The analysis of transfer systems that include both social benefit and taxation programs is complicated by the fact that the component programs comprising those systems interact. This paper develops a mathematical framework for the analysis of such systems at the micro‐level, i.e., using an individual or family as the unit of analysis. The first section describes the importance of income transfer issues and identifies criteria for evaluating proposed methodologies. Subsequent sections address the foundations for appropriate methods from two perspectives. The first perspective examines transfer systems using elementary concepts drawn from set theory, real analysis, and welfare economics; the assumptions and theorems presented allow the derivation of relevant system properties and serve to ensure that the systems discussed are well‐defined. The second perspective concentrates on the numerical methods required to execute income transfer analyses. The final section describes an implementation of this framework and briefly discusses the associated software.

Four related models of participation in group discussion are presented and compared in the accuracy with which they predict proportional participation, mean run length, mean recurrence time and the variances of runs and recurrences. For some quantities, such as proportional participation and mean run length, the most restricted model does virtually as well as the least restricted model; for other quantities it does not. None of the models does a good job of predicting variances of runs or recurrences. Notes I wish to thank Phillip Bonacich for making available the data, Joseph B. Kadane and John G. Ramage for helpful comments, and Yale University Computer Center for supporting the analysis.

an independent variable and on organization, efficiency, and satisfaction as dependent variables. Following the work of Guetzkow and Simon (1955), it has been clear that in large part the efficiency of a network depends on whether the network is able to achieve optimal organization. In some networks, such as the wheel, and for some tasks, such as that used by Leavitt ( 1951 ), this is a trivial problem-trivial, that is, if the members of the network accept the person at the center of the wheel as the person to form the answer. In other networks, such as the circle, the problem is not so simple, and our knowledge of why some groups organize and others do not is less than complete. In their study of factors affecting organization, Guetzkow and Dill (1957) analyzed the intertrial messages and concluded that perceiving the nature of the network is necessary for organization, that groups in which general suggestions for

Horvath's theory of participation in discussion groups is compared to data from several studies. Both visual evidence of graphs of the parameter space and tests of significance indicate to us that the theory is weak in its description of the proportion of acts initiated by members of the group. This failure is important since the theory was apparently developed to explain this aspect of group discussions. In 1951, Bales, Strodtbeck, Mills and Roseborough reported the collection of a large amount of data from task-oriented group discussions. Among the analyses, Bales et al. ranked the participants in each group according to the number of acts performed, added the number of acts performed by persons of the same rank in all groups of a given size, and proportionalized the aggregates. The resulting proportions were at first thought to be described by a harmonic function, but this notion was rejected. In 1952, using a slightly different unit of observation, but the same method of data analysis, Stephan and Mishler suggested that the data they had gathered from students in class discussions could be described by an exponential function

A recent mathematical model by Horvath which predicts the process of participation in group discussions is compared to several alternative models. The models can be applied to data for which the basic unit is the act and to data for which the basic unit is a continuous sequence of acts. In both cases, when statistical tests of significance are employed, most of the more restrictive models are rejected.

Reports have been published indicating striking regularities in the distribution of participation in group discussions, regularities potentially important in the understanding of small group processes. Several attempts to explain the form of the regularity contain implications for many sociological analyses. These attempts to explain the regularity are found to be inadequate; at the same time, the regularity is found to be somewhat doubtful.