If someone plays this game only once or twice, guessing the average of all the guesses is as much a matter of reading the others' intelligence and psychology as it is of following an idea to its logical conclusion.
By the same token and to return to the stimulus, understanding the constraints on legislators is often as important as assessing the legislation under consideration. And it's likely to be more difficult as well.
Economics is nowhere near as clear-cut as mathematics and the above analogy is no doubt a bit strained, but it is nevertheless suggestive. Insisting on being right mathematically (that is, choosing 0 as your number) or right economically (enacting a much larger stimulus bill) is not always a smart thing to do.
It's certainly not the same thing as being right psychologically (gauging others' number choices) or being right politically (assessing others' partisan commitments).
Some variant of this idea also helps answer the question perennially asked of academics and others: If you're so smart, why aren't you rich? The inverse question posed to financiers and Wall Street types remains unanswered: If you're so dumb, why are you rich?
John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.