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Unformatted text preview: Homework 8: The Schelling Experiment In 1971, Thomas C. Schelling performed the following experiment. Consider a population which consists of 2 different groups of people, let us call them reds and blues. On a rectangular grid randomly assign to each position either a 1 (for a red) or a 0 (for a blue). Each individual will be content, and not wish to move, if a certain percentage of its immediate neighbors are of the same type. Initially, we will determine immediate neighbors as those who live to the right, left, above, or below the individual. For the purpose of the experiment consider the left and right (and top and bottom) edges of the overall square as adjacent, - as if they live on a torus. Now consider an individual discontented if more than two-thirds of his neighbors are unlike itself. So, for instance, a red with three blue immediate neighbors will be inclined to move. But if red has 2 (or fewer) blue immediate neighbors, red is content and will not move. Survey the population and determine the reds and blues who wish to move - and then have them exchange positions. Should there be an unequal number of discontented reds and blues, exchange as many positions as possible (using a random selection - or lottery). Once this is complete survey the population again to determine who wishes to move, exchange more reds and blues, and continue the process indefinitely. Generally, after several iterations, we reach a distribution where no moves are possible. This may happen if all reds or all blues are finally content, and no movement is possible. Also, the experiment may at times result in very small numbers of reds and blues interchanging positions indefinitely - they will never...
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