Ten years ago, I graduated college and moved into a cockroach-infested flophouse in the Kensington Market, which back then was one of Toronto’s most decrepit neighborhoods. I rented the house with three other people, but we had a problem: All the rooms were different sizes, and we were all incredibly broke. Who should get the bigger or smaller rooms, and what rent should they pay, respectively? In essence, we faced a classic problem of “fair division” — how to assign values to differently-sized and differently-valued slices of a pie.

The problem with fair-division solutions is that they rarely satisfy everyone; there’s always someone who winds up feeling the acid sting of envy, certain that they were screwed by the others in the negotiation. But as it turns out, there are in fact reasonably solid game-theory ways to solve a fair-division problem to produce that cherished grail of economic hocus-pocus: The “envy-free” result. Back in 1999, mathematician Francis Edward Su wrote a paper for Scientific American explaining his solution and applying it, coincidentally enough, to the problem of apartment-rent division (PDF link).

Then he did something even cooler: He created the Fair Division Calculator, a java app that you can fire up the next time you’re fighting over how to divide a cake. You set the application running, and it enacts his fair-division algorithm. As he describes on his site:

- Players are named A, B, C, …

- The applet will suggest divisions and successively ask players which portion she would prefer.

- After polling several players though various scenarios, the “Suggest Division” button will light up. When it does, press it to see an approximate solution, good up to the displayed precision.

- Press “Continue Iteration” to run the algorithm longer and obtain solutions with better precision.

I am so going to try this out.

(Thanks to Jim Jazwiecki for this one!)