Munich Personal RePEc Archive

Two-person pie-cutting: The fairest cuts

Barbanel, Julius B. and Brams, Steven J. (2010): Two-person pie-cutting: The fairest cuts. Forthcoming in: College Mathematics Journal (2011)


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Barbanel, Brams, and Stromquist (2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two “almosts” removed. The latter, however, requires broadening the definition of a “procedure," which raises philosophical, as opposed to mathematical, issues. An analogous approach for cakes fails because of problems in eliciting truthful preferences.

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