Ellsberg paradox, take 2:

Looks like my Ellsberg paradox post below was pretty popular — about two dozen comments just in the first hour, between 11 p.m. and midnight (Eastern)! I'll repeat the problem below, then give my explanation. If you haven't done so before, you may want to think about what you would choose before reading the explanation.

There are three balls. One is red. Each of the others is either white or black. Now I give you a choice between two lotteries. Lottery A: You win a prize if we draw a red ball. Lottery B: You win a prize if we draw a white ball.

Which lottery do you choose? (Mini-update: I allow you to be indifferent, if you want.)

Now I give you another choice between two lotteries. Lottery C: You win a prize if we draw a ball that's not red. Lottery D: You win a prize if we draw a ball that's not white.

Now which lottery do you choose?

UPDATE: Just in case you're confused about this — and apparently some people were — we're talking about the SAME THREE BALLS each time. I haven't changed the balls. Nor have I drawn any balls. We haven't conducted any lotteries in the time it took you to read this post. All there is is a single box of balls, and me asking you your preferences over lotteries. (END OF UPDATE)

UPDATE 2: You ask one of these questions, and you find out all sorts of aspects that you weren't expecting people to find important. This will affect how I phrase the problem next time, but for now, let me just clear up one extraneous aspect. I'm not running the lottery. I don't own the balls. I'm not offering a prize. Someone else, who isn't connected with me, is doing all that. I'm just asking questions about which lotteries you prefer. Also, as I mentioned in the first update, we don't draw any balls between your first choice and your second choice. In fact, we're never going to draw any balls. Why? I'm not running the lottery! I'm just asking questions! If you want to draw balls, take it up with the guy actually running the lottery, who is not me.