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2. The original Schelling model

Thomas Schelling’s segregation model (Schelling, 1969, 1971) is one of the first and most well known AB models: the description that follows is based on Gallegati and Richiardi (2009). In the original model whites and blacks are (randomly) located over a grid, each individual occupying one cell. As a consequence, each individual has at most 8 neighbors (Moore neighborhood), located on adjacent cells. Preferences over residential patterns are represented as the maximum quota of racially different neighbors that an individual tolerates. For simplicity, we can assume that preferences are identical: a unique number defines the level of tolerance in the population. For example, if the tolerance level is 50% and an individual has only five neighbors, he would be satisfied if no more than two of his neighbors are racially different. If an individual is not satisfied by his current location, he tries to move to a different location where he is satisfied. The model generates high level of segregation, even for relatively high levels of tolerance.

To correctly assess the importance of the model, it must be evaluated against the social and historical background of the time. Up to the end of the 1960s racial segregation was institutionalized in the United States. Racial laws required that public schools, public places and public transportation, like trains and buses, had separate facilities for whites and blacks. Residential segregation was also prescribed in some States, although it is now widely recognized that it mainly came about through organized, mostly private efforts to ghettoize blacks in the early twentieth century – particularly the years between the world wars (Farley, 1986; Muth, 1986). But if the social attitude was the strongest force in producing residential segregation, the Civil Right movement of the 1960s greatly contributed to a change of climate, with the white population exhibiting increasing levels of tolerance. Eventually, the movement gained such strength to achieve its main objective, the abolition of the racial laws: this was sealed in the Civil Rights Act of 1968 which, among many other things, outlawed a wide range of discriminatory conduct in housing markets. Hence, both the general public attitude and the law changed dramatically during the 1960s. As a consequence, many observers predicted a rapid decline in housing segregation. The decline, however, was almost imperceptible. The question then was why this had not happened. Schelling’s segregation model brought an answer, suggesting that small differences in tolerance level or initial location could trigger high level of segregation even without formal (i.e. legal) constraints, and even for decent levels of overall tolerance.

The mechanism that generates segregation is the following. Since individuals are initially located randomly on the grid, by chance there will be someone who is not satisfied. His decision to move creates two externalities: one in the location of origin and the other in the location of destination. For example, suppose a white individual decides to move because there are too many black people around. As he leaves, the ethnic composition of his neighborhood is affected (there is one white less). This increases the possibility that another white individual, who was previously satisfied, becomes eager to move. A similar situation occurs in the area of destination. The arrival of a white individual affects the ethnic composition of the neighborhood, possibly causing some black individual to become unsatisfied. Thus, a small non-homogeneity in the initial residential pattern triggers a chain effect that eventually leads to high levels of segregation. This mechanism is reinforced when preferences are not homogeneous in the population.

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