Quantitative sociodynamics: stochastic methods and models of social interaction processes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1995
|
| Series: | [Theory and decision library / B]
31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 335 S. graph. Darst. |
| ISBN: | 0792331923 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Preface xiii
List of Figures xv
List of Tables xix
Introduction and Summary 1
Quantitative Models in the Social Sciences 2
The Logistic Model 2
Diffusion Models 3
The Gravity Model 3
The Game Theory 3
Decision Models 5
How to Describe Social Processes in a Mathematical Way 7
Statistical Physics and Stochastic Methods 7
Non Linear Dynamics 13
I Stochastic Methods and Non Linear Dynamics 17
Overview 19
1 Master Equation in State Space 21
1.1 Introduction 21
1.2 Derivation 23
1.2.1 Derivation from the Markov Property 24
1.2.2 External Influences (Disturbances) 20
V
vj Table of Contents
1.2.3 Internal Fluctuations 26
1.2.4 Derivation from Quantum Mechanics 29
1.3 Properties 36
1.3.1 Normalization 36
1.3.2 Non Negativity 36
1.3.3 The Liouville Representation 37
1.3.4 Eigenvalues 38
1.3.5 Convergence to the Stationary Solution 39
1.4 Solution Methods 40
1.4.1 Stationary Solution and Detailed Balance 40
1.4.2 Time Dependent Solution . 42
1.4.3 Path Integral Solution 43
1.5 Mean Value and Covariance Equations 50
2 BoLTZMANN Like Equations 53
2.1 Introduction 53
2.2 Derivation 54
2.3 Subdivision into Several Types of Subystems 57
2.4 Properties 58
2.4.1 Non Negativity and Normalization 58
2.4.2 The Gaskinetic Boltzmann Equation 58
2.4.3 The // Theorem for the Gaskinetic Boltzmann Equation 61
2.4.4 Solution of the Gaskinetic BOLTZMANN Equation .... 63
2.5 Comparison of Spontaneous Transitions and Direct Interactions 64
2.5.1 Transitions Induced by Interactions 65
2.5.2 Exponential Function und Logistic Equation 65
2.5.3 Stationary and Oscillatory Solutions 67
Table of Contents vii
3 Master Equation in Configuration Space 69
3.1 Introduction 69
3.2 Transitions in Configuration Space 70
3.2.1 Spontaneous Transitions 70
3.2.2 Pair Interactions 71
3.3 Mean Value and Covariance Equations 72
3.4 Corrections and Higher Order Interactions 76
3.5 Indirect Interactions and Mean Field Approaches 80
3.6 Comparison of Direct and Indirect Interactions 81
3.6.1 Differences Concerning the Covariance Equations .... 81
3.6.2 Differences Concerning the Mean Value Equations ... 82
4 The Fokker Planck Equation 83
4.1 Introduction 83
4.2 Derivation 83
4.3 Properties 87
4.3.1 The Continuity Equation 87
4.3.2 Normalization 87
4.3.3 The Liouville Representation 88
4.3.4 Non Negativity 89
4.3.5 Eigenvalues 89
4.3.6 Convergence to the Stationary Solution 89
4.4 Solution Methods 90
4.4.1 Stationary Solution 90
4.4.2 Path Integral Solution 91
4.4.3 Interrelation with the SchrÖdinger Equation 92
4.5 Mean Value and Covariance Equations 93
4.5.1 Interpretation of the Jump Moments 94
4.6 Boltzmann Fokker Planck Equations 95
4.6.1 Self Consistent Solution 99
vjii Table of Contents
5 Langevin Equations and Non Linear Dynamics 103
5.1 Introduction 103
5.2 Derivation 105
5.3 Escape Time 109
5.4 Phase Transitions, Liapunov Exponents and Critical Phenomenalll
5.5 Routes to Chaos 113
5.5.1 Ruelle Takens Newhouse Scenario and Liapunov
Exponents 115
5.5.2 Period Doubling Scenario and Power Spectra 116
II Quantitative Models of Social Processes 119
Overview 121
6 Problems and Terminology 123
6.1 Terms 123
6.1.1 System and Subsystems 123
6.1.2 State 123
6.1.3 Subpopulation 123
6.1.4 Socioconfiguration 126
6.1.5 Interaction 126
6.2 Problems with Modelling Social Processes 127
6.2.1 Complexity , 127
6.2.2 Individuality 129
6.2.3 Stochasticity and Disturbances 130
6.2.4 Decisions and Freedom of Decision Making 130
6.2.5 Experimental Problems 133
6.2.6 Measurement of Behaviours 133
6.3 Summary 135
Table of Contents ix
7 Decision Theoretical Specification of the Transition Rates 137
7.1 Introduction 137
7.2 Derivation 138
7.2.1 The Multinomial Logit Modell 139
7.2.2 Entropy Maximization 141
7.2.3 Fechner s Law 142
7.2.4 Utility and Distance Function 143
7.3 Pair Interaction Rates 146
7.3.1 Special Applications in the Social Sciences 154
7.4 Properties of the Utility Approach 155
7.4.1 Stationary Distribution 155
7.4.2 Contributions to the Utility Function 157
8 Opinion Formation Models 159
8.1 Introduction 159
8.2 Indirect Interactions 161
8.2.1 A Period Doubling Route to Chaos 163
8.2.2 A Ruelle Takens Newhouse Route to Chaos .... 163
8.3 Direct Pair Interactions 164
8.3.1 Kinds of Pair Interactions 165
8.3.2 Oscillations 169
8.3.3 Influence of the Interaction Frequencies 173
8.3.4 Period Doubling Scenarios and Chaos 180
8.4 Generalizations 195
8.5 Spatial Spreading of Opinions 196
8.5.1 Opinion Spreading by Diffusion 196
8.5.2 Opinion Spreading by Telecommunication 198
X Table of Contents
9 Social Fields and Social Forces 203
9.1 Introduction ¦ 203
9.2 Derivation 204
9.3 The Social Force Model 207
9.3.1 Comparison with Lewin s Social Field Theory 212
9.4 Computer Simulations 214
9.4.1 Imitative Processes 217
9.4.2 Avoidance Processes 223
10 Evolutionary Game Theory 227
10.1 Introduction 227
10.2 Derivation of the Game Dynamical Equations 228
