Ellsberg paradox, take 3:

Back to the Ellsberg paradox (so-called, 'cause it's not really a paradox). Based on a bunch of previous comments, let me summarize where we're at, with a simplified version of the paradox.

There are three balls. One is red. For each of the other balls, someone flipped a fair coin to determine whether they would be white or black.

You can imagine a number of lotteries based on a draw from these balls. For example, consider the following four lotteries:
Lottery A: Win $100 if we draw a red ball.
Lottery B: Win $100 if we draw a white ball.
Lottery C: Win $100 if we draw a ball that isn't red.
Lottery D: Win $100 if we draw a ball that isn't white.

Do you prefer Lottery A or Lottery B? Do you prefer Lottery C or Lottery D?

(This is different than the previous example in the following ways: First, I've given a specific set of probabilities for white vs. black. Second, I've made it clear that I'm not offering any lotteries, just eliciting your opinion. Third, I've made the prize $100, just to be more specific.)

It turns out that most people prefer A to B, and prefer C to D. This is inconsistent with expected utility theory, which says your preferences over lotteries should only depend on what the ultimate probabilities are and the utility of the item. More below the fold, including the answer to the question: "Who cares?"