Neighborhoods and Individual Preferences: A Markovian Model

Shripad Tuljapurkar, Stanford University
Elizabeth E. Bruch, University of Michigan
Robert D. Mare, University of California, Los Angeles

Demographers have a longstanding interest in the relationship between individual behavior and collective outcomes. Schelling’s (1971; 1978) seminal work shows that even relatively tolerant individuals may collectively produce segregated neighborhoods. More recently, Bruch and Mare (2006) use an agent-based (microsimulation) model to examine the implications of different assumptions about how individuals evaluate neighborhoods (based on their race/ethnic composition) for spatial inequality. Their model yields useful insights but is complex. Here we illuminate many aspects of their (and related) work using a simplified Markov model of individual choice. We obtain an exact condition for the minimum strength that individual preferences must have in order to yield stable segregation patterns. Thus we can relate observed preferences to observed macrolevel patterns of differentiation. We also show that under Schelling-type rules, segregation is the only stable equilibrium. We argue that formal models are useful in studying the relationship between individual choices and population-level outcomes.