## Geometric Perspectives on Fair Division |

**Julius Barbanel**

Union College

January 24, 2012

5 pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:45

Suppose that you and I are given a cake that we wish to divide between the two of us. We may value pieces of cake differently. For example, maybe I like the chocolate filling best, but you like the icing best, so a piece of cake that I value as half the cake, you might value as one third of the cake. What would constitute a “good” division of the cake? We shall consider two sorts of criteria, namely “fairness” and “efficiency.” Fairness involves such questions as “Did I get at least half?” or “Did I get at least as much as you?” Efficiency involves questions such as “Is this the best way to divide the cake or is there a way to divide the cake that would make each of us happier?” We will see that there are interesting mathematical ideas and revealing geometric pictures associated with these issues. We will also consider what happens when we wish to divide the cake among more than two people.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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