Computational and Mathematical Modeling in the Social Sciences

✍ Scribed by Scott de Marchi

• Publisher: Cambridge University Press
• Year: 2005
• Tongue: English
• Leaves: 222
• Category: Library

✦ Synopsis

Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical perfection. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling--game theory, statistics, and computational methods--and proposes a new framework for modeling.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Acknowledgments......Page 11
Prelude......Page 13
The book in a nutshell......Page 22
Introduction......Page 25
What this book is not......Page 29
A Simple Example: Applause, Applause......Page 30
Strife between methodological camps......Page 34
A short statement on epistemology......Page 42
Amendment 1: Constraints upon Assumptions......Page 48
Amendment 2 : Logical Implications......Page 54
Looking ahead......Page 57
Introduction......Page 58
Overfitting......Page 59
An Example: The Currency Game......Page 63
Parameter Spaces and the Curse of Dimensionality......Page 67
Feature Spaces......Page 73
Out-of-sample Forecasting and Deriving Testable Implications......Page 77
An extended example: predicting conflict between nations......Page 80
Torturing Innocent Data Always Produces a Confession......Page 81
Independent Variables......Page 83
Is There a Theory in the House? Not Without a Feature Space.........Page 86
How Do You Know When You Are Right? Evaluating Models......Page 90
A general statement on models......Page 96
Appendix: perl code for the currency game......Page 98
Introduction......Page 102
A detour: a brief critique of game theory (and sundry comments on machine chess)......Page 103
Extensive Game Forms, Utility Functions, and Feature Spaces......Page 106
Does Deep Blue use artificial intelligence?......Page 107
“Brittle” Encodings and Equivalence Classes of Games: Empirical Implications......Page 112
An existing model of conflict initiation......Page 114
Is Computational Political Economy Different?......Page 120
Combinatorial Game Theory......Page 121
A Return to the Currency Game......Page 122
An Example Alliance Game......Page 126
The Alliance Game......Page 127
Some Example Components......Page 129
Concluding remarks on a methodology for choosing components and idiosyncratic payoffs......Page 133
Introduction......Page 137
Choice #1: Programming Language......Page 139
Choice #2: Development Environment......Page 141
Building computational models......Page 145
A Failed Encoding for the Alliance Game......Page 146
A Better Encoding......Page 150
Optimization in the Alliance Game......Page 153
Fitness functions and equivalence classes......Page 157
Self-destruction is the answer......Page 161
Appendix 2: python code for the currency game, with functions......Page 164
Introduction......Page 168
Example: A “Complex” Objective Function – the Traveling Salesman Problem......Page 177
An encoding for preference complexity......Page 179
Encoding Preferences......Page 180
Kauffman’s N-K Model and Complexity Measures for Survey Data......Page 181
When data fail you, derive a logical implication (again)......Page 183
Results......Page 188
Applying the Measure to Survey Data......Page 190
Yet another implication......Page 194
Final comments......Page 195
Appendix: caveats, endless caveats to the measure of preference complexity......Page 196
6 A Short Conclusion......Page 200
References......Page 205
Index......Page 215