Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure

Authors Steven J. Brams, Michael A. Jones, Christian Klamler

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Steven J. Brams
Michael A. Jones
Christian Klamler

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Steven J. Brams, Michael A. Jones, and Christian Klamler. Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


Properties of discrete cake-cutting procedures that use a minimal number of cuts (n-1 if there are n players) are analyzed. None is always envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ≥ 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, then halves of these halves, and so on. Among other properties, D&C (i) ensures players of more than 1/n shares if their marks are different and (ii) is strategyproof for risk-averse players. 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.
  • Cake-cutting
  • proportionality
  • envy-freeness
  • efficiency
  • strategy-proofness


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