Collective preference and choice:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 255 S. graph. Darst. |
| ISBN: | 9780521897259 9780521722131 |
Staff View
MARC
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| 245 | 1 | 0 | |a Collective preference and choice |c Shmuel Nitzan |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XVII, 255 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Group decision making / Mathematical models | |
| 650 | 4 | |a Social choice / Mathematical models | |
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| 650 | 4 | |a Group decision making |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804140868915953664 |
|---|---|
| adam_text | Contents
List of figures page
xii
Preface
xiii
Acknowledgments
xvi
Parti: Introduction
1
1
The reason for the problems
3
1.1
Exercises
6
1.2
Summary
7
2
Brief overview of the problems
9
2.1
Exercises
15
2.2
Summary
16
3
The relationship between preferences and choice
19
3.1
Preference-driven choice
20
3.2
Rationalizable choice
23
3.3
Exercises
26
3.4
Summary
30
Paît
II: Different Prefereaees
33
4
Do social preferences exist? Arrow s and Sen s
impossibility theorems
35
4.
1
The social choice model
36
4.2
Arrow impossibility theorem
39
4.3
The
Paretian
liberał
paradox
50
4.4
Exercises
51
4.5
Summary
58
Vlil
CONTENTS
5
The desirable decision rale: axiomatization
60
5.1
Dichotomous choice and the simple majority rule
60
5.2
The
Borda
rule
64
5.3
Exercises
68
5.4
Summary
74
6
Rule selection based on compromise with the
unanimity criterion
76
6.1
The unanimity criterion
76
6.2
Distance between preferences
78
6.3
The metric compromise with the unanimity criterion
80
6.3.1
The example of the
Borda
rule
83
6.3.2
The example of the plurality rule
84
6.4
Extensions
84
6.5
Exercises
85
6.6
Summary
91
7
Paradoxes of voting
93
7.1
Condorcet s voting paradox
94
7.2
Condorcet s inconsistency
97
7.3
Violation of the Pareto criterion
99
7.4
Violation of consistency
100
7.5
Violation of consistency in contraction and in
expansion
102
7.6
Inverted order paradox
103
7.7
The winner-turns-Ioser paradox
104
7.8
The no-show paradox
105
7.9
Exercises
106
7.10
Summary
114
8
Majority tyranny
117
8.1
Scoring rules
118
8.2
Majority decisiveness
120
CONTENTS
IX
8.3 Resolution
of the problem of majority tyranny under
sincere voting
123
8.4
Resolution of the problem of majority tyranny under
insincere voting
124
8.5
Erosion in the majority principle vs. majority
tyranny
126
8.6
The golden scoring rule
127
8.7
Appendix
131
8.8
Exercises
132
8.9
Summary
142
9
The problem of inefficient provision of public
goods
146
9.1
The collective decision rule and inefficient provision
of a public good
147
9.2
Voting
148
9.2.1
The simple majority rule
151
9.2.2
The dictatorial rale
154
9.2.3
The
Borda rale
154
9.2.4
The unanimity rule
154
9.3
Voluntary provision of the public good
155
9.4
Appendix
158
9.5
Exercises
158
9.6
Summary
173
10
Do individuals reveal their true preferences?
176
10.1
Non-truthful revelation of preferences
177
10.2
The impossibility theorem of Gibbard-Satterthwaite
180
10.3
Revelation of preferences and the efficient provision of
a public good
-
the dichotomous case
186
1Ö.3.1
The Groves-Clarke revelation mechanism
188
10.4
Exercises
193
10.5
Summary
197
X
CONTENTS
Part III: Identical Preferences,
Diîferent Decisional
Skills
199
11
Which rule is better: the expert rule or the simple
majority rule? Decisional errors in dichotomous
choice and Condorcet s jury theorem
201
11.1
The expert rule vs. the simple majority rule: the case
of three identical decision makers
202
11.2
The expert rule vs. the simple majority rule: the case
of three decision makers with unknown decisional
skills
203
11.3
Condorcet s jury theorem
205
11.4
Extensions of Condorcet s jury theorem
207
11.4.1
The superiority of the simple majority rule
when the decisional skills of the
л
voters are
unknown
207
11.4.2
The superiority of the simple majority rule
when the decisional skills of the
π
voters are
different
207
11.5
Is Condorcet s theorem valid when decisional skills
are determined endogenously?
