You can't win it if you're not in it
With memories of the media retreat rapidly, er, retreating from my mind, I thought I'd better provide the answer to the question I posed on Friday. A reader named Xander (hi, Xander!) offered his solution via the comments:
People are generally loss-averse so most will choose the guaranteed loss of $3000 to avoid the likely hit of 4 grand. In the case of the winning money, nothing ventured, nothing gained, something cliche: people will roll the dice for the extra cash cause hey, if you don't win, you still lose nothing.
This strategy is the one David chose. Mathematically, it's the optimal tactic -- if you take the probabilities and amounts as a whole, the expected value of your lottery win on average is $3,200 (so, $200 more than you can guarantee yourself). Meanwhile, a certain loss of $3000 is better than an expected loss of $3,200. You could also argue that Will's strategy (take the guaranteed option in both situations) makes logical sense, because the scenarios are mirror images of each other -- what holds for one ought to hold for the other.
Here's the rub: people don't think "purely mathematically" or even logically, and according to the U of Chicago prof at the retreat, generally most of them choose the guaranteed $3K win and the loser lottery -- the exact opposite of the optimal strategy. I will confess to being in this group even though I had already done all the calculations of expected value and loss when I made my choice. I went on instinct, and in the process helped to annoy the living daylights out of thousands of economists, many of whom rely on models that assume rationality -- which, given the evidence, isn't the most rational thing they could do.
For more on how economists are trying to account for irrational dingbats like me, check out this article from Technology Review.