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Showing papers in "Journal of Mathematical Sociology in 1975"


Journal ArticleDOI
TL;DR: In this article, an extension of the dichotomous probit model for ordinal dependent variables is presented. But the model assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an interval level variable.
Abstract: This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.

2,520 citations


Journal ArticleDOI
TL;DR: In this article, a conceptualization of occupational mobility having system boundary properties and interrelated moves, tests of the job vacancy chain model to determine its predictive power for a civil service internal labor market, and additional use of the theory of absorbing Markov chains to gain further insight into the dynamics of job vacancies.
Abstract: This paper has three primary foci—a conceptualization of occupational mobility having system boundary properties and interrelated moves, tests of the job vacancy chain model to determine its predictive power for a civil service internal labor market, and additional use of the theory of absorbing Markov chains to gain further insight into the dynamics of job vacancies. The modes by which job vacancy chains entered the system by stratum are also examined for a twenty‐one year period. The job system analyzed is the police internal labor market of the Michigan State Police. The data are continuous for a forty‐three year period (1927–1970). Since, a reasonable degree of stationarity was not reached until 1949, the model was tested from 1949–1970. The model is viewed as having considerable predictive power. Moreover, when viewed as a system model rather than a formal organizational model, it can be used for internal labor markets and more general systems which link internal labor markets. It appears much less l...

36 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compared three methods (sequel, cardinal, maximal) for constructing a weak order from a partial order on a finite set and found that the cardinal mean error was lower than the sequel mean error.
Abstract: This paper compares three methods (sequel, cardinal, maximal) for constructing a weak order from a partial order on a finite set. The constructed weak orders include the partial order. To evaluate the methods, several different selection disciplines were used to stochastically generate partial orders from a fixed linear order. The error of a weak order which includes a generated partial order is a function of the number of ordered pairs added to the partial order to get the weak order which are the reverse of ordered pairs in the fixed linear order. In all cases, the sequel and cardinal mean errors were much lower than the maximal mean error. In most but not all cases, the cardinal mean error was lower than the sequel mean error.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the extent to which the electoral college induces candidates to advocate policies that they would not advocate under a direct vote, and the probability that the winner in a direct election is not the winner under the Electoral College.
Abstract: In this essay we address three issues from the debate over substituting a direct vote for the Electoral College: (1) the extent to which the Electoral College induces candidates to advocate policies that they would not advocate under a direct vote; (2) the probability that the winner under a direct vote is not the winner under the Electoral College; and, (3) the probability that third parties—both national and regional—force elections into Congress. We conclude, first, that while candidate platforms are sensitive to election procedure, the likelihood of politically significant differences has diminished over time. Second, computing the probability of reversals in 2‐candidate contests, we find that, even in close elections, this probability does not exceed 0.2. Finally, and contrary to our initial supposition, we conclude that regional as against national third parties are not necessarily more likely to induce indeterminate outcomes, ceteris paribus. We also explore situations in which the Electoral Colleg...

19 citations


Journal ArticleDOI
TL;DR: In this paper, the sampling probability distributions of the number of links and the cumulative distribution of the numbers of components are derived for structural properties in an organization, and the probability estimates of both the number and the component counts are derived.
Abstract: This paper considers the statistical inference of structural properties in organizations. Specifically, the sampling probability distributions of the number of links and the cumulative distribution of the number of components are determined. Probability estimates of both the number of links and the number of components are then found.

8 citations


Journal ArticleDOI
TL;DR: In this article, conditions are found under which the removal of an intransitivity in one triad of a sociometric or cognitive structure may be accomplished without in the process creating new intransitivities elsewhere in the structure.
Abstract: The conditions are found under which the removal of an intransitivity in one triad of a sociometric or cognitive structure may be accomplished without in the process creating new intransitivities elsewhere in the structure. The results are applied to modify and elaborate the theories holding intransitivity to be unstable so that sociometric or cognitive structures become more nearly transitive over time, and also to shed some light on the question of the extent to which observed intransitivities may properly be attributed to measurement error. Properties of tetrads play a central role in this theory, which thus challenges the widespread notion due to Simmel and others, that once group size exceeds three there are no significant new properties to consider. Empirical data document the relevance of this theory: “correction” of “errors” in the data or change in truly intransitive triads turns out not to significantly reduce the overall amount of observed intransitivity.

7 citations


Journal ArticleDOI
Allan Mazur1
TL;DR: In this paper, a simple model is presented, which orders the empirical results of eight experiments (27 conditions) on status-undifferentiated dyads in this situation, and makes additional predictions.
Abstract: Berger has developed a standard experimental situation for the study of influence processes in dyads. A simple model is presented’ which orders the empirical results of eight experiments (27 conditions) on status‐undifferentiated dyads in this situation. The model provides a good fit to the data and makes additional predictions.

4 citations



Journal ArticleDOI
TL;DR: In this paper, a theory of behaviour in n-person conflicts is presented, and its solution is predicated on the interdependency of coalition formation and pay-off determination in an n−person conflict.
Abstract: This paper presents a theory of behaviour in n‐person conflicts. The theory and its solution are predicated on the inter‐dependency of coalition formation and pay‐off determination in an n‐person conflict. The solution, therefore, involves not only pay‐off determination but also coalition formation in the game. The theory is developed using mathematical notions of fixed points together with some behavioural theories about choice behaviour and interdependency of persons in competitive situations. It predicts not only the final state of coalition formation but also transient choices and coalitions in the games. Finally, the model is tested on some experimental games of W. Riker.

2 citations