Mano and I get the same number; that helps me think I don’t have an appointment with Dr Alzheimer quite yet. On the other hand, there is a tacit assumption underlying these calculations: namely, that the judges make (stochastically) independent decisions. Since they are a jury and juries confer, this assumption is probably untenable. In addition, Orders may have Come Down From On High that actually make the situation deterministic, and then there’s review by the commanders up the food chain …

Mano Singham says

Oh Corvus,

You are stuck in the world of reality. Escape to the beautiful world of mathematical abstractions where we don’t have to worry about such grubby details as stacked trials.

Mano Singham says

You are right.

Corvus illustris says

“Escape to the beautiful world of mathematical abstractions … “Where do you think I live? When I want a vacation, I visit Renaissance polyphony. I only pick up my mail–and sometimes read the news–in reality.

Mano Singham says

It turns out that for the probability of a majority of a three-judge panel having greater probability of being sympathetic to Manning than the probability of a single judge requires the probability of a single judge being sympathetic to be

greater than half.So purely on the assumption we have made about the independence of the judges, it looks like Manning’s lawyers made a good call in going with just one judge, since such a high probability seems highly unlikely.

Corvus illustris says

Ya, I noticed that too: if

pis the probability of acquittal for one judge, then for a majority out of 3 the prob of acquittal (as a function ofp) is convex forp< 1/2 and concave forp> 1/2 with everything 1/2 forp= 1/2 by symmetry, so no tricky inequality-proving is necessary. If I wanted to behave properly here in the world of math abstractions, I would be tempted to replacepby some (Bayesian) beta-distributed RV with mean = 0.2, do the computations, and see how spread out the 3-judge acquittal probs would be–but Dr Carrier hss probably done that already.