The Fairest Way to Cut Cake | Steven Brams | Big Think

The Fairest Way to Cut Cake

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Steven Brams’ solution to math’s “cake-cutting problem” can be applied to everything from divorce settlements to land disputes in the Middle East. But does he use it on his own birthday?

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Steven Brams:

Steven Brams is a Professor of Politics at New York University. He graduated in 1962 from the Massachusetts Institute of Technology and received his Ph.D. in 1966 from Northwestern. His primary research interests include game theory and its applications, particularly in political science and international relations, and social choice theory, particularly as applied to voting and elections. He is one of the independent discoverers of approval voting and a co-discoverer of the first envy-free solution to the n-person cake cutting problem. Brams was a Guggenheim Fellow from 1986 to 1987 and is a member of the American Association for Advancement of Science.

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TRANSCRIPT:

Question: How can your work on fair division theory be applied to political problems?

Steven Brams: Well we actually did apply one of our procedures to the 1978 Camp David Agreement between Israel and Egypt, which eventuated in a peace treaty in 1979. And there were several major issues dividing Israel and Egypt; the return of the Sinai after the ’73 war, which had been captured in the ’67 war for Israel, was recognitioned, diplomatic recognition by the Egyptians. And there were several other issues. And we assessed how important winning on these issues, getting one’s way, was to Israel was on the one hand and Egypt on the other. And we had given these attributions of importance using the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement which took many months to negotiate; actually many years. And we think it would have been a much more efficient way to use the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement, which took many months to negotiate, actually many years, and we think it would have been a much more efficient way to use this procedure and have countries indicate their interests using the procedure and then the procedure, the algorithm, would say who wins on what issues.

And it also can be used in more mundane circumstances, in dividing the marital property in a divorce. Again, you indicate how important it is to get the car, the house, the boat, the children, and so on, and it tells who gets what. And what we’ve found using these procedures is that most disputants can get between two-third and three-quarters of what they want because they want different things.

So, if you use an algorithm that does things fairly, makes the division what we call “envy free” so you don’t envy what the other person got because you got at least as much, it makes it equitable so that you both get the same amount, about 50%, that because the parties want often different things, they both can win. So, we actually call this a win-win solution. But we give more than that, an algorithm for making this division. So that’s some of the work that we’ve done on fair division.

And then we’ve done more theoretical work. This is work primarily with Allen Taylor, the mathematician at Union College. We came up with an algorithm for cutting a cake. Not just dividing separate goods like the house, the car, the boat, and so on. But what if the cake is something divisible, like land. How do you divide the land so that it satisfies these fairness properties and we came up with a cake cutting algorithm that basically generalizes the procedure everybody knows; I cut, you choose. That’s for two people. One person cuts 50/50 in terms of his preferences, and the other person will chose one half or the other. But her preferences are likely to be different from his preferences. So, she’s going to see one piece is worth more than 50%, but he, the cutter, has protected himself by dividing it 50/50. So I think we are all familiar with that. But how do you extend that to three persons, or four persons?

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