Divide-and-conquer: A proportional, minimal-envy cake-cutting algorithm
We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation--as these terms are used in the fair-division literature--one, divide-and-conquer (D&C), minimizes the maximum number of players that any single player can envy. It works by asking n ≥ 2 players successively to place marks on a cake--valued along a line--that divide it into equal halves (when n is even) or nearly equal halves (when n is odd), then halves of these halves, and so on. Among other properties, D&C ensures players of at least 1/n shares, as they each value the cake, if and only if they are truthful. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed.
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- Barbanel, Julius B. & Brams, Steven J., 2010. "Two-person pie-cutting: The fairest cuts," MPRA Paper 22703, University Library of Munich, Germany.
- Steven Brams & Michael Jones & Christian Klamler, 2008. "Proportional pie-cutting," International Journal of Game Theory, Springer, vol. 36(3), pages 353-367, March.
- Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
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