The Economics of Splitting a Cab

Leave it to the Wall Street Journal to spend 2000+ words complexifying a a relatively straightforward question: what's the best way to split up a cab-fare when everyone is going in the same direction? We've faced this problem literally dozens of times, and usually end up with one of two situations: the person who gets off last pays for the entire thing (as an act of generosity, figuring that giving a lift to the other person going in the same direction hasn't actually increased his fare), or the two people split the fare (thus avoiding the embarassment of arguing over who has saved more and why.) Of course, economists love to argue. Here are their methods:

1. The trip-leg method: "Before consulting with economists, my sense was that all three passengers should evenly split the first leg of the trip to A's house, because each one needed to go that far anyway. Then B and C should split the leg from A's house to B's, and C should pay for the rest."

2. The proportional-savings method: "every passenger pays an amount proportional to what he would have paid without the savings. Proportional splitting of surplus and debts is a common approach in U.S. law, including bankruptcy cases."

3. The game-theory method: "the Nash bargaining strategy -- an approach based on game theory in which each cab passenger is seen as a party to the deal and is negotiating his best outcome -- would have the passengers split the savings equally, so that A, B and C each gets $2 knocked off his bill. Why share the savings equally? Think of the shared cab ride as a contract being struck to yield savings: Any party could walk away from the deal and kill it, so each should share equally in the fruits of the deal."

4. The game-theory method with coalition proviso: "Glenn Ellison, a professor of economics at the Massachusetts Institute of Technology, pointed out that the bargaining model can get more complicated if individuals can form coalitions and bargain jointly. For example, if B and C traveled together, without A, they could still save $5. So they could argue to A that they should get to split $5 of the $6 total savings, and that only $1 is up for the equal split."

5. The Talmudic method: "To solve the problem, you need to consider all three possible pairs of two riders from the group of three, imagine them haggling over the savings, and come up with an overall solution -- modeled after the Talmud's teaching on the divided estate -- that works for all three negotiations. The math was formalized in a Nobel Prize-winning paper by Robert Aumann and Michael Maschler 20 years ago, and is too involved for our purposes here, but the result is this: If the surplus is less than half the total cost, split the savings equally until one of the riders gets back half his original fare."

Yeah- we know, we didn't understand any of that either! Note to selves: avoid sharing cabs with an economics professors. Or, make sure you take a cab with an econ professor if we do have a strike.

And we wonder what New York City Hack would say. Also, grubby money turns hands dirty, natch.