(Originally posted at http://joelnoche.multiply.com/journal/item/78/On-Better-Ways-to-Cut-a-Cake on November 4, 2011 10:04 PM)
In a paper that was published in the December 2006 issue of the Notices of the American Mathematical Society, Steven J. Brams, Michael A. Jones, and Christian Klamler present a 2-person cake-cutting procedure that they call the surplus procedure. They claim that their procedure is better than the well-known cut-and-choose procedure because it satisfies proportional equitability, that is, it gives each person at least half of the cake as he or she values it, and generally more. (In the cut-and-choose procedure, the cutter gets only exactly half of the cake.)
I recently learned that the paper was found to contain some errors. An account of it can be found in this Scribd document, which refers to this Letter to the Editor, which refers to this arXiv paper, which refers to this arXiv paper.