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The index "the proportion of a cohort that have become delinquent by a given age," here called the "prevalence of delinquency," is an important social indicator. In the present paper, we indicate methods by which this index can be estimated from data, and correct errors in previous sex- and racespecific prevalence estimates published by Monahan (1960) for the city of Philadelphia. The difference between the sexes and between the races shown by these corrected prevalence estimates are of sufficient magnitude to render suspect any comparisons of prevalences of delinquency among cohorts which do not take account of the sex and race compositions of the cohorts to be compared. [ABSTRACT FROM AUTHOR]

The article focuses on prediction logic and quasi-independence in empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, a paradigm for the statement and empirical evaluation of a class of propositions predicting specific relations between qualitative variables was proposed. The approach represents a substantial departure from traditional modes of analysis. Consequently, it is not surprising that one encounters resistance and misunderstanding in those who work in different traditions. The lengthy critique of the paper by researchers L.A. Goodman and W.H. Kruskal, henceforth G&K, illustrates the inappropriateness of evaluating the paradigm using traditional perspectives. G&K operate in two contexts: measures of association and multiplicative models for probabilities in cross-classifications. The primary objective in the paper discussed by G&K was to design a general model that provides a distinct and operationally interpretable measure of the prediction success attained in a population by any logically distinct proposition stated, a priori, in the prediction logic.

Presents information regarding various articles which appear in January 1973 issue of the periodical "Journal of Mathematical Sociology." Presentation of two models of coalition formation and payoff allocation by James D. Laing and Richard J. Morrison; Problems related to sociometric studies.

The intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]

This paper expands the diffusion of information models developed by Funkhouser and McCombs (1972) to include situations involving simple interaction processes and more complicated situations involving both mass mediated messages and interactively mediated messages. This paper develops discrete time models of information diffusion as opposed to the continuous time models developed by Coleman (1964) and Bartholomew (1967) and others. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to data analysis that assists the investigator in discriminating among specific relations corresponding to alternative scientific predictions about qualitative variates. [ABSTRACT FROM AUTHOR]

Mathematical demography traditionally has been concerned with the dynamics of the growth and structure of a population that is undisturbed by migration. Recently, however, increasing attention has been directed at the relationships between interregional migration flows and the growth and structure of multiregional population systems that are open to internal migration. This paper contributes to that emerging body of knowledge by generalizing the notion of a life table to the multiregional case and showing how such a generalization leads to a mathematical theory of multiregional population growth that is consistent with the currently accepted single-region theory. [ABSTRACT FROM AUTHOR]

In this paper we develop two formal models predicting coalitions and payoffs among rank striving players in a sequential three-person game. We test the models' predictions with data from a laboratory study of eleven male triads. Each triad plays a sequence of games; in each game a two-person coalition forms and divides the coalition's point value between the two coalition partners. Participants know that the sequence of games will end without warning at a randomly chosen time; at the sequence's end each player's monetary payoff is a linear function of the rank of his accumulated point score, relative to those of the other members of his triad. The complexity of this situation prevents players and analysts from representing it as a single game; thus they are unable to use n-person game theory to identify optimal strategies. Consequently, we assume that players, unable to develop strategies that are demonstrably optimal in the long run, adopt certain bargaining heuristics and surrogate short run objectives. The two models follow the same basic outline; they differ, however, in the planning horizon they assume players to use. Proceeding from a priori assumptions concerning each player's decision calculus and the bargaining process, the two models state the probability that each coalition forms and predict the point divisions in the winning coalition. The laboratory data provide consistently strong support for the predictions of both models. [ABSTRACT FROM AUTHOR]

This essay is intended as an expository paper on how the seemingly abstract social choice models are related to the practical problems of formulating models of economic policy. The flexibility of the social choice models in dealing with the problem of relating ethical propositions to propositions concerning social actions is not widely understood. The paper is divided into five sections. In the first section, it is argued that an economic policy should be viewed as a decision process rather than a decision and that the social choice models are a natural framework for the representations of the concept of a decision process. In addition, it is argued that Arrow's controversial 'Independence of Irrelevant Alternatives' axiom is actually a defining property of a political-economic process. Problems of 'policy formulation' are viewed, then, as problems of 'systems design' with the axiom being used as the defining characteristic of a 'system.' The second section contains a discussion of the concept of an 'ethic' as related to political economic processes.

