Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division

Theory and Decision 43 (2):203-207 (1997)
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In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal



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