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Quantitative sociology has grown by burrowing methods from the experimental sciences even though. for the most part, our data are observational. Where the procedures of experimental science can he applied, data analysis can exploit simplifying assumptions because good experimental design removes correlations among independent variables that exist nature, outside the experiment, as well as effects or unmeasured variables. Where the science is of necessity, observational, these simplifications can not be guaranteed and, as a result, the analyses reached through by use of some of the standard "workhorse" techniques of the statistical repertoire may not be valid and conclusions reached by the application of these techniques are in doubt, This paper explores an alternative framework for data analysis in quantitative sociology, bypassing the statistics associated with experimental methods. Specifically, it explores generalizations of the method and quantitative theory used by physical surveyors, generalizing them to the needs of observational data. Application of this framework to text, including editorials and free answers to questionnaires as well as application to (social) survey data, supports their its for these purposes and the cartographic methods suggest that micro theories embedded in these methods reduce the load of a priori assumptions "normally" required for both text analysis and survey analysis. The applications suggest a research path applicable to "ordinary" sociological variables, including education, income, occupation, and gender. that shifts the burden of argument away from variance explained criteria and toward an integration of theory and method, guided by principles of parsimony and consistency. [ABSTRACT FROM AUTHOR]

This paper extends a recently proposed model of dynamical interactions between the macro structures of a society to hierarchically ordered societies. The so extended model helps interpreting some social and political phenomena such as coalitions, their hierarchical level and the degree of anarchy on a certain hierarchical level. The surprising property of the underlined model that stability is certain in the constant parameter case strikingly extends to this model. One of the main results of the paper is that the system has a unique equilibrium exactly when there is no anarchy on the highest hierarchical level. These results apply to a study of changes in the equilibria as determined by the changes in the system parameters [ABSTRACT FROM AUTHOR]

This paper argues for a heuristic rather than a fundamental role for mathematics in the social sciences. The a priori argument for insisting on a natural-scientific and mathematical approach to the study of social phenomena is found to rest on an untenable assumption about the powers of standard logic. Further, the requirements of description in the natural sciences are found to conflict irreconcilably with the nature of social interaction and social organization. As an alternative to the natural-science model, it is proposed that the regularities described by mathematical models depend upon and reflect underlying institutional arrangements. Consequently, mathematical models represent the outcomes of basic social processes rather than those processes directly. Nevertheless, it is argued, mathematical models are extremely useful and, indeed, indispensable in attempting to unravel the complexities of social phenomena. [ABSTRACT FROM AUTHOR]

In their original exposition of the fundamental concepts of game theory, John von Neumann and Oskar Morgenstern followed a definitional procedure. That is, they defined the principal instruments of the theory and supplemented their definitions with what might be called plausible reasoning to support their choices of definitions. This paper presents postulates which are necessary and sufficient that a social decision process is cooperative game according to the formulation of von Neumann and Morgenstem. In the von Neumann-Morgenstern formulation of a cooperative game, and in its subsequent extensions, one has generally a set of individuals, certain subsets of which are called coalitions, and a set of possible outcomes for which the individuals' preferences are given. The object of the formulation is to establish a relation of social preference among the outcomes through consideration of the powers and preferences of the coalitions. The definitional procedure consists of three suppositions: first, that there are given exogenously certain rules of the game which specify the powers of the coalitions; second, that the preferences of a coalition are determined by the rule of unanimity among its members; and third, that social preference coincides with the conjunction of power and preference for some coalition.

This article reports a test of theories of payoff allocation in n-person game--theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4person, 2-strategy non-sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α-effectiveness (von Neumann--Morgenstern) and β-effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the β-imputation set was more accurate than the α-imputation set, the β-stable set was more accurate than the α-stable set, and the β-core was more accurate than the α-core; in other words, for each of the solutions tested, the prediction from any solution concept based on β-effectiveness was more accurate than the prediction from the same solution based on α-effectiveness. Second, the β-core was the most accurate of the six theories tested. Results are interpreted as showing that β-effectiveness is superior to α-effectiveness as a basis for payoff predictions in cooperative non-sidepayment games. [ABSTRACT FROM AUTHOR]

The article focuses on various aspects of mathematical sociology. Mathematical sociology includes mathematical or formal models to expand the scope, precision and explanatory power of sociological theory. The enthusiasm of those who wanted a successful marriage between sociological theory and mathematics, was heightened by the rapid spread of computer technology. Today, the relationship between mathematics and sociological theory seems to be more ephemeral than ever. On the disciplinary landscape, mathematical sociology has now acquired the status of a struggling specialty.