Let Them Halve Cake

Reported March 2007

NEW YORK (Ivanhoe Broadcast News) -- How do you divide a piece of birthday cake so both kids are happy with what they get? Wise men and women have been trying to answer that question since the time of King Solomon, and it's a problem every parent is familiar with.

"I will ask the girls, 'Which one of you would like to cut, and which would like to choose?'" says mother Rachel Fishman Green.

The method is called divide and choose. Works fine for a plain vanilla cake. The cutter slices it right down the center. Chooser gets one half; cutter the other -- all is fair. But what if the dispute is over something more complex, like a country or the house and kids in a divorce? You can't just slice them down the middle.

How do we divide these things? It's all about fairness.

"I think fairness is one of the most important, if not the most important, problem in the world today," Steven Brams, Ph.D., a mathematical political scientist at New York University, tells Ivanhoe.

Dr. Brams carved out a new mathematical formula, called the Surplus Procedure, that promises to make settling disputes a little easier. It works by numerically taking into account the values people place on the different aspects of what's in dispute. Each party first gets at least 50 percent of what they want most. What's left over is then divided proportionally, so both parties get half of what they wanted and then some!

"More than a fair share," Dr. Brams says. "They couldn't have done better. There's no allocation that gives them both more."

He says you may one day be able to solve disputes by downloading the Surplus Procedure right from the Internet. And it's also strategy-proof. A person cannot game the system to get more than their fair share. And that's great news for moms.

Click here to Go Inside This Science or contact:

Steven Brams, Ph.D.
New York University
(212) 998-8510
steven.brams@nyu.edu

American Mathematical Society
Providence, RI 02904-2294
(800) 321-4267
http://www.ams.org

The Mathematical Association of America
Washington, DC 20036-1358
(800) 741-9415
http://www.maa.org

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