This article was taken from the August 2014 issue of Wired magazine. Be the first to read Wired's articles in print before they're posted online, and get your hands on loads of additional content by <span class="s1">subscribing online.
George Stigler, a 1982 Nobelist in economics, used to say: "If you never miss the plane, you're spending too much time in airports." That's counter-intuitive, especially if you've missed a flight recently. When I'm stuck in Chicago's O'Hare airport eating a cruddy chicken Caesar wrap, I seldom find myself applauding my good economic sense. But as weird as Stigler's slogan sounds, a simple mathematical computation shows it's correct -- at least for frequent flyers. To simplify matters, we can consider three choices:
Option 1: Arrive two hours before flight, miss flight two per cent of the time.
Option 2: Arrive 90 mins before flight, miss flight five per cent of the time.
Option 3: Arrive an hour before flight, miss flight 15 per cent of the time.
Here we see the basic trade-off. Option 1 offers you the most certainty of making your flight, but wastes the most of your time.
Option 3, however, is stingy with your airport time, but carries a risk of leaving you stranded. The standard mathematical means of negotiating such a trade-off is the doctrine of expected utility.
In order to compare time wasted and flights missed, we have to denominate both in the same currency: the unit of this is the util.
Say an hour of your time is worth one util; then arriving two hours before your flight departs costs you two utils. Missing a plane is worse than wasting an hour. If you think it's worth six hours of your time, you can think of a missed plane as costing you six utils.
But what's relevant here isn't the cost of missing your flight, but the cost of a slim chance of missing your flight -- not the same thing. The expected utility of a two per cent chance of missing the flight is simply two per cent of the utility of missing the flight: (0.02) x (-6) or -0.12. You might think of it as the cost of that chance on average; if you accept a two per cent chance of missing the plane every time you fly, and you fly 100 times, you're going to miss about two flights, a cost of 12 utils per 100 flights, or 0.12 per flight:
Option 1:-2 + 2% × (-6) = −2.1 utils
Option 2:-1.5 + 5% × (-6) = −1.8 utils
Option 3:-1 + 15% × (-6) = −1.9 utils
Option 2 costs you the least utility, even though it comes with a non-trivial chance of missing your flight. Yes, getting stuck in the airport is unpleasant -- but is it so unpleasant that it's worth spending extra time at the terminal in order to make the small chance of missing your plane even smaller?
Maybe you say yes. Maybe you hate missing your plane, and that missed flight costs you 20 utils, not six. Then the previous computation changes, and option 1 becomes the preferred choice. No matter what, though, if you have an absolute zero chance of missing your flight, your strategy is more conservative than the optimal 1.
Just as Stigler says, you should save your utils and miss more planes.
Stigler's argument is a handy tool for all sorts of problems.
You don't go a month without reading about a public-sector worker who gamed the system to get a huge pay-off, or a supplier who got away with inflated prices, or a city agency which has outlived its function but persists at the public expense thanks to inertia and powerful patrons.
Why do we allow this? Simple -- eliminating waste has a cost, just as getting to the airport early has a cost. Enforcement and vigilance are worthy goals, but eliminating all waste carries a cost that outweighs the benefit. If we're going to count utils, we shouldn't be asking: "Why are we wasting the taxpayer's money?" but: "What's the right amount of money to be wasting?" To paraphrase Stigler: if your government isn't wasteful, you're spending too much time fighting government waste.
Jordan Ellenburg is a professor of mathematics at the University of Wisconsin. He wrote How Not To Be Wrong.
This article was originally published by WIRED UK
