Dynamic Models of Segregation - Thomas C. Shelling
Thomas Schelling in the late 1960s and early 1970s set out to investigate segregation effects with a specific interest in racial segregation produced by individual behaviour (independent of potentially further organized behaviour or economical effects like separating rich from poor, educated from uneducated etc. or even other additional effects and behaviours). Ultimately, his analysis extended to a general level where his effects and theory could be reproduced and would be applicable in any environment where the distinction of the examined variable (like in this case race) is two-fold (black or white), exhaustive (everybody is either black or white), and recognizable (it is externally obvious if somebody is black or white). In his own words: "This paper, then, is about those mechanisms that translate unorganized individual behavior into collective results." (page 3).
Roughly, the paper is divided into two parts. In the first part Shelling simply considers the individual as happy or unhappy with his current neighbourhoods distribution. If at least 50% of somebody's neighbours are the same color of him he is happy and stays. If less than 50% are of the same race he moves somewhere else (Note that every position can either be white, black or currently empty). Shelling then analyzed how this played out over a certain time period with people moving or staying based on this logic.
Several further variations were analyzed including "Intensity of Demand for Like Neighbors" (preference not simply min. 50% but other distributions like minimum 33% etc.), "Unequal Demands" (Blacks and Whites have different preferences like Whites min. 50% and Blacks min. 33%), "Unequal Numbers, Equal Demands" (symmetrical preferences but not the same number of Blacks and Whites in the population), "Size of Neighborhood" (how far-reaching the neighborhood is defined, immediate neighbors only or further additional neighbors as well), "Congregationist Preferences" and "Integrationist Preferences" (minimum number of other race people required to be happy). Furthermore, effects regarding the "Population Densities" of states were analyzed (how many spaces remained unoccupied after both groups reached satisfactory distributions).
Key results were that there were much stronger segregation effects of "ratios of like neighbors to opposite neighbors [...] upwards of four to one for demands of one-half or more [instead of two to one which 50% would naively suggest], and less than 1.5 for demands of about one-third [i.e. typically minimum 4.5 instead of about 3 out of 9 being the same color for that constraint]." (page 16/17)
Furthermore, it became obvious that there is a strong tendency that "everybody [...] moves toward whatever cluster of like-colored individuals he can find; and the number of such clusters declines disproportionately as the minority becomes smaller. The result is that the minority forms larger clusters, large enough to cause even a tolerant majority to become locally dissatisfied." (page 19) As these clusters are the only clusters which satisfy the minorities search for similar individuals this additionally increases the density in such spots (i.e. not only the Black/White ratio changes but also the number of unoccupied spots drastically declines) and further amplifies the segregation effect beyond the otherwise from a macro perspective required level. Concerted action could avoid this but as under this model everybody solely acts from his individual perspective it is not possible to create smaller alternate clusters satisfying everybody's individual requirements.
In the second part of his paper Shelling analyzed just one bigger neighborhood with people either being in the neighborhood or outside of it. In this section he analyses population groups and their preferences across a continuuom of completely tolerant to completely intolerant attitudes. In this section of the paper he moves from looking at individual actors and determining their action independently for every one of them according to the rules of the model towards solely focusing on ratios. Again, he shows that there usually is an equilibrium in the extremes (pure White or pure Black populations). Based on the distribution of tolerance and size as well as after introducing some other measures like an externally enforced constraint of a maximum number of residents of a certain type there can also be other equilibrium states which are mixed. He notes though, that in general, "for a stable mixture, the minority must be the more tolerant of the two groups." (page 37)
Finally, Shelling finishes this section with some observations regarding tipping points. His model shows that while tipping can occur as a cumulative effect of natural turn-over, limited supply (if the initial neighborhood didn't have any unoccupied spaces) or other cases (e.g. in some cases there might be a big pool of potentially interested people from the other group to move into this neighborhood while in other cases moving in from the other group would be purely accidental or coincidental), this effect is independent of the actual tolerance value. "In none of the cases shown does any important discontinuity necessarily occur at the modal or typical tolerance value." (page 40)
Read the full paper here: http://www.stat.berkeley.edu/~aldous/157/Papers/Schelling_Seg_Models.pdf