This paper develops a formal model for exchange within a system of action. The system of action is defined by actors, events, control of actors over events, and interests of actors in the outcomes of events. The system is designed to deal with divisible events (best exemplified by private goods) or indivisible events (such as a bill on which a vote is taken), and events with or without externalities, This paper considers mostly divisible events, but some steps are taken toward analysis of indivisible events on which there are opposing interests. [ABSTRACT FROM AUTHOR]

This paper argues that social choice from among more than two feasible alternatives should not be based on social choice from two-alternative subsets. It considers in some detail the case where one alternative ties or beats every other alternative on the basis of simple majorities, and raises the question of whether such an alternative should be chosen. A condition of 'stochastic unanimity', introduced in this context, is shown to be incompatible with the simple majority rule when it can apply. This new condition plus a consideration of ties leads into a brief discussion of the use of individual expected utility in social choice theory. [ABSTRACT FROM AUTHOR]

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 describes a model and associated computer program for carrying out clustering of elements in a space of a predetermined number of dimensions. In addition to clustering of elements, the model may be used for multi-dimensional scale analysis and for construction of sociograms. The model takes as input data a set of 'affinities' between elements, the inverse of which may be considered as psychological or sociological distances. It then moves elements in a Euclidean n-space toward the point at which the geometric distance is equal to the given psychological or social 'distance,' as if a set of attractive and repulsive forces was acting upon each element from other elements. The second major portion of the paper consists of ten examples, which are analyzed by means of the accompanying computer program. [ABSTRACT FROM AUTHOR]

This paper examines Caplow's model of coalitions in the triad and identifies several shortcomings. Retaining the basic structure of Caplow's arguments, it recasts the problem as one of interdependent rational decision making. The reformulation allows increased generality in several directions, including a more general notion of strength, relaxation of the additivity assumption about strength, and the adoption of probabilistic choice to allow predictions about the relative frequencies of the various coalitions. [ABSTRACT FROM AUTHOR]

This paper reports research using a psychological theory, R. D. Luce's (1959) individual choice theory, to provide a ratio-level measurement basis for an important sociological variable, occupational prestige. It is shown that earlier measurement procedures to scale this sociological variable are essentially arbitrary, although heuristically useful. Luce's Axiom of Choice and his Ranking Postulate are then tested on choice sets of occupations where subjects are asked to pair-compare or rank the occupations on the basis of their prestige. The Axiom receives qualified support, while the Ranking Postulate is not supported. It is concluded that Luce's choice theory can provide a ratio-level measuremerit basis for occupational prestige, although a procedure using rankings must he appropriately structured in order to be an adequate instrument of measurement. [ABSTRACT FROM AUTHOR]

This paper generalizes the Kemeny-Snell distance function for distances between weak orderings to a distance function for the collection of all partial orderings of a set. This generalization explains some of the seemingly strange properties of the Kemeny-Snell distance, and extends it to such important classes of orderings as semiorders and interval orders. In section four I consider possible applications of the distance function and describe a number of problems that arise in attempts to apply the distance function. In section 3 I discuss the concept of a distance function in more general terms and introduce a new distance function defined by a set of axioms different from those given in Section 2. [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]

This paper addresses the problem of using roll call voting data to ascertain the ideal points of legislators in a multi-dimensional space. After identifying difficulties inherent in factor analytic studies of roll call data, I present a simple formal model of legislative voting that resolves these difficulties. Finally, I derive some implications of the model and use them to outline a technique for estimating legislators' ideal points. [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.

The article presents information on factoring and weighing approaches to status scores and clique identification. Three very different techniques for devising indices or popularity or centrality have, with small variation, one basic solution for symmetric social structure. The resulting popularity or centrality scores have the advantage that they can be interpreted in all three different ways and the isolation of the essential identity of the techniques will be shown that this solution gives the clique structure at a glance. The solution described in this paper only works for symmetric structures. Some social structures are naturally symmetric or can reasonably be made so. For example, talking to one another, spending time together, dating and other behavioral relations are naturally symmetric. Friendship could be defined to include only reciprocal choices. An index of centrality in a commuication structure might be desired as a clue to how fast information will spread from an individual or to how much power an individual has because of his key position in the communication network.

