Technical perspective: An answer to fair division's most enigmatic question
Technical perspective: An answer to fair division's most enigmatic question
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技术视角：公平分配最神秘问题的答案
DOI：
10.1145/3382131
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发表时间：
2020
影响因子：
22.7
通讯作者：
Ariel D. Procaccia
中科院分区：
文献类型：
--
作者：
Ariel D. Procaccia
切蛋糕的问题是著名数学家雨果·斯坦豪斯的创意，他在20世纪40年代初提出并研究了这个问题，当时他正在躲避占领他的祖国波兰的纳粹。施泰因豪斯问的这个问题肯定也是其他许多人也想到的(尽管可能是在更容易获得蛋糕的情况下)：一个人如何在多个人之间公平地分配蛋糕？困难在于蛋糕是不同的，参与者有不同的偏好，所以简单地给他们同等大小的蛋糕是不行的。在概念层面上，斯坦豪斯的主要见解是公平--一个表面上抽象的概念--可以用数学来指定。一个特别的概念已经成为公平的缩影：无嫉妒，这意味着每个参与者都更喜欢自己的那块蛋糕，而不是其他参与者得到的那块蛋糕。
The cake-cutting problem is the brainchild of the noted mathematician Hugo Steinhaus, who formulated and studied it in the early 1940s, even as he was hiding from the Nazis who occupied his native Poland. The question Steinhaus asked is one that must have occurred to many others too (albeit probably under circumstances that afford greater accessibility to cake): How does one fairly divide a cake between multiple people? The difficulty is that the cake is heterogeneous, and the participants have different preferences, so simply giving them pieces of equal size will not do.On a conceptual level, Steinhaus' main insight was that fairness—an ostensibly abstract idea—can be specified mathematically. One particular notion has emerged as the epitome of fairness: envy-freeness, which means that each participant prefers her piece of cake to the piece given to any other participant.