Journal Article

Game Theory Meets Threshold Analysis: Reappraising the Paradoxes of Anarchy and Revolution

Peter Vanderschraaf

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 59, issue 4, pages 579-617
Published in print December 2008 | ISSN: 0007-0882
Published online December 2008 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axn025
Game Theory Meets Threshold Analysis: Reappraising the Paradoxes of Anarchy and Revolution

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I resolve a previously unnoticed anomaly in the analysis of collective action problems. Some political theorists apply game theory to analyze the paradox of anarchy: War is apparently inevitable in anarchy even though all warring parties prefer peace over war. Others apply tipping threshold analysis to resolve the paradox of revolution: Joining a revolution is apparently always irrational even when an overwhelming majority of the population wish to replace their regime. The usual game theoretic analysis of anarchy yields the conclusion that the suboptimal equilibrium of war is inevitable. The usual tipping threshold analysis of revolution yields the conclusion that the optimal equilibrium of successful revolution is possible. Yet structurally the collective action problems of anarchy and potential revolution are much the same. This suggests that tipping threshold analysis and game theory are incompatible methodologies, despite their widespread use in the social sciences. I argue that there is no real tension between game theory and tipping threshold analysis, even though these methodologies have developed largely independently of each other. I propose a Variable Belief Threshold model of collective action that combines elements of game theory and tipping threshold analysis. I show by example that one can use this kind of hybrid model to give compatible explanations of conflict in anarchy and successful revolution.

Introduction

Two Classic Problems, and Two Popular Analyses

2.1

The paradox of anarchy

2.2

The paradox of revolution

Restating the Puzzle

Evaluating the Prisoners’ Dilemma and S-Curve Models

The Variable Belief Threshold Model

Example 5.1. A population of moderates with independent deviations

Example 5.2 A heterogeneous population with independent deviations

Example 5.3 A heterogeneous population with coordinated deviations

Conclusion

Appendix: Computer Simulations

Journal Article.  15187 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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