Some mathematicians study pi, but for Julius B. Barbanel, the challenge is pie – and it’s no cut-and-dry matter.
“Cutting a Pie is Not a Piece of Cake” according to a recent headline in Science News for a story that describes research by Barbanel, professor of Mathematics, and New York University political scientist Steven J. Brams.
The two collaborators, who have turned their skills toward cake-cutting in the past, are now getting a taste for the intricacies of cutting a decorated pie. Both desserts work as a metaphor for dividing things, be they land borders or homes in settlement disputes.
Julie J. Rehmeyer’s article highlights the professors’ work in detail. The two wanted to find a way to slice a pie that is envy-free, equitable and efficient.
Their original paper can be found at http://www.nyu.edu/gsas/dept/politics/faculty/brams/pie-cutting.pdf.
Barbanel is quick to point out that while Science News focuses on his research, there are actually three Union faculty members who’ve done work in this field. The other two are Alan Taylor, the Marie Louise Bailey Professor of Mathematics, and William Zwicker, the William D. Williams Professor of Mathematics.
“Alan was the first here to get interested, and he introduced Bill and me to the area,” Barbanel said. “I’ve enjoyed working on this and have a book that came out on fair division last year (‘The Geometry of Efficient Fair Division,’ Cambridge University Press,featuring an introduction by Taylor). Most of my work is different from, but related to, that described in the article. Most of it involves what mathematicians would call abstract existence results. By contrast, much of Alan’s work is directly applicable and is accessible to non-specialists.”
Taylor and NYU’s Brams have worked on fair division problems in the context of divorce settlements and inheritance disputes. The two are the authors of “The Win-Win Solution: Guaranteeing Fair Shares to Everybody.” The book espouses a procedure called “adjusted winner” as a solution for fairly dividing assets between people.