Mathematics and politics: strategy, voting, power and proof
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Edition: | 2. ed., 1. corr. printing |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XV, 364 S. graph. Darst. |
| ISBN: | 9780387776439 0387776435 |
Staff View
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| 245 | 1 | 0 | |a Mathematics and politics |b strategy, voting, power and proof |c Alan D. Taylor and Allison M. Pacelli |
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Record in the Search Index
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| adam_text |
Gofíliiíts
Preface
va
1
SOCIAL
CHOICE
1.1.
Introduction
1
1.2.
May's Theorem for Two Alternatives
4
1.3.
Six Examples of Social Choice Procedures
5
1.4.
Five Desirable Properties of Social Choice Procedures
10
1.5.
Positive Results
—
Proofs
13
1.6.
Negative Results
—
Proofs
20
1.7.
A Glimpse of Impossibility
28
1.8.
Approval Voting
31
1.9.
Conclusions
34
Exercises
35
2
YES-NO VOTING
2.1.
Introduction
49
2.2.
Four Examples of Yes-No Voting Systems
50
2.3.
Weighted Voting and the U.N. Security Council
53
x¡¡
CONTENTS
2.4.
Swap Robustness and the Nonweightedness
of the Federal System
56
2.5.
Trade Robustness and the Nonweightedness of the
Canadian System
59
2.6.
Statement of the Characterization Theorem
62
2.7.
Conclusion
63
Exercises
64
■ 3
POLITICAL POWER
3.1.
Introduction
71
3.2.
The Shapley-Shubik Index of Power
73
3.3.
Calculations for the European Economic Community
78
3.4.
The Banzhaf Index of Power
83
3.5.
Two Methods of Computing Banzhaf Power
85
3.6.
The Power of the President
90
3.7.
The Chairs Paradox
98
3.8.
Conclusions
104
Exercises
105
■ 4
CONFLICT
4.1.
Introduction
112
4.2.
Two-By-Two Games
113
4.3.
Dominant Strategies and Nash Equilibria
116
4.4.
Prisoners Dilemma and the Arms Race
117
4.5.
Chicken and the Cuban Missile Crisis
122
4.6.
The Yom Kippur War
126
4.7.
The Theory of Moves
128
4.8.
Conclusions
137
Exercises
137
■ 5
FAIRNESS
5.1.
Introduction
152
5.2.
The Problem of Apportionment
153
5.3.
Divisor Methods of Apportionment
155
Contents xüi
5.4.
A Glimpse of Impossibility
157
5.5.
Dispute Resolution and Fair Division
159
5.6.
An Alternative to Divide-and-Choose
163
5.7.
Adjusted Winner
165
5.8.
Adjusted Winner and the Middle East
171
5.9.
Conclusions
173
Exercises
174
■ 6
ESCALATION
6.1.
Introduction
179
6.2.
The Dollar Auction
180
6.3.
Game-Tree Analyses
181
6.4.
Limitations and Back-ol-the-Envelope Calculations
188
6.5.
Statement of O'Neill
s
Theorem
192
6.6.
Vickrey Auctions
195
6.7.
Conclusions
199
Exercises
200
■ 7
MORE SOCIAL CHOICE
7.1.
Introduction
205
7.2.
Social Welfare Functions
206
7.3.
A Generalization of May's Theorem
209
7.4.
Arrows Impossibility Theorem
211
7.5.
The Gibbard-Satterthwaite Theorem
222
7.6.
Single Peakedness
—
Theorems of Black and Sen
231
7.7.
Conclusions
240
Exercises
240
■ 8
MORE YES-NO VOTING
8.1.
Introduction
247
8.2.
A Magic Square Voting System
248
8.3.
Dimension Theory and the U.S. Federal System
251
xiv CONTENTS
8.4.
Vector-
Weigh ted Voting Systems
255
8.5.
Conclusions
260
Exercises
261
■ 9
MORE POLITICAL POWER
9.1.
Introduction
264
9.2.
The Johnston Index of Power
265
9.3.
The Deegan-Packel Index of Power
271
9.4.
Ordinal Power: Incomparability
275
9.5.
Ordinal Power: Comparability
279
9.6.
A Theorem On Voting Blocs
285
9.7.
Conclusions
288
Exercises
289
■ 10
MORE CONFLICT
10.1.
Introduction
293
10.2.
Models of Deterrence
293
10.3.
A Probabilistic Model of Deterrence
298
10.4.
Two-Person Zero-Sum Games
303
10.5.
