## 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

1 | |

Concepts of Rational Action | 32 |

Collective Actions | 61 |

Further Concepts and Applications | 90 |

The Dynamic System and Other Elaborations | 131 |

161 | |

Computer Program and Output | 167 |

187 | |

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### Common terms and phrases

analysis applications assumed assumption average treatment effect behaviour Bernoulli trials best reply calculated causal Chapter Coleman collective action collective decisions committee concept of rationality conditional probabilities consequences constitutional control continuous-time continuous-time Markov process CONTROL BY ACTOR control of events control over event defined dependent described distribution empirical equal equation equilibrium estimate example exchange expected realization expected utility expected value external favour final control FINAL DIRECTED CONTROL fraction game theory given gives increment independent individual interest in event interest matrix INTEREST OF ACTOR issue legislator legislature linear marginal utility Markov chain Markov process MAT PRINT mathematical maximization minimax mixed strategy Poisson process positive outcome possible prisoner's dilemma probabilistic decision rule proportional allocation pure conflict purposive action purposive theories realization of interests representing social Sociological statistical structure Table tion transition probabilities transition rates utility differences variables vector

### Popular passages

Page xxxi - We're an empire now, and when we act, we create our own reality. And while you're studying that reality - judiciously, as you will - we'll act again, creating other new realities, which you can study too, and that's how things will sort out. We're history's actors . . . and you, all of you, will be left to just study what we do'.

Page xxii - They are independent of the unit of measurement and are computed by multiplying the regression coefficient by the ratio of the standard deviation of the explanatory variable to the standard deviation of the dependent variable.

Page li - American Journal of Sociology 86 (May): 1203-35. . 1983. "Restricted Access in Networks and Models of Power." American Journal of Sociology 88 (January): 686-17. Merton, Robert. 1947. "Manifest and Latent Functions." Pp. 19-84 in Social Theory and Social Structure. New York: Free Press. Mintz, Beth, and Michael Schwartz. 1985. The Power Structure of American Business. Chicago: University of Chicago Press. North, D., and R. Thomas. 1973. The Rise of the Western World. Cambridge: Cambridge University...

Page 2 - ... Which type of explanation ought to be conceived of? One cannot avoid a confrontation with the methodology of social science. In his book on "collective action" J. Coleman stresses the difference between two separate approaches of action. The first a causal one, the second a teleological one. He says : There are two quite different streams of work in the study of social action, both of which begin at the level of the individual.

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

Page l - Simulation and Gaming in Social Science (New York: The Free Press, 1972).

Page 2 - The two streams of work represent fundamentally different conceptions of man. The first conception explains man's behaviour as response to his environment; the second explains his behaviour as pursuit of a goal. The first searches for causal processes and determinants of behaviour, and often uses a mechanistic explanatory frame, which employs the concepts of 'forces