Sometimes, a birthday celebration goes awry when a pair of partygoers squabble over the cake, both preferring the slice with the cherry or with the thickest icing. That sort of spat caught the attention of mathematicians, inspiring a new idea for making divisions fairly.
The problem hinges on the definition of fair. Steven Brams of New York University and his colleagues propose that a division is fair if, after it's made, each person's assessment of the value of his or her piece is the same. In the December Notices of the American Mathematical Society, the team rep