Fagone on Cash WinFall

Great, thoroughly reported piece by Jason Fagone (author of The Woman Who Smashed Codes, which everybody says is great) about the Cash WinFall Massachusetts lottery story, which I wrote about at length in How Not To Be Wrong.  My chapter focused on a group of MIT students who became high-volume bettors; Fagone spends more time with Michigan retiree Jerry Selbee, and gets lots of information on the story I wasn’t able to uncover.  That’s why it’s good to have an actual journalist cover these stories!

Reader survey: how seriously do you take expected utility?

Slate reposted an old piece of mine about the lottery, on the occasion of tonight’s big Mega Millions drawing.  This prompted an interesting question on Math Overflow:

I have often seen discussions of what actions to take in the context of rare events in terms of expected value. For example, if a lottery has a 1 in 100 million chance of winning, and delivers a positive expected profit, then one “should” buy that lottery ticket. Or, in a an asteroid has a 1 in 1 billion chance of hitting the Earth and thereby extinguishing all human life, then one “should” take the trouble to destroy that asteroid.

This type of reasoning troubles me.

Typically, the justification for considering expected value is based on the Law of Large Numbers, namely, if one repeatedly experiences events of this type, then with high probability the average profit will be close to the expected profit. Hence expected profit would be a good criterion for decisions about common events. However, for rare events, this type of reasoning is not valid. For example, the number of lottery tickets I will buy in my lifetime is far below the asymptotic regime of the law of large numbers.

Is there any justification for using expected value alone as a criterion in these types of rare events?

This, to me, is a hard question.  Should one always, as the rationality gang at Less Wrong likes to say, “shut up and multiply?” Or does multiplying very small probabilities by very large values inevitably yield confused and arbitrary results?

Update:  Cosma Shalizi’s take on lotteries and utilities, winningly skeptical as usual.