Fallacy of composition

Paul Krugman's column yesterday focused on an application of the fallacy of composition: the false belief that what is true of the parts must be true of the whole. This is one of my favorite fallacies to teach because I never learned about it as a student and it can be surprisingly counterintuitive.

Imagine that one year growing corn turns out to be more profitable than growing soybeans. The logical thing for each farmer to do is plant more corn the next spring; in fact to maximize your profit you should plant all your fields in corn, right? But if all farmers do this, corn prices will plummet and soybeans will become very valuable. Planting a lot more corn is a logical thing to do for one farmer, but not for farmers as a whole.

Krugman's column does not use the term fallacy of composition, but it is essentially the same idea for debt: each family has to balance its budget, so the government has to also, right? Wrong. When I was younger I swallowed this argument hook, line, and sinker when I heard it from politicians. But the analogy is false. When society as a whole goes into debt, it goes into debt to itself, or some subset of itself. The dynamic is completely different, because this type of borrowing can spur the economy as a whole.  This is not to say that government debt is always harmless, but those who make debt-is-harmful arguments should at least give substantive reasons rather than a false analogy. Any politician who makes this analogy now instantly loses all credibility with me.

A related effect is Simpson's paradox. A school may have improving test scores for each racial/ethic group individually, but it can still be true that the school as a whole has decreasing test scores. How? The racial/ethnic composition of the school is changing, with more disadvantaged groups living in the area. This brings the overall average down regardless of improvements within each group.

I taught this fallacy when I taught a first-year seminar in scientific reasoning, and it may seem like one of those counterintuitive puzzles that has little application in the real world. But Krugman's final sentence reminded me of the real-world importance of effective reasoning: "if the euro does fail, here’s what should be written on its tombstone: 'Died of a bad analogy.'”