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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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