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Interesting Decision Rule

Rick Larrick at Duke, writing at his blog GPM, has a neat article on the difference between miles per gallon and gallons per mile, MPG versus GPM.

Rick asks:

"What is the problem with MPG?

Consider a decision between two cars--a current vehicle and a new vehicle that is more efficient.

Which improvement will save the most gas over 10,000 miles?

A) An improvement from 10 to 11 MPG B) An improvement from 16.5 to 20 MPG C) An improvement from 33 to 50 MPG

When I looked this over, quickly I "calculated" that the improvement from 33 to 50 would save the most amount of gas. I understand from Rick's experiments on MGP that most people would do the same.

And we are all wrong.

As Rick explains:

Surprisingly, all save the same amount of gas over 10,000 miles: About 100 gallons

The way to calculate the amount of gas used is to divide distance by MPG. A quick check of the numbers above will confirm the following gas usage over 10,000 miles:

10 MPG = 1000 gallons
11 MPG = 900 gallons
16.5 MPG = 600 gallons
20 MPG = 500 gallons
33 MPG = 300 gallons
50 MPG = 200 gallons

This is pretty clever. It makes the most amount of sense when you are deciding which of your two cars you are going to upgrade - the gas guzzling SUV to a slightly smaller gas guzzler versus your old hybrid to a snazzy new hybrid.

But from a societal point of view, maximizing the total gallons of gas saved, it makes more sense to focus on getting people to gradually get upgrade their SUV's to slightly more efficient SUV's rather than try to and fail to convert them to hybrids.

Here is an example of a fast and frugal rule, which gives us the wrong answer if we were asking for tradeoffs but the right answer if we just wanted to know which car to buy.

The MPG rule would tell us to rank the cars from best mileage to least, but only the GPM rule would tell us how important, in terms of the gallons saved, of how important it was to go from A to B versus C to D.

I wonder if this relationship can be generalized for other rules? What do you think?

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Full post as published by Misleading Advertising Law on June 26, 2008 (boomark / email).