Cash For Clunkers

This sounds a like a really smart program.

And, as Freakonomics points out, using the fraction, getting clunkers off the road saves a ton more gas than if everyone who already drives a Honda were to get a Prius.

Why does 10 m.p.g. matter more than 22? The reason is that the relationship between m.p.g and fuel savings is not linear but curvilinear. Ten m.p.g. at the bottom of the range matters a lot more than 22 m.p.g. higher up.

This is a hard concept for us to get our brains around. Richard B. Larrick and Jack B. Soll, reporting in Science (gated) found that only 1 percent of college students studied correctly perceived that an improvement from 14 to 24 m.p.g. saves considerably more fuel than an improvement from 24 to 46.

To give our brains a break, we might adopt a better way to look at fuel efficiency, aided by the manipulation of a mathematical tool in use in the Indus Valley almost 5,000 years ago — the unglamorous fraction.

The trick is one that even fourth-graders can master: invert the fraction. Let’s consider not miles per gallon but gallons per mile (or, to make the numbers prettier, gallons per hundred miles). By this metric, we get an unclouded picture: the Prius uses 2.17 gallons per hundred miles, the RAV4 uses 4.17, and the Range Rover uses 7.14.

Thanks to the mileage mirage, our efforts as a society may be somewhat misplaced. There are plenty of policy ideas afoot to get people into state-of-the-art, fuel-efficient cars, but a lot less interest in simply getting people out of the worst gas guzzlers into moderately more efficient alternatives, even within the same fuel-hungry class.

I wish I had a clunker.