Cobra Effect · Incentives and systems
Braess’s paradox
Why adding a road can make everyone’s journey slower.
6 cards, read aloud in 2:33, with a test and sources.
Stuttgart, 1969. The city opens a new road, and the traffic gets worse.
Planners had added a link to ease a busy part of the network. Instead the jams grew. When the new stretch was closed again, the traffic flowed. A mathematician had shown how it could happen the year before.
Dietrich Braess had done the sums in 1968.
Imagine a town with two routes from the station to the harbour. Each route has a wide road that always takes 45 minutes, and a narrow road that takes a minute for every 100 cars using it. With 4,000 cars, drivers split evenly and everyone takes 65 minutes.
Now build a shortcut between the two narrow roads.
It is free and instant. Every driver looks at it and thinks, I can take both narrow roads and skip the wide one. So every driver does. Now all 4,000 cars are on both narrow roads, and every journey takes 80 minutes. Fifteen minutes worse, for everyone, because a road was added.
That is Braess’s paradox.
Adding capacity to a network can make it slower for everybody. Nobody is being stupid. Each driver picks the fastest route given what everyone else is doing. That is the trap. The choice that is best for each driver is worst for all of them, and no driver can fix it alone.
Cities have found it the hard way.
Braess published in 1968, in German, and it took decades for traffic planners to take him seriously. Seoul demolished an elevated motorway in 2003 to restore the Cheonggyecheon stream, and reports say the traffic did not get worse. When New York shut 42nd Street for a day in 1990, the papers reported that traffic flowed better without it. Neither case is a controlled experiment. The maths is.
The question for anyone adding a link.
More roads, more servers, more meetings, more channels. Before you add one, ask what every selfish user will do with it once it exists. If they all pile onto it, the shortcut becomes the jam. Sometimes the best thing you can build is a barrier.
Sources
- Braess’s paradox, Wikipedia. The four-road example with the sums, the 1968 paper, the Stuttgart closure and the physical versions built out of springs and strings.
- Selfish Routing and the Price of Anarchy, Tim Roughgarden, 2005. The mathematics of what selfish route choice costs a network, with Braess as the opening act. Technical, but the first chapters are readable.
- Cheonggyecheon, Wikipedia. The Seoul stream, the elevated motorway that covered it, and what happened to the city when the motorway came down.
Nearby ideas
- Second order effects. Every fix has consequences, and those have consequences too.
- The Jevons paradox. Why making something efficient can make us use more of it.
- Brooks’s law. Adding people to a late project makes it later.
- Path dependence. Why early choices stay locked in long after better ones appear.
- The Lindy effect. The longer an idea has lasted, the longer it is likely to last.
- Antifragility. Some things get stronger from knocks, and fail without them.
- The Streisand effect. Trying to hide something is often the best way to spread it.
- The principal-agent problem. When someone acts for you, their own interests quietly steer the work.