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There's an open textbook (David Lippman's Math in Society -- "a survey of mathematics for the liberal arts major") which covers several topics like this. The chapter on fair division is bite-sized, so you can read it without investing a lot of time.

The book's page is

http://www.opentextbookstore.com/mathinsociety/

from whence you can download the entire book or just the fair division chapter. The method discussed in the post and a separate method discussed in a comment are both covered by this book.

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