In recent years, a number or authors have identified conditions on individual preference orders that imply transitive majorities or which imply that at least one alternative is not beaten by any other alternative under simple majority comparison. Within the context of a three-alternative situation, this paper summarizes these contributions and proves several new results that complete an analysis of sets of individual preference orders that guarantee a simple-majority winner among the three alternatives. Along with guarantees and odd-guaratees for sets of strict partial orders authors of this article consider the guaratees notions when all orders are required to be weak orders. Four definitions will be used to identify restrictions on individual preference orders taht will be used in the analysis. The article further presents numerical presentation of the research topic.

The role of probabilistic models, with special reference to application of the Semi-Markov model to the analysis of internal migration, is discussed. Advantages of probabilistic models over more conventional methods based on regression analysis are detailed. Probabilistic models have stood apart from the rest of the literature, in migration as well as other areas of application, because they have no substantive content. It is argued that unless their parameters are related to the causal structure and exogenous determinants of the migration process, probabilistic models will be of little practical and scientific use. A strategy for integrating probabilistic models with theoretical and empirical analysis is sketched, to be carried out in the next article. [ABSTRACT FROM AUTHOR]

In this, paper the authors use information theory to restate R.K. Merton's classification of deviant behavior in mathematical terms. Merton's classification scheme has been very widely used but does not appear to have been "mathematized" to any extent. In consequence the usefulness of the schema is somewhat diminished. For example, it is difficult to measure directly the amount of anomie prevalent in a situation, and it is difficult to decide Whether, one situation is. more anomic than another. The authors illustrate the usefulness of information theory as a descriptive tool by discussing a highly simplified situation; however, the measurement techniques to be developed are applicable to more complex and realistic situations. The authors restrict their attention to the set of all motorists with 9-5 weekday jobs who are at any intersection at 8:00 a.m. seven days a week, and one will consider the following to be an exhaustive list of the goals, norms, and actions of these motorists.

The general measurement scale hierarchy developed by S. S. Stevens has had widespread use and discussion, but has suffered from various criticisms, many of which may be traced to the informal descriptions and minimal mathematical formulations used in the original definitions and claims. In this paper, a mathematical model of measurement and specific scale forms is developed, using the minimum mathematical structure necessary to define each scale type. Measurement is defined, and a series of restrictions are applied to measurements to yield a precisely specified hierarchy of measurement scale forms including nominal, ordinal, interval, and ratio scales, as well as several others. Equivalences are mathematically defined for each scale form, and theorems are presented specifying the sets of transformations under which equivalence is preserved, thus yielding the scale form invariances discussed by Stevens. The hierarchy of measurement scale forms is summarized in a pictorial 'spectrum' diagram. The development of the model in terms of the structure of possible measurement comparisons (e.g., whether one can establish that one item is 'less' than another, or, alternatively, establish how much the one is less than the other, etc.) is in marked contrast to Stevens definition in terms of scale invariances. This approach avoids several criticisms raised against Stevens' approach. One might hope that the alternative approaches would yield corresponding results, and indeed this is found to be generally true. Those cases where differences do occur, however, prove to be vital, and yield several striking unanswered questions about scale forms and their invariances. [ABSTRACT FROM AUTHOR]

Data from 118 members of three consecutive cohorts of students at a private Southern medical school are employed to develop a discrete parameter stationary Markov chains model of the medical specialty choice process. This model was then tested on independent subsamples from the same population, generating a series of predicted specialty choices which did not differ from observed choices by more .than chance expectations. Suggestions for future research, beyond the present demonstration of the utility of a simple Markovian model of a choice process, are offered. [ABSTRACT FROM AUTHOR]

A stochastic model of migration, occupational and vertical mobility, based on the theory of Semis Markov processes, is presented and important features of these processes derived. The model is a generalization of the Markov process in which the probability of leaving a state can depend in any arbitrary way on the length of time the state has been occupied (duration-of-stay) and on the next state entered (pushes and pulls). For mobility processes it thus captures McGinnis' `axiom of cumulative inertia' Several distributions with cumulative inertia are presented and the relationship between the Semi-Markov model and the Mover-Stayer model explored. A method of including age effects is described. The model is shown to have applications to many other social processes, in addition to mobility, which have duration-of-stay effects. [ABSTRACT FROM AUTHOR]

