## Mathematics of Collective Action"Philosophers, social scientists, and laymen have used two perspectives in analyzing social action. One sees man's action as the result of causal forces, and the other sees action as purposive and goal directed. Mathematical treatment of social action has shown this same dichotomy. Some models of behavior describe a causal process, in which there is no place for intention or purpose. Most stochastic models of behavior, whether individual or group, are like this. Another body of work, however, employs purpose, anticipation of some future state, and action designed to maximize the proximity to some goal. Classical microeconomic theory, statistical decision theory, and game theory exemplify this direction. This book examines these two directions of work, and makes original contributions to the second. An introductory chapter outlines these two bodies of work, and casts them in a common frame, to display their similarities and differences. Chapter 2 reviews at length recent work in stochastic processes that makes up the first body of work, which sees social action as the resultant of causal forces. The remaining chapters develop a mathematical framework for the study of systems of social action using a purposive theoretical base. These chapters are designed particularly to contribute to the study of collective decisions, a form of social action that has proved particularly challenging to theoretical analysis. First published in 1973, this became a significant work both in problem solving and in the future career of the author. It is of continuing importance to researchers and students interested in statistical analysis."--Provided by publisher. |

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### Contents

Preface | xxxvi |

Hie Mathematics of Social Action | 1 |

Concepts of Rational Action | 32 |

Collective Actions | 61 |

Farther Concepts and Applications | 103 |

Examples of applicationsThe problem of data | 128 |

The Dynamic System and Other Elaborations | 131 |

the probabilistic decision ruleSequential introduction | 154 |

References | 161 |

Computer Program and Output | 167 |

187 | |

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action actor allocation analysis appears applications assumed assumption behaviour calculated carried causal Chapter choice Coleman collectivity committee concept conditional consequences constitutional continuous decision rule defined demand dependent described determine developed directed discussed distribution effect elements empirical equal equation equilibrium estimate event examination example exchange expected extensions external fact favour final fraction function gain given gives greater important increases increment independent individual interests introduction issue lead legislator legislature less majority Markov mathematical matrix maximization means observed occurs outcome parameters persons positive possible present principle PRINT probability problem proportion pure rationality realization of interests relation relative representing response result shown shows simple single situation social statements statistical strategy structure Table theory tion transition rates treatment utility variables vote

### Popular passages

Page xiv - To develop statistical methods that quantify such causes his general approach is: "(1) to begin with the idea of a process, (2) to attempt to lay out a mathematical model that mirrors this process, and then (3) given particular kinds of data, to transform the mathematical model into a statistical model for estimating parameters of the process