Ariel Procaccia has thought a lot about how to cut cake over the past 15 years. That’s partly because he has three children. As a group, they’ve celebrated more than two dozen birthdays. So Procaccia knows what it’s like to stand with a knife before a tempting dessert. Sweet layers of cake. Buttercream frosting and chocolate curls. And a crowd of small, eager partygoers who will instantly spot if someone else gets a better slice.
But Procaccia is also a computer scientist at Harvard University in Cambridge, Mass. There, he studies the mathematical rules for dividing stuff up. And dessert is a handy way to think about that. It comes down to a deceptively simple question about fairness: How can you cut a cake to make sure everyone at the party is happy with what they get?
The answers reach far beyond birthday parties. For more than 75 years, mathematicians have puzzled over how to fairly divide resources. Such questions have real-world uses. How can food be divvied up between hungry communities, for example? How should roommates split up rent or chores? How can communities draw boundaries for fair voting districts.
These questions include more than math, too. They must consider what people prefer and other issues. So they become interesting to scientists, economists and legal experts.
But cake works as a stand-in for anything that can be divided, says Steven Brams. He’s a game theorist and political scientist at New York University (NYU) in New York City. Cake-cutting ideas can easily be applied to splitting up land, time or other limited resources.
Recipes for fair cake-cutting
Experts have come up with many rules, called algorithms, for how to cut a cake fairly. (Nearly all focus on rectangular cakes. The related but more recent “pie-cutting” problem addresses circular desserts or pizza.) The simplest rules show how two people can fairly share a cake: One person cuts the cake into two pieces that they believe to be…
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