I think there’s another, more fundamental reason why Aumann agreement doesn’t matter in practice. It requires each party to assume the other is completely rational and honest.
Acting as if the other party is rational is good for promoting calm and reasonable discussion. Seriously considering the possibility that the other party is rational is certainly valuable. But assuming that the other party is in fact totally rational is just silly. We know we’re talking to other flawed human beings, and either or both of us might just be totally off base, even if we’re hanging around on a rationality discussion board.
I was unfamiliar with the case. I came up with: 1 − 20% 2 − 20% 3 − 96% 4 - probably in the same direction, but no idea how confident you were.
From reading other comments, it seems like I put a different interpretation on the numbers than most people. Mine were based on times in the past that I’ve formed an opinion from secondhand sources (blogs etc.) on a controversial issue like this, and then later reversed that opinion after learning many more facts.
Thus, about 1 time in 5 when I’m convinced by a similar story of how some innocent person was falsely convicted, then later get more facts, I change my mind about their innocence. Hence the 20%.
I don’t think it’s correct to put any evidential weight on the jury’s ruling. Conditioning on the simple fact that thier ruling is controversial screens off most of its value.