Think twice / 09
The Shortcut
You have the keys to a new road. Surely another way home can only help?
How to play
- The map opens with twelve drivers sharing two routes. Look at their average journey, then press Open the shortcut. The same drivers choose again.
- Look at which route they now use and how long it takes. Press Try a coordinated plan to see the lowest average the same open roads can achieve if everyone follows an assignment.
- Switch back to individual choices or close the shortcut. Compare the journeys in the table. The short explanation below the map shows why a driver would keep or change their route.
What to notice
Your usual drive is slow. Then a connecting road opens, cutting across the middle of the journey. You try it, save time, and tell everyone. The next morning they try it too. Your decision was sensible when you made it. Their decisions might be sensible as well. That still does not tell you what the whole morning will look like.
In 1968, mathematician Dietrich Braess described a traffic network in which adding a road could make everybody’s journey longer when each driver chose a quickest route. The important distinction is between a pattern nobody wants to leave on their own and a pattern that is best for the group. Those can be different places to end up.
Here, the new connection makes both slow, crowded stretches available in one trip. It looks especially tempting to the first driver. When everyone uses it, those same two stretches carry everyone. Try the coordinated plan: the road can help the group, but only if some people accept routes they could personally improve by switching. A lower average does not mean every driver gets the same benefit.
The road is a small way to look at a wider problem. A new option changes the choices other people make, and those choices change what the option is worth. The room uses an invented twelve-driver network with exact costs, not a forecast for a real city. When something gives each person more choice, what else changes for the people sharing the system?
A little further: Braess, Nagurney and Wakolbinger’s English translation of the original paper explains the distinction between individual route choices and group outcomes. Our road times and twelve indivisible drivers are an adaptation.
One morning, twelve journeys
Shortcut closedEveryone travels from Home to Town. Green roads get slower when more drivers use them. The other roads always take 30 minutes.
- Average journey
- 42 min
- Compared with closed
- Same
- Drivers through shortcut
- 0 of 12
Two routes, shared evenly.
Setting up the roads.
Same drivers. Different arrangements.
| Arrangement | Upper / lower / shortcut | Average trip | Individual trip times |
|---|
Rules & model
The little network
Twelve indivisible drivers travel once from Home to Town. Upper means the upper green road followed by a fixed 30-minute road. Lower means a fixed 30-minute road followed by the lower green road. Opening the one-way connection from the upper junction to the lower junction creates a third route: both green roads and a zero-minute connection. There is no reverse connection or fourth route.
Each green road takes two minutes multiplied by the number of drivers using that road, including the driver whose time is being calculated. A green road with six drivers takes 12 minutes; with twelve it takes 24. The fixed roads remain 30 minutes even when unused. The zero-minute connection is a teaching simplification. These are static journey costs, without traffic-light phases, queues, physical collisions or time-of-day changes.
When drivers choose for themselves
The model checks every allowed assignment: 13 with the connection closed and 91 with it open. It selects a pattern where no single driver can shorten their own journey by switching alone, including their effect on the destination route’s traffic. These settings have one such pattern each. This is an equilibrium calculation, not an animation of drivers learning or a prediction that real people always find it.
Closed, six drivers use each outer route and everyone takes 42 minutes. Open, everyone uses the connection and both green roads, taking 48 minutes. A lone switch to an outer route would take that driver 54 minutes, so it does not help them.
The coordinated plan
The model checks the same assignments for the lowest sum of journey times. Equal totals prefer fewer shortcut users, then a more even outer split, then fewer upper-route users. Closed, the plan is still six and six. Open, it selects five upper, five lower and two shortcut users: ten trips take 44 minutes and two take 28. The average is 41⅓ minutes, rounded to 41.3 on screen. It is not a stable individual-choice pattern: an upper-route driver could switch alone and reduce their own trip from 44 to 30 minutes. Coordination here assumes assigned routes are followed; it does not supply a way to enforce that agreement.
Scope
The comparison keeps all twelve journeys, destinations and cost formulas fixed. It does not claim new roads always hurt, coordinated travel always feels fair, or closing a real road will improve traffic. This adaptation illustrates the difference between an individual incentive and a shared outcome. Every result is calculated locally on a click, with no timer, uploads, saved data or server work.