Fair Division: From Cake-Cutting to Dispute Resolution
Brams, Steven J.; Taylor, Alan D. 199603 Cambridge University Press，286p.
■Brams, Steven J.; Taylor, Alan D. 199603 Fair Division: From Cake-Cutting to Dispute Resolution，Cambridge University Press，286p. (ペーパーバック版) ISBN-10: 0521556449 ISBN-13: 978-0521556446 4092 ［amazon］
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.
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
9. Fair Division by Auctions
10. Fair Divisions by Elections
‘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.