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 choices. One model is a simulation in which individual members of two recognizable groups 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.
~
SCHELLING, Thomas C., 1971. Dynamic models of segregation†. The Journal of Mathematical Sociology. 1 July 1971. Vol. 1, no. 2, p. 143–186. DOI 10.1080/0022250X.1971.9989794. [Accessed 16 December 2023].
† This study was sponsored by The RAND Corporation with funds set aside for research in areas of special interest, and was issued as RM-6014-RC in May 1969. The views expressed are not necessarily those of RAND or its sponsors.
People get separated along many lines and in many ways. There is segregation by sex, age, income, language, religion, color, taste, comparative advantage and the accidents of historical location. Some segregation results from the practices of organizations; some is deliberately organized; and some results from the interplay of individual choices that discriminate. Some of it results from specialized communication systems, like different languages. And some segregation is a corollary of other modes of segregation: residence is correlated with job location and transport.
If blacks exclude whites from their church, or whites exclude blacks, the segregation is organized, and it may be reciprocal or one-sided. If blacks just happen to be Baptists and whites Methodists, the two colors will be segregated Sunday morning whether they intend to be or not. If blacks join a black church because they are more comfortable among their own color, and whites a white church for the same reason, undirected individual choice can lead to segregation. And if the church bulletin board is where people advertise rooms for rent, blacks will rent rooms from blacks and whites from whites because of a communication system that is correlated with churches that are correlated with color.
Some of the same mechanisms segregate college professors. The college may own some housing, from which all but college staff are excluded. Professors choose housing commensurate with their incomes, and houses are clustered by price while professors are clustered by income. Some professors prefer an academic neighborhood; any differential in professorial density will cause them to converge and increase the local density. And house-hunting professors learn about available housing from other professors and their wives, and the houses they learn about are the ones in neighborhoods where professors already live.
The similarity ends there, and nobody is about to propose a commission to desegregate academics. Professors are not much missed by those they escape from in their residential choices. They are not much noticed by those they live among, and, though proportionately concentrated, are usually a minority in their neighborhood. While indeed they escape classes of people they would not care to live among, they are more conscious of where they do live than of where they don't, and the active choice is more like congregation than segregation, though the result may not be so different.
This article is about the kinds of segregation—or separation, or sorting—that can result from discriminatory individual behavior. By 'discriminatory' I mean reflecting an awareness, conscious or unconscious, of sex or age or religion or color or whatever the basis of segregation is, an awareness that influences decisions on where to live, whom to sit by, what occupation to join or to avoid, whom to play with or whom to talk to. The paper examines some of the individual incentives, and perceptions of difference, that can lead collectively to segregation. The paper also examines the extent to which inferences can be drawn, from the phenomenon of collective segregation, about the preferences of individuals, the strengths of those preferences, and the facilities for exercising them.
The ultimate concern is segregation by 'color' in the United States. The analysis, though, is so abstract that any twofold distinction could constitute an interpretation —whites and blacks, boys and girls, officers and enlisted men, students and faculty, teenagers and grownups. The only requirement of the analysis is that the distinction be twofold, exhaustive, and recognizable.
[…]
Figure 7 shows an initial random distribution. There are 13 rows, 16 columns,
Fig. 7
208 squares (for reasons of convenience that I won't go into here). It might seem unnecessary to reproduce an actual picture of randomly distributed stars and zeros and blank squares; but some of the results are going to be judged impressionistically, and it is worthwhile to get some idea of the kind of picture or pattern that emerges from a random distribution. If one insists on finding 'homogeneous neighborhoods' in this random distribution, he can certainly do so. Randomness is not regularity. If we are going to look at 'segregated areas' and try to form an impression of how segregated they are, or an impression of how segregated they look, we may want a little practice at drawing neighborhood boundaries in random patterns.
Patterns, though, can be deceptive, and it is useful to have some measures of segregation or concentration or clustering or sorting. One possible measure is the average proportion of neighbors of like or opposite color. If we count neighbors of like color and opposite color for each of the 138 randomly distributed stars and zeros in Figure 7, we find that zeros on the average have 53% of their neighbors of the same color, stars 46%. (The percentages can differ because stars and zeros can have different numbers of blank neighboring spaces.)
There are, of course, many regular patterns that would yield everybody a set of neighbors half his own color and half the opposite color. Neglecting blank spaces for the moment, a checkerboard pattern will do it; alternate diagonal lines of stars and zeros will do it; dividing the board into 2x2 squares of four cells each, and forming a checkerboard out of these four-cell squares, will also yield everybody four neighbors of like color and four of opposite. And so forth. Patterning is evidently related to, but distinct from, any measures of neighborhood homogeneity that we may work out.
Patterning—departure from randomness—will prove to be characteristic of integration, as well as of segregation, if the integration results from Choice and not chance.
Now play the game of solitaire. […]