Schelling's Spatial Proximity Model of Segregation Revisited

Pancs, Romans; Vriend, Nicolaas J.

doi:10.2139/ssrn.375080

Cited by 26 publications

(32 citation statements)

References 15 publications

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“…3 Schelling concluded that small preferences for similarity can lead to massive segregation. This conclusion is quite robust across many changes to the model, including different utility functions (Zhang 2004;Bruch and Mare 2006;Pancs and Vriend 2007), different rules for updating (Bruch and Mare 2006), differing neighborhood sizes, and different spatial configurations (Fossett and Dietrich 2009). These studies show that it is extremely hard to avoid segregation when agents have some preference for like neighbors.…”

Section: Schelling's Models Of Segregation Thomas Schelling Famouslymentioning

confidence: 73%

Segregation That No One Seeks

Muldoon¹,

Smith²,

Weisberg³

2012

Philos. of Sci.

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This article examines a series of Schelling-like models of residential segregation, in which agents prefer to be in the minority. We demonstrate that as long as agents care about the characteristics of their wider community, they tend to end up in a segregated state. We then investigate the process that causes this and conclude that the result hinges on the similarity of informational states among agents of the same type. This is quite different from Schelling-like behavior and suggests (in his terms) that segregation is an instance of macrobehavior that can arise from a wide variety of micromotives.

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Section: Schelling's Models Of Segregation Thomas Schelling Famouslymentioning

confidence: 73%

Segregation That No One Seeks

Muldoon¹,

Smith²,

Weisberg³

2012

Philos. of Sci.

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“…To perform this maximization procedure, we follow standard physics methods used in the study of phase transitions [like liquid-vapor coexistence (18)], which can be summarized as follows. If f (ρ) coincides with its concave hull at a given density ρ 0 , then the state of the city is homogeneous, and all blocks have a density ρ 0 .…”

Section: Resultsmentioning

confidence: 99%

“…To illustrate the dramatic influence of the cooperativity parameter α, we use the asymmetrically peaked utility function (18), which indicates that agents prefer mixed blocks (Fig. 2).…”

Section: Resultsmentioning

confidence: 99%

Competition between collective and individual dynamics

Grauwin

Bertin²,

Lemoy

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

110

135

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Linking microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: Although physical particles are assumed to optimize the global energy, economic agents maximize their own utility. Here, we solve exactly a Schellinglike segregation model, which interpolates continuously between cooperative and individual dynamics. We show that increasing the degree of cooperativity induces a qualitative transition from a segregated phase of low utility toward a mixed phase of high utility. By introducing a simple function that links the individual and global levels, we pave the way to a rigorous approach of a wide class of systems, where dynamics are governed by individual strategies.socioeconomy | statistical physics | segregation | phase transition | coordination T he intricate relations between the individual and collective levels are at the heart of many natural and social sciences. Different disciplines wonder how atoms combine to form solids (1, 2), neurons give rise to consciousness (3, 4), or individuals shape societies (5, 6). However, scientific fields assume distinct points of view for defining the "normal", or "equilibrium", aggregated state. Physics looks at the collective level, selecting the configurations that minimize the global free energy (2). In contrast, economic agents behave in a selfish way, and equilibrium is attained when no agent can increase its own satisfaction (7). Although similar at first sight, the two approaches lead to radically different outcomes.In this paper, we illustrate the differences between collective and individual dynamics on an exactly solvable model similar to Schelling's segregation model (8). The model considers individual agents that prefer a mixed environment, with dynamics that lead to segregated or mixed patterns at the global level. A "tax" parameter monitors continuously the agents' degree of altruism or cooperativity, i.e., their consideration of the global welfare. At high degrees of cooperativity, the system is in a mixed phase of maximal utility. As the altruism parameter is decreased, a phase transition occurs, leading to segregation. In this phase, the agents' utilities remain low, in spite of continuous efforts to maximize their satisfaction. This paradoxical result of Schelling's segregation model (8) has generated an abundant literature. Many papers have simulated how the global state depends on specific individual utility functions, as reviewed by ref. 9. There have been attempts at solving Schelling's model analytically, in order to provide more general results (10, 11). However, these approaches are limited to specific utility functions. More recently, physicists have tried to use a statistical physics approach to understand the segregation transition (12-14). The idea seems promising because statistical physics has successfully bridged the micro-macro gap for physical systems governed by collective dynamics. However, progress was slowed by lack of an appr...

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“…After the publication of Schelling's model, several studies (see e.g. Fossett and Dietrich, 2009, Pancs and Vriend, 2007, and Zhang, 2004 have documented the robustness of Schelling's result across a wide range of modifications in his model (e.g. think of changes in neighbourhood sizes, spatial configurations, and individuals' tolerance thresholds for individuals of a different type).…”

Section: Schelling's Checkerboard Modelmentioning

confidence: 99%

Why We Cannot Learn from Minimal Models

Fumagalli

2015

Erkenn

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Philosophers of science have developed several accounts of how consideration of scientific models can prompt learning about real-world targets. In recent years, various authors advocated the thesis that consideration of so-called minimal models can prompt learning about such targets. In this paper, I draw on the philosophical literature on scientific modelling and on widely cited illustrations from economics and biology to argue that this thesis fails to withstand scrutiny. More specifically, I criticize leading proponents of such thesis for failing to explicate in virtue of what properties or features minimal models supposedly prompt learning and for substantially overstating the epistemic import of minimal models. I then examine and refute several arguments one may put forward to demonstrate that consideration of minimal models can prompt learning about real-world targets. In doing so, I illustrate the implications of my critique for the wider debate on the epistemology of scientific modelling.

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Schelling's Spatial Proximity Model of Segregation Revisited

Cited by 26 publications

References 15 publications

Segregation That No One Seeks

Segregation That No One Seeks

Competition between collective and individual dynamics

Why We Cannot Learn from Minimal Models

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