208
11.5.1
The extended model: identical endogenous
decisional skills
209
11.5.2
Centrally determined decisional skills
209
11.6
Is Condorcet s theorem valid when individual
decisions are insincere?
211
11.6.1
Strategic considerations and insincere voting
212
11.6.2
Condorcet s theorem and strategic
considerations
213
11.7
Exercises
218
11.
8
Summary
224
12
The optimal decision rule under uncertain
dichotomous choice
227
CONTENTS Xl
12.1 Dichotomous
decision making
-
the model
227
12.2
The optimal decision rale
230
12.2.1
Qualified weighted majority rale
232
12.2.2
Qualified majority rule
233
12.3
The optimal decision rule in the symmetric case
235
12.3.1
Weighted majority rule
235
12.3.2
Simple majority rale
235
12.3.3
The expert rule
235
12.4
Extensions
236
12.4.1
Dependence of decisional skills on the state
of nature
236
12.4.2
Dependent decisions
236
12.4.3
The number of decision makers is not fixed
236
12.4.4
Decisional skills are not fixed
237
12.4.5
Partial information on decisional skills
237
12.4.6
Sequential decision
238
12.4.7
More than two alternatives
238
12.5
Exercises
238
12.6
Summary
243
Bibliography
246
Author index
251
Subject index
253
Figures
1.1
The relationship between preferences and choice page
7
2.1
The classification of the problems and their
disciplinary relevance
17
9.1
The optimal quantity of the public good for
individual
і
149
9.2
The optimal quantity of the public good for
individuals
1,2
and
3 150
9.3
The efficient and equilibrium quantities of the
public good
157
9.4
Diagrammatic exposition of the answer to
Question
9.5
(over-provision of the public good)
163
9.5
Diagrammatic exposition of the answer to
Question
9.7
(under-provision of the public good)
166
|
| any_adam_object | 1 |
| author | Nitsan, Shemuʾel 1948- |
| author_GND | (DE-588)111268532 |
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| dewey-ones | 302 - Social interaction |
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| dewey-search | 302.3 |
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| discipline | Soziologie Wirtschaftswissenschaften |
| edition | 1. publ. |
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| language | English |
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| physical | XVII, 255 S. graph. Darst. |
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| spelling | Nitsan, Shemuʾel 1948- Verfasser (DE-588)111268532 aut Collective preference and choice Shmuel Nitzan 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XVII, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Group decision making / Mathematical models Social choice / Mathematical models Mathematisches Modell Group decision making Mathematical models Social choice Mathematical models 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 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018750508&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nitsan, Shemuʾel 1948- Collective preference and choice Group decision making / Mathematical models Social choice / Mathematical models Mathematisches Modell Group decision making Mathematical models Social choice Mathematical models Kollektiventscheidung (DE-588)4022393-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4022393-0 (DE-588)4114528-8 |
| title | Collective preference and choice |
| title_auth | Collective preference and choice |
| title_exact_search | Collective preference and choice |
| title_full | Collective preference and choice Shmuel Nitzan |
| title_fullStr | Collective preference and choice Shmuel Nitzan |
| title_full_unstemmed | Collective preference and choice Shmuel Nitzan |
| title_short | Collective preference and choice |
| title_sort | collective preference and choice |
| topic | Group decision making / Mathematical models Social choice / Mathematical models Mathematisches Modell Group decision making Mathematical models Social choice Mathematical models Kollektiventscheidung (DE-588)4022393-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Group decision making / Mathematical models Social choice / Mathematical models Mathematisches Modell Group decision making Mathematical models Social choice Mathematical models Kollektiventscheidung |
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