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Last diminisher
The last diminisher procedure is a procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and ''n'' partners with different preferences over different parts of the cake. It allows the ''n'' people to achieve a proportional division, i.e., divide the cake among them such that person receives a piece with a value of at least 1/''n'' of the total value according to his own subjective valuation. For example, if Alice values the entire cake as $100 and there are 5 partners then Alice can receive a piece that she values as at least $20, regardless of what the other partners think or do.
== History ==
During world war II, the Polish-Jewish mathematician Hugo Steinhaus, who was hiding from the Nazis, occupied himself with the question of how to divide resources fairly. Inspired by the Divide and choose procedure for dividing a cake between two brothers, he asked his students, Stefan Banach and Bronisław Knaster, to find a procedure that can work for any number of people, and published their solution.
This publication has initiated a new research topic which is now studied by many researchers in different disciplines; see fair division.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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