25 August 2005

The foolishness of The Wisdom of Crowds

Two competing memes predict what happens when a choice is made by a group of non-geniuses: “the wisdom of crowds”; “design by committee”. Same scenario; two opposite predictions. What gives?

This book review spills the goods. Only some crowds are wise. The author thinks he knows which ones: they are diverse, their members are independent, control is decentralized, and preferences are properly aggregated.

I have a cynical theory about this book. It takes an idea everyone on the right already believes. It repackages the idea for center-left consumption, scrubs it of all math references, adds lots of stories (for interest) and studies (to pass it off as novel), and phrases the thesis such that you can swallow it and retain every political notion you came in with. That is, the thesis has no real consequences. It's unuseful. I guess the book deserves praise for having a thesis at all; cf. the blob of factoids that is Freakonomics.

I have a less cynical thought about this book, too. It reminds me of control systems.

A control system is something like a thermostat. There's some variable it's trying to control (the temperature); and to do that it has sensors to measure that variable (thermocouples) and some kind of machinery that can affect it (your air conditioner). One of its important features is that it deals with random external factors that threaten to screw up the system (it was 110° outside today until noon, when it suddenly became rainy and cold).

Another example: in a robot arm, a control system drives the motors to move the arm to the desired location without overshooting it or taking all day to get there. (This is harder to design than you'd think.)

A typical control system can be described by a system of differential equations. The equations describe not only how the control itself works, but also how the world responds to the things the control can do (for example, how fast your house cools when the air conditioner is on). If the control system is good, the equations converge to a desirable state, in the absence of external disturbances. If the control system is bad, the equations result in ringing (unwanted fluctuations) or don't converge at all (your house freezes over). These equations are a precise mathematical model of the system; you can actually solve them to determine the real-world outcome. A qualitative description of the properties of a good control system might appear on page iv of a nine-hundred-page textbook. The equations tell the real story.

Now the private-sector economy could be seen as a huge system of differential equations. In the absence of external disturbances (weather, new technology, natural resources being exhausted, war, Congress, and life generally), how would it behave? Conservatives think it would converge to a balmy 72°F. Liberals think your house would freeze over.

In comes The Wisdom of Crowds with the brilliant resolution to this hairy* math problem: it depends on four unmeasurable variables, and whether they fall above or below certain unspecified thresholds.


*To English majors, hard problems are thorny; to geeks, they're hairy.

No comments: