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Technical Perspective: An Answer to Fair Division's Most Enigmatic Question


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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.


 

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