Conclusions
309
Exercises
309
■ 11
MORE FAIRNESS
11.1.
Introduction
314
11.2.
Efficiency in Adjusted Winner
315
11.3.
Adjusted Winner and Manipulabilitv
319
11.4.
Fair Division Procedures for Three or More Parties
322
11.5.
Envy-Free Procedures
325
11.6.
Envy-Free Procedures for Four or More Parties
328
11.7.
Another Impossibility Result
330
11.8.
Conclusions
331
Exercises
332
Contents xv
12
MORE ESCALATION
.
12.1.
Introduction
337
12.2.
Statement of the Strong Version of
O'Neills Theorem
337
12.3.
Proof (By Mathematical Induction) of the Strong
Version of O'Neill's Theorem
344
12.4.
Vickrey Auctions as a Generalized
Prisoner's Dilemma
346
12.5.
Conclusions
348
Exercises
349
Attributions
350
References
354
Index
360 |
| any_adam_object | 1 |
| author | Taylor, Alan D. 1947- Pacelli, Allison M. |
| author_GND | (DE-588)114332959 |
| author_facet | Taylor, Alan D. 1947- Pacelli, Allison M. |
| author_role | aut aut |
| author_sort | Taylor, Alan D. 1947- |
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| building | Verbundindex |
| bvnumber | BV036645401 |
| classification_rvk | MB 2520 SK 990 |
| classification_tum | MAT 015f POL 010f MAT 929f MAT 024f |
| ctrlnum | (OCoLC)611119519 (DE-599)BVBBV036645401 |
| discipline | Politologie Mathematik |
| edition | 2. ed., 1. corr. printing |
| format | Book |
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| indexdate | 2024-07-20T10:45:15Z |
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| language | English |
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| physical | XV, 364 S. graph. Darst. |
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| publishDateSearch | 2009 |
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| spelling | Taylor, Alan D. 1947- Verfasser (DE-588)114332959 aut Mathematics and politics strategy, voting, power and proof Alan D. Taylor and Allison M. Pacelli 2. ed., 1. corr. printing New York, NY Springer 2009 XV, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kollektiventscheidung (DE-588)4022393-0 gnd rswk-swf Politik (DE-588)4046514-7 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Politische Wissenschaft (DE-588)4076229-4 gnd rswk-swf Politische Wissenschaft (DE-588)4076229-4 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Spieltheorie (DE-588)4056243-8 s Politik (DE-588)4046514-7 s Kollektiventscheidung (DE-588)4022393-0 s 1\p DE-604 Pacelli, Allison M. Verfasser aut Erscheint auch als Online-Ausgabe 10.1007/978-0-387-77645-3 Erscheint auch als Online-Ausgabe 978-0-387-77645-3 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3044763&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020565048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Taylor, Alan D. 1947- Pacelli, Allison M. Mathematics and politics strategy, voting, power and proof Kollektiventscheidung (DE-588)4022393-0 gnd Politik (DE-588)4046514-7 gnd Spieltheorie (DE-588)4056243-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Politische Wissenschaft (DE-588)4076229-4 gnd |
| subject_GND | (DE-588)4022393-0 (DE-588)4046514-7 (DE-588)4056243-8 (DE-588)4114528-8 (DE-588)4076229-4 |
| title | Mathematics and politics strategy, voting, power and proof |
| title_auth | Mathematics and politics strategy, voting, power and proof |
| title_exact_search | Mathematics and politics strategy, voting, power and proof |
| title_full | Mathematics and politics strategy, voting, power and proof Alan D. Taylor and Allison M. Pacelli |
| title_fullStr | Mathematics and politics strategy, voting, power and proof Alan D. Taylor and Allison M. Pacelli |
| title_full_unstemmed | Mathematics and politics strategy, voting, power and proof Alan D. Taylor and Allison M. Pacelli |
| title_short | Mathematics and politics |
| title_sort | mathematics and politics strategy voting power and proof |
| title_sub | strategy, voting, power and proof |
| topic | Kollektiventscheidung (DE-588)4022393-0 gnd Politik (DE-588)4046514-7 gnd Spieltheorie (DE-588)4056243-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Politische Wissenschaft (DE-588)4076229-4 gnd |
| topic_facet | Kollektiventscheidung Politik Spieltheorie Mathematisches Modell Politische Wissenschaft |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3044763&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020565048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tayloraland mathematicsandpoliticsstrategyvotingpowerandproof AT pacelliallisonm mathematicsandpoliticsstrategyvotingpowerandproof |