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Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure Brams, Steven J. Jones, Michael A. Klamler, Christian Cake-cutting proportionality envy-freeness efficiency strategy-proofness 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Steven J. Brams and Michael A. Jones and Christian Klamler 2007 Is Part Of Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.07261.6 urn:nbn:de:0030-drops-12211 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.6 eng https://creativecommons.org/licenses/by/4.0/legalcode