Judgment aggregation: a primer
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[San Rafael, California]
Morgan & Claypool Publishers
[2014]
|
| Schriftenreihe: | Synthesis lectures on artificial intelligence and machine learning
27 |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xvii, 133 Seiten Diagramme |
| ISBN: | 9781627050876 |
Internformat
MARC
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| 035 | |a (OCoLC)1015885266 | ||
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| 100 | 1 | |a Grossi, Davide |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Judgment aggregation |b a primer |c Davide Grossi (University of Liverpool), Gabriella Pigozzi (Université Paris Dauphine) |
| 264 | 1 | |a [San Rafael, California] |b Morgan & Claypool Publishers |c [2014] | |
| 300 | |a xvii, 133 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Synthesis lectures on artificial intelligence and machine learning |v 27 | |
| 700 | 1 | |a Pigozzi, Gabriella |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-030046524 | ||
Datensatz im Suchindex
| _version_ | 1804178075374583808 |
|---|---|
| adam_text | Contents
Preface...................................................................xvi
Acknowledgments...........................................................xviii
1 Logic Meets Social Choice Theory...........................................1
1.1 A Concise History of Social Choice Theory..............................1
1.1.1 The Early History................................................2
1.1.2 Modern Social Choice Theory......................................6
1.2 A New Type of Aggregation..............................................8
1.2.1 From the Doctrinal Paradox to the Discursive Dilemma.............8
1.2.2 Preference Aggregation and Judgment Aggregation.................11
1.3 Further Topics........................................................13
2 Basic Concepts.............................................................15
2.1 Preliminaries.........................................................15
2.1.1 Agendas in Propositional Logic..................................15
2.1.2 Judgment Sets and Profiles......................................17
2.1.3 Aggregation Functions...........................................18
2.1.4 Examples: Aggregation Rules.....................................18
2.2 Agenda Conditions.....................................................22
2.2.1 How Interconnected is an Agenda?................................22
2.2.2 Comparing Agenda Conditions.....................................26
2.3 Aggregation Conditions................................................27
2.3.1 How Should an Aggregation Function Behave? .....................28
2.3.2 On the ‘Meaning’ of the Aggregation Conditions..................30
2.4 Further Topics........................................................32
2.4.1 Abstract Aggregation............................................32
2.4.2 General Logics..................................................33
3 Impossibility................................................................35
3.1 What is the Majority Rule Like?.......................................35
3.1.1 Properties of Propositionwise Majority..........................36
3.1.2 Characterizing Propositionwise Majority.................... . ______37
3.2 An Impossibility Theorem.......................................... ֊ ֊ 37
3.2.1 Winning Coalitions.....................................................
3.2.2 Winning Coalitions as Ultrafilters.......................... 39
3.2.3 Dictators................................................. ..........43
3.2.4 The Theorem................................................ ։ _ 44
3.3 (Ultra)filters, Dictators and Oligarchs................................ 44
3.3.1 Impossibility of Non-Oligarchic Aggregation....................... 45
3.3.2 Proof: from Ultrafilters to Filters..................................45
3.3.3 Impossibility via (Ultra)filters.....................................47
3.4 Further Topics.................................................... ֊ 4g
3.4.1 Other Impossibility Results ....................................... 4g
3.4.2 Infinite Agendas and Infinite Voters............................... 49
3.4.3 Judgment Aggregation vs. Preference Aggregation.................. 52
4 Copingwith Impossibility................................................ ... 53
4.1 Relaxing Universal Domain......................................... ... 54
4.1.1 Unidimensional Alignment.......................................... 54
4.1.2 Value-Restriction ........................................ .... 57
4.2 Relaxing the Output Conditions.............................................58
4.2.1 Abstention.......................................................... 5g
4.2.2 Quota Rules............................................... ... 59
4.3 Relaxing Independence..................................................... 60
4.3.1 The Premise-Based Approach.................................... ... 61
4.3.2 The Sequential Priority Approach ................................. 63
4.3.3 The Distance-Based Rules.......................................... 65
4.4 Further Topics............................................................ 67
4.4.1 More Domain Restrictions............................................67
