Fair Division: From Cake-Cutting to Dispute Resolution

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Cambridge University Press, Feb 23, 1996 - Business & Economics - 272 pages
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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.
 

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Contents

Proportionality for n 2
6
12 Divideandchoose and applications
8
13 Filterandchoose and applications
12
14 The role of information
16
15 Austins movingknife procedure and applications
22
Proportionality for n 2 the divisible case
30
22 The SteinhausKuhn lonedivider procedure
31
23 The BanachKnaster lastdiminisher procedure
35
67 A fourperson movingknife procedure
126
Envyfree procedures for arbitrary n
129
72 Two approximate procedures
130
73 J An infinite procedure
133
74 A finite procedure
138
75 Applying the trimming procedure to indivisible goods
143
76 Efficiency entitlements and chores
148
Appendix
156

24 The DubinsSpanier movingknife procedure
36
25 Applications of lastdiminisher and its movingknife version
38
26 The Fink lonechooser procedure
40
27 Woodalls and Austins extensions of Finks procedure
41
28 Efficiency entitlements and chores
44
Proportionality for n 2 the indivisible case
51
32 Knasters procedure of sealed bids
52
33 Lucas method of markers
57
34 Efficiency and entitlements
62
Envyfreeness and equitability for n 2
65
42 Bargaining and fair division
66
43 The AdjustedWinner AW procedure
68
44 The ProportionalAllocation PA procedure
75
45 The combined procedure
78
46 Three or more players
80
47 Conclusions
83
Appendix
85
Applications of the pointallocation procedures
95
53 A hypothetical divorce settlement
98
54 A real divorce settlement
102
55 AW versus Knasters procedure
108
56 Conclusions
113
Envyfree procedures for n 3 and n 4
115
62 The SelfridgeConway discrete procedure
116
63 The Stromquist movingknife procedure
120
64 The LevmoreCook movingknife procedure
122
65 The Webb movingknife procedure
124
66 Two other movingknife procedures for n 3
125
Dividethedollar
158
a reasonable payoff scheme
160
adding a second stage
163
combining DD1 and DD2
168
85 The solutions with entitlements
170
86 Conclusions
173
Appendix
174
Fair division by auctions
178
92 Twostage auctions
181
the privatevalue case
183
the winners curse
188
the commonvalue case
191
96 Conclusions
198
Appendix
201
Fair division by elections
204
102 The Hare system of single transferable vote STV
206
103 The Borda count
209
104 Cumulative voting
212
105 Additionalmember systems
213
106 Controlled roundings
216
the search may be futile
219
108 Constrained approval voting CAV
225
109 Conclusions
228
Conclusions
231
Glossary
237
Bibliography
248
Index
264
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About the author (1996)

Steven J. Brams is professor of politics at New York University.

Alan D. Taylor is Marie Louise Bailey Professor of Mathematics at Union College.

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