The Markov chains with stationary transition probabilities have not proved satisfactory as a model of human mobility. A modification of this simple model is the 'duration specific' chain incorporating the axiom of cumulative inertia: the longer a person has been in a state the less likely he is to leave it. Such a process is a Markov chain with a denumerably infinite number of states, specifying both location and duration of time in the location. Here we suggest that a finite upper bound be placed on duration, thus making the process into a finite state Markov chain. Analytic representations of the equilibrium distribution of the process are obtained under two conditions: (a) the maximum duration is an absorbing state, for all locations; and (b) the maximum duration is non-absorbing. In the former case the chain is absorbing, in the latter it is regular. [ABSTRACT FROM AUTHOR]

The article focuses on empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, henceforth HLR, proposed an index to measure the adequacy of a particular kind of theory when confronted with harsh facts. The authors L.A. Goodman and W.H. Kruskal, henceforth GK, presented a critical analysis, together with constructive proposals towards partial mitigation of the flaws and gaps they found in HLR. The authors do not agree with the rationales given in HLR for the independence like denominator of the proposed index. One can, however, take the index as given and ask how it performs. It was noted in GK that the HLR index compares the theoretically empty cells with the multiplicative yardstick probabilities for those cells, and no adequate justification for this comparison was found. This is so for both the unweighted and weighted forms of the index. In GK, some modest ways around this problem was suggested without claiming necessarily wide applicability for the suggestions.

In the context of analyzing social structures through the use of graph theory, some binary matrix operations for valued graphs are presented. These operations are demonstrated in the analysis of social network data presented by Kapferer. Further examples of where the procedures should prove useful are suggested. [ABSTRACT FROM AUTHOR]

The article focuses on empirical evaluation of formal theory. Researchers D.K. Hildebrand, J.D. Laing, and H.L. Rosenthal, henceforth H-L-R, propose an index to measure the adequacy of a theory that asserts or predicts emptiness of some cells in a two-way cross classification. There are two separate motivating arguments used by H-L-R to justify the independence-like products of marginals in the denominator of their index. The first argument establishes a kind of null or benchmark hypothesis for saying something about y in ignorance of both "x" and "y" to compare with statements of the theory. But that benchmark procedure seems to us arbitrary and inappropriate. The second argument for benchmark independence turns on arbitrary, tendentious definitions of the terms scope and precision for the theory. There have been many attempts to frame useful quantitative notions of degree of confirmation of a theory. H-L-R and also much of the literature mentioned treat highly simplified notions of theory. The very concept of a scientific theory is not simple, and in any case it seems to us confusing to deal with scientific theories as if they were reducible to cross-classifications with some cells asserted empty.

Measurement error, an inherent quality of any empirical data collection technique, is discussed in the context of sociometric data. These data have long been assumed to possess face validity and to be the data of choice in any study of the sentiment structure of small scale social systems. However, it is argued that while methods of sociometric analysis have become increasingly more sophisticated they have failed to yield unequivocal results because they do not distinguish structural complexity from measurement error. Through a discussion of increasingly more complex examples the distortion laden character of most sociometric data is illustrated. This distortion is introduced by the formalities of the sociometric test and it will not be removed by developing increasingly more sophisticated structural models or throwing out some of the data. Instead, when issues concerning the nature of specific relational networks are raised data of much higher quality than those which are commonly available are required. A technique for generating high quality sociometric data is briefly discussed. On the other hand, it is suggested that the extant body of sociometric data ought to be adequate when sizeable aggregations are examined for evidence of statistical tendencies in structure. [ABSTRACT FROM AUTHOR]

Examines the Bogart model and its potential application in social sciences. Derivation of a distance measure and computing devices by Bogart; Features of the model; Possible applications of the model.

Multi-person versions of Prisoner's Dilemma are widely applicable in the social sciences. Examination of two important classes of real-world situations reveals that although both can appropriately be called Prisoner's Dilemma, they have incompatible payoff structures. Thus Prisoner's Dilemma games constitute an important but apparently ambiguous set of models. We therefore undertake a taxonomy of multi-person Prisoner's Dilemma. Some aspects of the well-studied two-person case provide a useful beginning for the task. In the general multi-person form, however, some properties of the two-person game are found incompatible with others and so are dropped. Additional properties are suggested by strategic considerations and the associated social phenomena. We demonstrate interdependencies among the various properties and relate some of them to a simple graphical representation. [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]

There are of course many factors that influence social policy in a democratic society, one factor being that the rulers of a democratic society cannot totally ignore the will of the people. Recent years have witnessed an increasing interest in the problem of making social choices. The ruler of a democratic society may be more concerned with maintaining power than with having his society incur a minimal loss. In these later works the authors do not consider the position that would be assumed by a beneficent dictator. It is instructive to look at this position for several reasons. First, in the Davis and Hinich model a dominant strategy cannot always be guaranteed. This can put the candidate in a quandary, and, not being able to think of a strategy more suited to his desire for re-election, he might try to adopt the position of the beneficent dictator which is easy to find under mild restrictions. He also might wish to pay lip-service to this strategy in any case. Second, the position of the beneficent dictator may actually be his best strategy under a slightly different model of the electoral process.

