Thursday, April 27, 2006

A Hung Jury is Bad, But....

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.

5 comments:

Anonymous said...

The independence assumption behind Condorcet's jury theorem greatly limits its appeal in real world applications (esp. with regards to public opinion).

Individuals within a social group form their opinions in a way that clearly does NOT satisfy independence.

Anonymous said...

“Information Aggregation, Rationality and the Condorcet Jury Theorem”

Austin-Smith and Banks

American Political Science Review, 1996

mungowits said...

Um...I was a discussant on that A-S & Banks paper at professional meetings. And David presented the paper in my workshop at UNC in 1995.

I'm not saying I added anything to the discussion, but you surely can't think I am not aware of it. If you are worried that someone might get the wrong idea from reading the post...well, it is a short funny story, not an essay on social choice.

The idea that anonymous commenters are going to teach me anything technical is....well, I can understand why you would comment anonymously.

As I have myself often said in talks, and in class, the idea that Condorcet's theorem tells us anything about democracy is unlikely. It is not just the independence axiom that kills it, but the "identical" part of the IID requirement. Scott de Marchi and I have talked about this often: the need for the DGP for beliefs to be IID is central. I think too much attention goes to independence, though as the commenter notes (though everyone with more than a 5th grade education already knew) independence is the first thing they teach the little children.

I am going to assume that the commenter, being him/herself IN the fifth grade and just learned about this exciting concept, wanted to share it.

And thanks for that.

Chris Lawrence said...

Clearly, you've found proof of Condorcet's (less-well-known) Jackass Theorem.

Anonymous said...

I think too much attention goes to independence, though as the commenter notes (though everyone with more than a 5th grade education already knew) independence is the first thing they teach the little children.
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Really? Something is wrong with your discipline then. Many a professor overlooks both the identically and the independently parts of the iid assumption. Maybe they should let their kids read their papers before submitting them for publication?