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Frontiers
Creating a Fair World Through Math

December 1996

One piece of cake and two siblings. It may sound like a recipe for a fight, but it doesn't have to be. According to mathematical theory there are ways of dividing resources fairly.

"Philosophers have argued about fairness for thousands of years, what's different now is we have a mathematical structure. That takes it out of ideological debate. There's science here," John Ledyard, head of California Institute of Technology's social science division told the Los Angeles Times.

CalTech's exploration of the issue of fairness through the use of mathematics was helped by an NSF equipment award.

Mathematicians usually do their fairness research based on the "cake-cutting problem." This model says that, in order for two people to share a small cake, the fairest division can be accomplished by having one person cut the cake and the other person choose the first piece.

CalTech researchers take another approach. Using the idea of auctions, participants are given an equal number of tokens to spend. Competitive bidding counteracts the natural tendency to ask for more than you really need, Ledyard told the Times.

Recently, mathematician Alan Taylor and political scientist Steven Brams designed yet another system based on "preference points" which they say can divide almost anything into "envy-free pieces."

In their Adjusted Winner system, each participant receives 100 points which he or she distributes based on personal preferences. The person that spends the most points on an item is awarded that item. Because everyone values things differently, each participant feels he or she received a fair percentage of the distributed items after spending the points.


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