In a democratic society, many social choice are made by means of a competitive political process in which the final choice between competing alternatives is by vote or ballot by the members of some constituency or representative body. Among the problems which might arise for consideration in this manner might be that of deciding the levels at which each oft set of governmental activities shall be run; or the amounts to be provided of each of a variety of governmental services or public goods; or the values at which each of several policy instruments shall be set. A theory or model of the political process capable of explaining public sector behavior with respect to this class of problems would be of considerable interest and potential applicability. In societies with bicameral legislature or separate executive and legislative branches, elected separately and perhaps from different constituencies, the decisive coalitions are more complicated still. Conditions for voting equilibrium in these complex institution are presumably quite different from those for an equilibrium under simple majority rule, yet they have received little attention in the voting literature. It may be that democratic institution based on majority rule are indeed in a perpetual slate of turmoil, with new majorities continually forming to overturn the current the status quo, and the system unable to achieve a viable resolution to the underlying choice problem.

Information diffusion is the process by which information spreads through a population. There are many types of information, many types of populations and many diffusion mechanisms. From the standpoint of sheer bulk of information diffused, the most prevalent diffusion process in operation today is probably from the mass media to mass audiences. News events are, if not necessarily the most important type of information at least the easiest to study while diffusing, since they have definite starting points in time and are generally easy to comprehend and define. A number of studies have traced the diffusion of major news events over time and have noted regularities in the way that news events diffuse. Several attempts have been made to apply mathematical models to the process of information diffusion. It can be shown that diffusion theoretically can be predicted as a function of probabilities of audience exposure to the disseminating media over a series of time increments, provided that several assumptions are met.

Several methods of analyzing the parameters of the Semi-Markov model and incorporating exogeneous information about its states are presented. Regression analysis of parameter estimates and doubly stochastic processes are discussed. Theoretical models for the structure of transition matrices, based on Luce's theory of choice behavior, are derived. Gravity models of varying specificity, useful in the study of migration, are special cases. Maximum likelihood procedures for estimating parameters, with fully operational numerical methods for solution of the likelihood equations, are given. Thus the integration of probabilistic models with theoretical and empirical analysis of causal structure, called for in the previous article, is carried out. [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]

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. [ABSTRACT FROM AUTHOR]

A one-parameter exhaustible Poisson process mode! is formulated to represent the cumulative divorce trajectory of marriage cohorts. On the basis of recently published data of nine-year cumulative records of all one-year United States marriage cohorts, 1949-1958, it is found that the one-parameter model does not provide an empirically adequate representation of cohort divorce trajectories. Therefore, two modifications of the basic model are explored. First, it is assumed that the longer the couples remain married the smaller is the probability of their becoming divorced (a cumulative inertia modification), Second, it is assumed that the cohort can be divided into two groups one of which is subject to risk of divorce while the other is not (a mover-stayer modification). It is concluded that the latter model provides a better approximation to the empirically observed divorce trajectories, Given availability of disaggregated observations of divorces for marriage cohorts, the model could be used as a mathematical language for the construction of a theory of divorce differentials and changes in the divorce condition over time. [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]

The checkerboard model is a computer simulation of social interaction among members of two groups. The checkerboard represents a social field on which two groups of checkers move on the board on the basis of positive, neutral or negative attitudes toward one another assigned to them. The resulting pattern of positions of the pieces represents the social structure. The theoretical basis for the checkerboard model is explained and the rules for operating the model are outlined. This is followed by illustrative runs named Crossroads. Mutual Suspicion, Segregation, Social Climber, Social Worker, Boy-Girl, Couples and Husband-Wives, showing intermediate and final positions on the board for each. It is concluded that the checkerboard model is capable of demonstrating the intimate connection between attitudes of group members toward their own group and toward others to a continuous social interactional process and to the resulting social structure. [ABSTRACT FROM AUTHOR]