Can a new road make traffic worse?
A town builds a new bridge to shorten the commute. Every driver takes whatever route is fastest for them. Everyone's commute goes from 65 minutes to 80.
4,000 drivers commute from Home to Work every morning
Narrow roads get slower the more cars use them. Highways always take 45 minutes.
Half the drivers go over the top, half go around the bottom. Each route is one narrow road and one highway.
The first few drivers try it: narrow road, bridge, narrow road. They skip both highways.
Now both narrow roads carry all 4,000 cars and jam up. The highways sit empty.
Each driver makes the smart choice, and together they make everyone slower. At every step, the bridge really is faster for whoever switches next, so drivers keep switching. But each new car also slows the narrow roads for everyone else. When everyone has switched, the trip takes 80 minutes, and no single driver can do better by going back: the old route would now take 85. This is Braess's paradox, described by mathematician Dietrich Braess in 1968.
What's best for each person isn't always best for the group. Adding an option can make everyone worse off when each person picks it for themselves and the costs land on others.
Where else does everyone's smart choice add up to a worse result for all?
Has this happened on real roads?
Several cities have seen traffic improve after closing a road. In Seoul, traffic around the city sped up after the Cheonggye Expressway was torn down in the early 2000s to restore a stream. In Stuttgart in 1969, conditions didn't improve after new road building until a section of new road was closed again. In New York, closing 42nd Street for Earth Day in 1990 reduced congestion, and later closures around Broadway and Herald Square improved traffic flow.
It doesn't happen every time. Real traffic is messier than this model, and most new roads don't backfire. The paradox shows it can happen, which is why traffic planners model the whole network instead of assuming more road always helps.
See the math
Each narrow road takes 1 minute for every 100 cars on it. Each highway always takes 45 minutes. Before: drivers split 2,000 and 2,000, so each narrow road takes 20 minutes and each route takes 20 + 45 = 65. After: if a share of drivers uses the bridge, each narrow road carries the bridge users plus half of everyone else. With everyone on the bridge, each narrow road carries 4,000 cars: 40 + 0 + 40 = 80 minutes. A driver who goes back to an old route would get 40 + 45 = 85 minutes, so nobody does.
Related exhibits
Sources: The network is the standard textbook example of Braess's paradox (Braess, D., 1968, "Über ein Paradoxon aus der Verkehrsplanung"), with 4,000 drivers. Real-world cases (Seoul's Cheonggye Expressway, Stuttgart 1969, New York's 42nd Street 1990, Broadway and Herald Square 2009) from Wikipedia, "Braess's paradox."