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.
• Analysis of procedures for the fair division of goods, and the resolution of disputes; theory plus numerous examples and applications • Written by a political scientist and mathematician in an accessible way, with most mathematics in appendices rather than main text • Several procedures are entirely new, including the solution to a 50-year-old mathematical problem - the envy-free division of a cake among any number of people
Contents
Introduction; 1. Proportionality for n=2; 2. Proportionality for n>2: the divisible case; 3. Proportionality for n>2: the indivisible case; 4. Envy-freeness and equitability for n=2; 5. Applications for the point-allocation procedures; 6. Envy-free procedures for n=3 and n=4; 7. Envy-free procedures for arbitrary n; 8. Divide-the-dollar; 9. Fair division by auctions; 10. Fair divisions by elections; 11. Conclusions; Glossary; Bibliography; Index.
Reviews
‘In this remarkable book, Brams and Taylor bring to the attention of social scientists a literature thus far confined to puzzle-solving and other mathematical magazines. The book’s emphasis on Envy-Freeness will please economists; numerous practical mechanisms for negotiation will appeal to the political scientist and the lawyer; finally, Brams and Taylor’s original fair division procedures are of interest to all researchers.’ Herve Moulin, Duke University
‘… explains everything a layperson might need to know about fair division … lawyers should love the book’. Discover
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