EMBARGOED UNTIL 5 P.M. DECEMBER 4, 2006

PRINCETON, N.J., December 4, 2006 – A new study in the Proceedings of the National Academy of Science (PNAS) written by Dejan Vinković, a physicist and former Member in the School of Natural Sciences and current Visitor in the Program for Interdisciplinary Studies at the Institute for Advanced Study, and Alan Kirman, an economist from GREQAM, EHESS, Université d'Aix-Marseille, who was a Member of the Institute last year, brings a new insight into the Schelling model of socio-economic segregation in society. In this study, the team presents a mathematical link between Schelling’s model and models used for solving the physical problem of surface tension force in liquids and solids.

Segregation is an important sociological and economic phenomenon where people cluster together according to some shared similarity such as race, nationality, income or education level. Some 40 years ago, Thomas Schelling, who won last year's Nobel Prize in economics, suggested a simple model to explain this phenomenon. He constructed a model where individual housing properties are approximated with squares on a checkerboard. Squares are colored according to the race of the occupant. Then he played a game where people unhappy with their current neighborhood move to areas that they prefer. The result was surprising: even if individuals have a relatively mild preference for not being outnumbered by neighbors of a different color, total segregation may emerge.

Since Schelling introduced the model, many variants have been proposed and studied by economists and sociologists puzzled by this emergence of unintended macroscopic phenomena from seemingly small and uncoordinated individual actions. The study by Vinković and Kirman brings a new insight into these models, showing that the structure of the Schelling model is undistinguishable from models used for solving the physical problem of surface tension force in liquids and solids.

“Using this analogy, we reveal the mechanism that generates racial clustering and explain how the shape and stability of the clusters depend on the rules governing the movement of individuals and the amount of free space available,” Kirman explains. “As the appropriate parameters are changed the clustering can yield solids, liquids or glass-like structures. ”

Replacing people with lifeless particles may seem strange, but Vinković disagrees: “The intuition is simple. In the economic system people can be described as ‘unhappy’ or having ‘low utility.’ Economic models are, therefore, focused on increasing people's happiness or utility. In the physical system we are solving exactly the same problem, only the terminology is different; we deal with particles with high energies and systems which try to minimize their energy.”

“When dealing with people, the model creates city quarters populated by people with a similar attribute, while when dealing with particles, the model may create a crystal or a liquid droplet,” Kirman adds. “The liquid situation corresponds in the social model to one in which there are always people who are changing locations.”

The authors point out that their physics analogy can be used to examine the size, shape and evolution of the empirically observed segregated zones in cities and to compare these with the model's predictions. Moreover, similar clustering phenomena appear in other social animals and thanks to this analogy scientists can better understand the dynamics of such biological systems.

Contact:
Dejan Vinković: dejan_AT_ias.edu
Alan Kirman: alan.kirman_AT_univmed.fr

Preprint: Vinkovic, D. & Kirman, A. 2006, PNAS, 103(51), 19261 (PNAS, PDF)

According to the new study, just by looking at this model of red and blue moving squares we cannot say if this represents people in a town or particles in a liquid. This confusion is the basis for the analogy between models of social segregation and physical systems of surface tension force. (HighRes figure)