Let’s say a pollster walks up to you and asks you the following question:

“A town maintains a fleet of vehicles for town employee use. It has two types of vehicles. Type A gets 15 miles per gallon. Type B gets 34 miles per gallon. The town has 100 Type A vehicles and 100 Type B vehicles. Each car in the fleet is driven 10,000 miles per year.” The town wants to replace these vehicles with corresponding hybrid models in order to to reduce gas consumption of the fleet and thereby reduce harmful environmental consequences.

Should they (1) replace the 100 vehicles that get 15 mpg with vehicles that get 19 mpg , or (2) replace the 100 vehicles that get 34 mpg with vehicles that get 44 mpg?

If you are like the people who were actually surveyed by Richard Larrick and Jack Soll of Duke University, you chose option two. After all, an increase of 10 mpg clearly sounds better than a measly 4 mpg. And yet, some simple number crunching reveals that the town fuel efficiency is improved more in option one (by 14,035 gallons) than in option two (by 6,684 gallons).

Fuel efficiency, write Larrick and Soll in the current issue of *Science* magazine, is systematically misunderstood by car consumers in the United States, where the standard of measure is miles per gallon.

“People falsely believe that the amount of gas consumed by an automobile decreases as a linear function of a car’s mpg. The actual relationship is curvilinear. Consequently, people underestimate the value of removing the most fuel-inefficient vehicles.”

They cite a 2006 *New York Times* Op-Ed in which an automotive expert likened hybrid cars to “fat-free desserts” — they “can make people feel as if they’re doing something good, even when they’re doing nothing special at all.” The *Times* writer had questioned the logic of granting tax incentives to buyers of “a hypothetical hybrid Dodge Durango that gets 14 miles per gallon instead of 12 thanks to its second, electric power source” but not to a “buyer of a conventional, gasoline-powered Honda Civic that gets 40 miles per gallon.”

According to Larrick and Soll, the basic argument is correct:

“The environment

wouldbenefit most if all consumers purchased highly efficient cars that get 40 mpg, not 14, and incentives should be tied to achieving such efficiency. An implicit premise in the example, however, is that an improvement from 12 to 14 mpg is negligible. However, the two mpg improvement is actually a significant one in terms of reduction in gas consumption. A car that gets 12 mpg consumes 833 gallons to cover 10,000 miles (10,000/12); a car that gets 14 mpg consumes 714 gallons (10,000/14). The roughly 120-gallon reduction in fuel used is larger than the reduction achieved by replacing a car that gets 28 mpg with a car that gets 40 mpg over that distance.

It’s not exactly intuitive (especially to a non-mathematically jiggered brain like mine), but essentially fuel efficiency abides by the law of diminishing returns: The greatest savings in terms of gas consumption occur at the guzzler end of the spectrum, where the miles-per-gallon ratio — and the denominator in the fractions above — is a small number.

If relying on linear reasoning about mpg leads us to undervalue small improvements, Larrick and Soll think there’s a relatively simple fix. Let’s invert the numbers. Instead of miles per gallon, “the United States should express fuel efficiency as a ratio of volume of consumption to a unit of distance.” A gallons per mile rating “allows consumers to understand exactly how much gas they are using on a given car trip or in a given year and, with additional information, how much carbon they are releasing. GPM also makes cost savings from reduced gas consumption easier to calculate.”

Which brings us back to the original vehicle fleet survey. When Larrick and Soll gave participants in the same instructions, but in addition to mpg also included gpm data, far more people chose the better answer: Option one. Overall, they found, the percentage choosing the more fuel-efficient option increased from 25 percent in the mpg frame to 64 percent in the gpm frame.

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