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The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a 'functorial' mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the 'theory of categories,' a branch of modem algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach. [ABSTRACT FROM AUTHOR]

This paper presents a synthesis of the necessary and sufficient restrictions that insure a transitive group preference if majority rule is the aggregation procedure. We show the equivalence between transitivity and an extension of the condition of Condorcet which states that if an alternative receives a majority over every other, then it should be the social choice. This extension is equivalent to finding a solution to a system of linear inequalities. We use these inequalities to demonstrate that the recent work on restrictions of voter preferences can be derived from this Extended Condorcet Condition. [ABSTRACT FROM AUTHOR]

Both functionalism and exchange theory presuppose the existence of a worth ordering of some sort enabling members of a group to evaluate contributions to the group. Thus it is possible for participants to tell which of two patterns of behavior is more functional, or whether or not two social gifts are equivalent etc. Statements by earlier authors regarding this worth ordering are examined. It is shown that they imply that associated with any social group there exists a non-arbitrary set of exchange ratios (social prices) between various social actions. These social prices can be used to evaluate the contributions of individuals to the group and to determine the rankings of individuals within the group. [ABSTRACT FROM AUTHOR]

Inverse semigroups are introduced as a model for kinship structures. It is shown that semigroups are implied by the traditional anthropological law of uniform descent, and that inverses are suggested by the principle of reciprocity. A separation into a 'surface' and a 'deep' level of analysis was induced by viewing a kinship system as a partition on an underlying inverse semigroup. Some Omaha-type kinship systems are decomposed into direct and semidirect products. Additional assumptions are made to derive a theoretical similarity measure, which is then compared with a judged similarity task on Tenejapan Indians. The results of this preliminary experiment seem to he encouraging. [ABSTRACT FROM AUTHOR]

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non-random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choicest One model is a simulation in which individual members of two recognizable coups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to `neighborhood tipping? The systemic effects are found, to be overwhelming; there is no simple correspondence of individual incentive to collective results, Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of `tipping' begins to emerge. [ABSTRACT FROM AUTHOR]