10.2.1 Payoff Matrix and Expected Success 228
10.2.2 Customary Derivation 228
10.2.3 Fields of Application 229
10.2.4 Derivation from the BoLTZMANN Like Equations .... 230
10.3 Properties of Game Dynamical Equations 232
10.3.1 Non Negativity and Normalization 233
10.3.2 Formal Solution 233
10.3.3 Increase of the Average Expected Success in Symmetrical
Games 234
10.3.4 Invariant of Motion for Antisymmetrical Games 235
10.3.5 Interrelation with the Lotka Volterra Equations . . 236
10.3.6 Limit Cycles and Chaos 238
10.4 Stochastic Version of the Game Dynamical Equations 239
10.4.1 Self Organization of Behavioural Conventions for the
Case of Two Equivalent Competing Strategies 242
Table of Contents xi
11 Determination of the Model Parameters from Empirical Data255
11.1 Introduction 255
11.2 The Case of Complete Data 255
11.3 The Case of Incomplete Data 258
11.3.1 Parameter Estimation 262
11.3.2 Model Reduction 268
11.4 Migration in West Germany 269
11.4.1 First Model Reduction 272
11.4.2 Second Model Reduction 272
11.4.3 Comparison of the Weidlich Haag Model and the Ge
neralized Gravity Model 276
11.4.4 Third Model Reduction 279
11.5 Evaluation of Empirically Obtained Results 279
11.5.1 Sensitivity Analysis 279
11.5.2 Decomposition of the Utility Functions with Respect to
Explanatory Variables 281
11.5.3 Prognoses 282
11.6 Examples for Decompositions of Utility Functions 283
11.6.1 Purchase Pattern 283
11.6.2 Voting Behaviour 285
11.6.3 Gaps in the Market and Foundations of New Parties . . 289
List of Symbols 291
Notation and Conventions 291
Frequently Occuring Symbols 293
Greek Symbols 301
Operators and Special Symbols 303
References 307
Index 323
|
| any_adam_object | 1 |
| author | Helbing, Dirk |
| author_facet | Helbing, Dirk |
| author_role | aut |
| author_sort | Helbing, Dirk |
| author_variant | d h dh |
| building | Verbundindex |
| bvnumber | BV010200095 |
| classification_rvk | MR 2800 |
| ctrlnum | (OCoLC)260219276 (DE-599)BVBBV010200095 |
| dewey-full | 302.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 302 - Social interaction |
| dewey-raw | 302.0151 |
| dewey-search | 302.0151 |
| dewey-sort | 3302.0151 |
| dewey-tens | 300 - Social sciences |
| discipline | Soziologie |
| format | Book |
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| series2 | [Theory and decision library / B] |
| spelling | Helbing, Dirk Verfasser aut Quantitative sociodynamics stochastic methods and models of social interaction processes by Dirk Helbing Dordrecht u.a. Kluwer 1995 XIX, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Theory and decision library / B] 31 Quantitative Methode (DE-588)4232139-6 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Interaktion (DE-588)4027266-7 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Sozialer Prozess (DE-588)4134118-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Interaktion (DE-588)4027266-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Stochastisches Modell (DE-588)4057633-4 s DE-188 Sozialer Prozess (DE-588)4134118-1 s 2\p DE-604 Stochastik (DE-588)4121729-9 s 3\p DE-604 Quantitative Methode (DE-588)4232139-6 s 4\p DE-604 B] [Theory and decision library 31 (DE-604)BV000021513 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006778510&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Helbing, Dirk Quantitative sociodynamics stochastic methods and models of social interaction processes Quantitative Methode (DE-588)4232139-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Interaktion (DE-588)4027266-7 gnd Stochastik (DE-588)4121729-9 gnd Sozialer Prozess (DE-588)4134118-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4232139-6 (DE-588)4057633-4 (DE-588)4114528-8 (DE-588)4027266-7 (DE-588)4121729-9 (DE-588)4134118-1 (DE-588)4057630-9 (DE-588)4113937-9 |
| title | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_auth | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_exact_search | Quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_full | Quantitative sociodynamics stochastic methods and models of social interaction processes by Dirk Helbing |
| title_fullStr | Quantitative sociodynamics stochastic methods and models of social interaction processes by Dirk Helbing |
| title_full_unstemmed | Quantitative sociodynamics stochastic methods and models of social interaction processes by Dirk Helbing |
| title_short | Quantitative sociodynamics |
| title_sort | quantitative sociodynamics stochastic methods and models of social interaction processes |
| title_sub | stochastic methods and models of social interaction processes |
| topic | Quantitative Methode (DE-588)4232139-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Interaktion (DE-588)4027266-7 gnd Stochastik (DE-588)4121729-9 gnd Sozialer Prozess (DE-588)4134118-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Quantitative Methode Stochastisches Modell Mathematisches Modell Interaktion Stochastik Sozialer Prozess Stochastischer Prozess Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006778510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000021513 |
| work_keys_str_mv | AT helbingdirk quantitativesociodynamicsstochasticmethodsandmodelsofsocialinteractionprocesses |