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.
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.
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.