Mathematics of social choice: voting, compensation, and division
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM, Soc. for Indust. and Appl. Math.
2010
|
| Schriftenreihe: | Other titles in applied mathematics
119 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XI, 245 S. graph. Darst. |
| ISBN: | 9780898716955 |
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| 100 | 1 | |a Börgers, Christoph |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics of social choice |b voting, compensation, and division |c Christoph Börgers |
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| 650 | 4 | |a Voting |x Mathematical models | |
| 650 | 4 | |a Elections |x Mathematical models | |
| 650 | 4 | |a Social choice |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804141080020516864 |
|---|---|
| adam_text | Contents
Preface
ix
I Voting
1
1
Winner Selection
3
Exercises
..................................... 9
2
Rule of the Majority
11
Exercises
..................................... 15
3
Election Spoilers
17
Exercises
..................................... 21
4
The Smith Set
23
Exercises
..................................... 30
5
Smith-Fairness and the No-Weak-Spoiler Criterion
31
Exercises
..................................... 35
6
Schulze s Beatpath Method
37
Exercises
..................................... 41
7
Monotonicity
43
Exercises
..................................... 52
8
Elections with Many or Few Voters
55
Exercises
..................................... 58
9
Irrelevant Comparisons and the Muller-Satterthwaite Theorem
61
Exercises
..................................... 69
10
Strategic Voting and the Gibbard-Satterthwaite Theorem
71
Exercises
..................................... 74
V
VI
Contents
11
Winner Selection versus Ranking
75
Exercises
..................................... 81
12
Irrelevant Alternatives and Arrow s Theorem
83
Exercises
..................................... 90
II Compensation
93
13
Fairness and Envy-Freeness
95
Exercises
.....................................103
14
Pareto-Optimality and Equitability
105
Exercises
.....................................
Ill
15
Equality, Equitability, and Knaster s Procedure
113
Exercises
.....................................117
HI Division
119
16
Envy-Free, Pareto-Optimal, and Equitable Cake Cutting
121
Exercises
.....................................126
17
I Cut, You Choose for Three: Steinhaus s Method
129
Exercises
.....................................131
18
Hall s Marriage Theorem
133
Exercises
.....................................136
19
I Cut, You Choose for More than Three: Kuhn s Method
139
Exercises
.....................................141
20
The Method of Selfridge and Conway
143
Exercises
.....................................145
21
The Geometry of Pareto-Optimal Division between Two People
149
Exercises
.....................................154
22
The Adjusted Winner Method of
Bramš
and Taylor
157
Exercises
.....................................161
23
Conflict Resolution Using the Adjusted Winner Method
165
24
The Effect of Dishonesty on the Adjusted Winner Method
169
Exercises
.....................................172
25
Proportional Allocation
175
Exercises
.....................................179
Contents
vii
26
Dividing a Piecewise Homogeneous Cake among ¿V
> 2
People
181
Exercises
..................................... 191
IV Appendices
193
A Sets
195
Exercises
..................................... 198
В
Logic
199
Exercises
..................................... 203
С
Mathematical Induction
205
Exercises
.....................................209
D
Solutions to Selected Exercises
211
Index
243
How do you select a winner from a field of candidates? How do you rank a field of
candidates? How do you share a divisible resource, like a cake, or an indivisible one, like
a pet or a house? These are the questions addressed in this fun and accessible book
that takes an entertaining look at the choices made by groups of people with different
preferences, needs, and interests.
The text is divided into three parts:
•
The first part examines voting methods for selecting or ranking candidates.
•
A brief second part addresses compensation problems wherein an indivisible item
must be assigned to one of several people who are equally entitled to ownership
of the item, with monetary compensation paid to the others.
•
The third part discusses the problem of sharing a divisible resource among several
people.
Mathematics of Social Choice: Voting, Compensation, and Division can be used by
mathematics majors as well as students whose only mathematical background is
elementary algebra. Material geared toward more sophisticated readers can be skipped
without any loss of continuity. The book includes many elementary and usually simple but
rigorous mathematical proofs appropriate for beginning mathematics majors. Students will
also find appendices with background material on set notation, logic, and mathematical
induction and solutions to many of the homework exercises.
This book is primarily addressed to readers without a high-level mathematical background,
such as college students majoring in subjects other than mathematics and advanced high
school students. However, some material appropriate for more sophisticated readers is
included in small print and makes the text appealing to undergraduate mathematics majors
interested in learning about applications of mathematics in the social sciences. The book
can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem,
Arrow s theorem, and fair division for readers with more of a background in mathematics.
Christoph Borgers
is a Professor in the Department of Mathematics at Tufts University.
For more information about SIAM books, journals,
conferences, memberships, or activities, contact:
5ÍaJ1L.
Society for Industrial and Applied Mathematics
3600
Market Street, 6th Floor
Philadelphia, PA
19104-2688
USA
+ 1-215-382-9800 ·
Fax
+1 -215-386-7999
siam@siam.org
·
www.siam.org
BKOT0119
|
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| dewey-tens | 300 - Social sciences |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
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| spelling | Börgers, Christoph Verfasser aut Mathematics of social choice voting, compensation, and division Christoph Börgers Philadelphia SIAM, Soc. for Indust. and Appl. Math. 2010 XI, 245 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier OT 119 Mathematisches Modell Voting Mathematical models Elections Mathematical models Social choice Mathematical models Wahl (DE-588)4064286-0 gnd rswk-swf Kollektiventscheidung (DE-588)4022393-0 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kollektiventscheidung (DE-588)4022393-0 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Wahl (DE-588)4064286-0 s Other titles in applied mathematics 119 (DE-604)BV023088396 119 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018937387&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018937387&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Börgers, Christoph Mathematics of social choice voting, compensation, and division Other titles in applied mathematics Mathematisches Modell Voting Mathematical models Elections Mathematical models Social choice Mathematical models Wahl (DE-588)4064286-0 gnd Kollektiventscheidung (DE-588)4022393-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4064286-0 (DE-588)4022393-0 (DE-588)4114528-8 |
| title | Mathematics of social choice voting, compensation, and division |
| title_auth | Mathematics of social choice voting, compensation, and division |
| title_exact_search | Mathematics of social choice voting, compensation, and division |
| title_full | Mathematics of social choice voting, compensation, and division Christoph Börgers |
| title_fullStr | Mathematics of social choice voting, compensation, and division Christoph Börgers |
| title_full_unstemmed | Mathematics of social choice voting, compensation, and division Christoph Börgers |
| title_short | Mathematics of social choice |
| title_sort | mathematics of social choice voting compensation and division |
| title_sub | voting, compensation, and division |
| topic | Mathematisches Modell Voting Mathematical models Elections Mathematical models Social choice Mathematical models Wahl (DE-588)4064286-0 gnd Kollektiventscheidung (DE-588)4022393-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematisches Modell Voting Mathematical models Elections Mathematical models Social choice Mathematical models Wahl Kollektiventscheidung |
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