Fair division

Name: Fair division
ISBN: 9780521556446

Steven J. Brams · 1996

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or "bads" like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, "I cut, you choose," the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular, they focus on procedures which provide "envy-free" allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

Business & Management Mathematics

Open Library Amazon

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What Hacker News says

rbcgerardApr 2014
Found this fairly annoying - only because I went through this exercise recently, and now all the research i did has been made redundant.
I bought this book to help me out:
http://www.amazon.com/Fair-Division-Cake-Cutting-Dispute-Res...
It's a great book, though it didn't include exactly what i was looking for regarding this subject. I emailed one of the authors and he kindly pointed me in the direction of Sperner's Lemma:
http://www.inet.tu-berlin.de/fileadmin/fg234_tdc1-s11/FDS_SS...
and I was able to find:
http://www.math.hmc.edu/~su/fairdivision/calc/
Which is the same sort of calculator...
Anyway same end result...though i highly recommend the book above if anyone is interested in the subject.
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cschmidtApr 2013
Oh, fun! This is sometimes called an envy free division. A nice book on this topic is
Fair Division: From Cake-Cutting to Dispute Resolution www.amazon.com/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449
Stable matchings are a related problem (sometimes called the stable marriage problem), where you want to match men and women to "marry", such that no two couples would want to swap partners. It is applied in real life to matching medical interns to hospital placements. One of my all time favorite technical books* is on this subject:
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis http://www.amazon.com/Two-Sided-Matching-Game-Theoretic-Econ...
(* yes, that may make me weird)
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