How Not to Be Wrong

From the book:

LESS LIKE SWEDEN

A few years ago, in the heat of the battle over the Affordable Care Act, Daniel J. Mitchell of the libertarian Cato Institute posted a blog entry with the provocative title “Why Is Obama Trying to Make America More Like Sweden when Swedes Are Trying to Be Less Like Sweden?”

Good question! When you put it that way, it does seem pretty perverse. Why, Mr. President, are we swimming against the current of history, while social welfare states around the world—even rich little Sweden!—are cutting back on expensive benefits and high taxes? “If Swedes have learned from their mistakes and are now trying to reduce the size and scope of government,” Mitchell writes, “why are American politicians determined to repeat those mistakes?”

Answering this question will require an extremely scientific chart. Here’s what the world looks like to the Cato Institute:

The x-axis represents Swedishness, and the y-axis is some measure of prosperity. Don’t worry about exactly how we’re quantifying these things. The point is just this: according to the chart, the more Swedish you are, the worse off your country is. The Swedes, no fools, have figured this out and are launching their northwestward climb toward free-market prosperity. But Obama’s sliding in the wrong direction.

At the top of the facing page I’ve drawn the same picture from the point of view of people whose economic views are closer to President Obama’s than to those of the Cato Institute.

This picture gives very different advice about how Swedish we should be. Where do we find peak prosperity? At a point more Swedish than America, but less Swedish than Sweden. If this picture is right, it makes perfect sense for Obama to beef up our welfare state while the Swedes trim theirs down.

The difference between the two pictures is the difference between linearity and nonlinearity, one of the central distinctions in mathematics. The Cato curve is a line;* the non-Cato curve, the one with the hump in the middle, is not. A line is one kind of curve, but not the only kind, and lines enjoy all kinds of special properties that curves in general may not. The highest point on a line segment—the maximum prosperity, in this example—has to be on one end or the other. That’s just how lines are. If lowering taxes is good for prosperity, then lowering taxes even more is even better. And if Sweden wants to de-Swede, so should we. Of course, an anti-Cato think tank might posit that the line slopes in the other direction, going southwest to northeast. And if that’s what the line looks like, then no amount of social spending is too much. The optimal policy is Maximum Swede.

Usually, when someone announces they’re a “nonlinear thinker” they’re about to apologize for losing something you lent them. But nonlinearity is a real thing! And in this context, thinking nonlinearly is crucial, because not all curves are lines. A moment of reflection will tell you that the real curves of economics look like the second picture, not the first. They’re nonlinear. Mitchell’s reasoning is an example of false linearity—he’s assuming, without coming right out and saying so, that the course of prosperity is described by the line segment in the first picture, in which case Sweden stripping down its social infrastructure means we should do the same.

But as long as you believe there’s such a thing as too much welfare state and such a thing as too little, you know the linear picture is wrong. Some principle more complicated than “More government bad, less government good” is in effect. The generals who consulted Abraham Wald faced the same kind of situation: too little armor meant planes got shot down, too much meant the planes couldn’t fly. It’s not a question of whether adding more armor is good or bad; it could be either, depending on how heavily armored the planes are to start with. If there’s an optimal answer, it’s somewhere in the middle, and deviating from it in either direction is bad news.

Nonlinear thinking means which way you should go depends on where you already are.

This insight isn’t new. Already in Roman times we find Horace’s famous remark “Est modus in rebus, sunt certi denique fines, quos ultra citraque nequit consistere rectum” (“There is a proper measure in things. There are, finally, certain boundaries short of and beyond which what is right cannot exist”). And further back still, in the Nicomachean Ethics, Aristotle observes that eating either too much or too little is troubling to the constitution. The optimum is somewhere in between, because the relation between eating and health isn’t linear, but curved, with bad outcomes on both ends.*