I was lecturing on Condorcet's "Jury Theorem."
It bears on many problems in political theory, but my point that day was that a group of schlubs (chance of being correct: 0.51) might be "smarter", if we require unanimity, than one well trained judge (chance of being correct: .95). The reason exploits statistical independence: the probabilities of 12 jurors all (independently) being wrong is very small. So a unanimous guilty verdict of people off the street is better than one smart judge. The chance of 12 .51 folks all, separately, being wrong is [(0.49)^12]=.0002. So, *if* the jury is unanimous in favor of one outcome, the chance that they are correct is .9998.
A student asked, "But what if the jury isn't unanimous?"
I said, "That may not be a bad thing; it means you aren't sure. And in our system, 'not sure' means NOT GUILTY."
A pause. Then is where I made my misstep. I wanted to compare juries with judges.
"If the jury is NOT uanimous, that's a hung jury. You know what to do with a hung jury. Either a misstrial, or just call it not guilty. BUT, what would you do with a hung judge?" I stopped, horrified; the students stared.
Then, a young woman at the back yelled: "Marry him!"
It took several minutes for order to be restored. And I still haven't quite recovered.