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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]

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 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]