4.4.2 Dropping Consistency................................................68
4.4.3 Other Distance-Based Rules .........................................69
4.4.4 Judgment Aggregation and Abstract Argumentation ....................70
5 Manipulability..................... 73
5.1 Types of Manipulation..................................................... 73
5.1.1 Agenda Manipulation.................................................74
5.1.2 Vote Manipulation................................................. ,75
5.1.3 Manipulability: Definition and Characterization.....................76
xiii
5.1,4 Sincere and Insincere Manipulation................................77
5.2 Non-Manipulable Aggregation: Impossibility...............................78
5.2.1 Auxiliary Results.................................................79
5.2.2 The Impossibility Theorem.........................................83
5.3 Further Topics: Manipulation Beyond Impossibility Results................83
5.3.1 The Possibility of Non-Manipulable Aggregation....................83
5.3.2 Strategy-Proof Judgment Aggregation...............................84
5.3.3 Complexity as a Safeguard Against Manipulation....................87
Aggregation Rules..............................................................91
6.1 Introduction.............................................................91
6.2 Rules Based on the Majoritarian Judgment Set.............................93
6.3 Rules Based on the Weighted Majoritarian Judgment Set.................. 95
6.4 Rules Based on the Removal or Change of Individual Judgments.............96
6.5 Further Topics...........................................................97
Deliberation ..................................................................99
7.1 Deliberation and Opinion Pooling ........................................99
7.1.1 Probabilistic Judgments...........................................99
7.1.2 A Stochastic Model of Deliberation...............................100
7.1.3 Opinion Pooling and Judgment Aggregation.........................104
7.2 Deliberation as Judgment Transformation.................................105
7.2.1 Deliberation and Voting ....................................... 105
7.2.2 Judgment Transformation Functions................................106
7.2.3 Examples of Transformation Functions.............................107
7.3 Limits of Judgment Transformation.......................................107
7.3.1 Conditions on Transformation Functions...........................108
7.3.2 An Impossibility Result .................................♦......109
7.4 Further Topics and Open Issues .........................................110
Bibliography...................................................................HI
Authors* Biographies..........................................................129
Index.........................................................................131
Judgment aggregation is a mathematical theory of collective decision-making. It concerns the meth-
ods whereby individual opinions about logically interconnected issues of interest can, or cannot, be
aggregated into one collective stance. Aggregation problems have traditionally been of interest for
disciplines like economics and the political sciences, as well as philosophy, where judgment aggrega-
tion itself originates from, but have recently captured the attention of disciplines like computer sci-
ence, artificial intelligence and multi-agent systems. Judgment aggregation has emerged in the last
decade as a unifying paradigm for the formalization and understanding of aggregation problems.
Still, no comprehensive presentation of the theory is available to date. This Synthesis Lecture aims at
filling this gap presenting the key motivations, results, abstractions and techniques underpinning it.
|
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| series2 | Synthesis lectures on artificial intelligence and machine learning |
| spelling | Grossi, Davide Verfasser aut Judgment aggregation a primer Davide Grossi (University of Liverpool), Gabriella Pigozzi (Université Paris Dauphine) [San Rafael, California] Morgan & Claypool Publishers [2014] xvii, 133 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Synthesis lectures on artificial intelligence and machine learning 27 Pigozzi, Gabriella Verfasser aut Erscheint auch als Online-Ausgabe 978-1-62705-088-3 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030046524&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030046524&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Grossi, Davide Pigozzi, Gabriella Judgment aggregation a primer |
| title | Judgment aggregation a primer |
| title_auth | Judgment aggregation a primer |
| title_exact_search | Judgment aggregation a primer |
| title_full | Judgment aggregation a primer Davide Grossi (University of Liverpool), Gabriella Pigozzi (Université Paris Dauphine) |
| title_fullStr | Judgment aggregation a primer Davide Grossi (University of Liverpool), Gabriella Pigozzi (Université Paris Dauphine) |
| title_full_unstemmed | Judgment aggregation a primer Davide Grossi (University of Liverpool), Gabriella Pigozzi (Université Paris Dauphine) |
| title_short | Judgment aggregation |
| title_sort | judgment aggregation a primer |
| title_sub | a primer |
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