Schelling Model Of Segregation Research Articles

Aging effects in Schelling segregation model

The Schelling model has become a paradigm in social sciences to explain the emergence of residential spatial segregation, even in the presence of high tolerance to mixed neighborhoods by the side of citizens. In particular, we consider a noisy constrained version of the Schelling model, in which agents maximize its satisfaction, related to the composition of the local neighborhood, by infinite-range movements towards satisfying vacancies. We add to it an aging effect by making the probability of agents to move inversely proportional to the time they have been satisfied in their present location. This mechanism simulates the development of an emotional attachment to a location where an agent has been satisfied for a while. The introduction of aging has several major impacts on the model statics and dynamics: the phase transition between a segregated and a mixed phase of the original model disappears, and we observe segregated states with a high level of agent satisfaction even for high values of tolerance. In addition, the new segregated phase is dynamically characterized by a slow power-law coarsening process similar to a glassy-like dynamics.

Exploring Simulated Residential Spending Dynamics in Relation to Income Equality with the Entropy Trace of the Schelling Model

The Schelling model of segregation has provided researchers with a simple model to explore residential dynamics and their implications upon the spatial distribution of resident identities. Due to the simplicity of the model, many modifications and extensions have been produced to capture different aspects of the decision process taken when residents change locations. Research has also involved examining different metrics for track segregation along the trace of the simulation states. Recent work has investigated monitoring the simulation by estimating the entropy of the states along the simulation, which offers a macroscopic perspective. Drawing inspiration from empirical studies which indicate that financial status can affect segregation, a dual dynamic for movements based on identity and financial capital has been produced so that the expenditure of a monetary value occurs during residential movements. Previous work has only considered a single approach for this dynamic and the results for different approaches are explored. The results show that the definition of the expenditure dynamic has a large effect on the entropy traces and financial homogeneity. The design choice provides insight for how the housing market can drive inequality or equality.

A model simulation of political segmentation through an estimation of the entropy

The interconnectivity of a global communication system has allowed exchanges of ideas and expression producing a plethora of positive results. There have also been notable exceptions where clashes of ideas produce friction between people and even violence in the effort to dominate a political discourse. Various models have been proposed on how these ideas arise, grow and interact with each other. This paper explores how the Schelling model of segregation can be modified to represent ideological states and from this new formulation is proposed to assess the entropic trajectory of its simulation. The simple yet expressive model proposed is modified where simulations are monitored from the entropic measures of the system based upon ideological interactions and movements. A key result is that the entropy displays spikes due to randomized outside influences, and that the total entropy of the system decreases. This provides insight into how a system of politically engaged agents can be monitored for stability.

Incorporating a monetary variable into the Schelling model addresses the issue of a decreasing entropy trace

The Schelling model of segregation has been shown to have a simulation trace which decreases the entropy of its states as the aggregate number of residential agents surrounded by a threshold of equally labeled agents increases. This introduces a paradox which goes against the second law of thermodynamics that states how entropy must increase. In the efforts to bring principles of physics into the modeling of sociological phenomena this must be addressed. A modification of the model is introduced where a monetary variable is provided to the residential agents (sampled from reported income data), and a dynamic which acts upon this variable when an agent changes its location on the grid. The entropy of the simulation over the iterations is estimated in terms of the aggregate residential homogeneity and the aggregate income homogeneity. The dynamic on the monetary variable shows that it can increase the entropy of the states over the simulation. The path of the traces with both variables in the results show that the shape of the region of entropy is followed supporting that the decrease of entropy due to the residential clustering has a parallel and independent effect increasing the entropy via the monetary variable.

Intriguing effects of underlying star topology in Schelling's model with blocks.

We explore the intriguing effects of the underlying star topological structure in the framework of Schelling's segregation model with blocks. The significant consequences exerted by the star topology are both theoretically analyzed and numerically simulated with and without introducing a fraction of altruistic agents, respectively. The collective utility of the model with egoists alone can be optimized and the optimum stationary state is achieved with the underlying star topology of blocks. More surprisingly, once a proportion of altruists is introduced, the average utility gradually decreases as the fraction of altruists increases. This presents a sharp contrast to the results in Schelling's model with a lattice topology of blocks. Furthermore, an adding-link mechanism is introduced to bridge the gap between the lattice and the star topologies and extend our analysis to more general scenarios. A scaling law of the average utility function is found for the star topology of blocks.

Segregation dynamics with reinforcement learning and agent based modeling

Societies are complex. Properties of social systems can be explained by the interplay and weaving of individual actions. Rewards are key to understand people’s choices and decisions. For instance, individual preferences of where to live may lead to the emergence of social segregation. In this paper, we combine Reinforcement Learning (RL) with Agent Based Modeling (ABM) in order to address the self-organizing dynamics of social segregation and explore the space of possibilities that emerge from considering different types of rewards. Our model promotes the creation of interdependencies and interactions among multiple agents of two different kinds that segregate from each other. For this purpose, agents use Deep Q-Networks to make decisions inspired on the rules of the Schelling Segregation model and rewards for interactions. Despite the segregation reward, our experiments show that spatial integration can be achieved by establishing interdependencies among agents of different kinds. They also reveal that segregated areas are more probable to host older people than diverse areas, which attract younger ones. Through this work, we show that the combination of RL and ABM can create an artificial environment for policy makers to observe potential and existing behaviors associated to rules of interactions and rewards.

An extension of Schelling's segregation model: Modeling the impact of individuals’ intolerance in the presence of resource scarcity

Individuals often form their identity based on their membership in a group and may exhibit a bias towards favoring members of the in-group (Greenwald and Pettigrew, 2014). When resources are plentiful, individuals are more likely to be tolerant of members of out-group sharing the resources. However, when there is a scarcity of resources, the resource stress could lead to a negative attitude towards members of the out-group as sharing of resources may be viewed as a zero-sum game. Schelling's spatial proximity model (Schelling, 1971; Schelling, 1978) shows how residential segregation emerges even when households only have a slight preference for members of their in-group. The original formulation by Schelling as well as many of its extensions have assumed that the amount of space available to agents to relocate was fixed. Agents' preference for members of the in-group also had been assumed to be invariant during the simulation run. This paper presents an extension of Schelling's model by relaxing these two assumptions to focus on the context of growing scarcity of environmental resources (e.g. habitable land) and the resulting decline in the tolerance for members of the out-group. Drawing upon theories in social psychology, it was assumed that declining resources lead to lower tolerance for members of the out-group as this scarce resource had to be shared. An agent-based simulation examined the impact of varying the degree of intolerance towards members of the out-group on the level of segregation in an artificial society. Several what-if scenarios were analyzed where the availability of an environmental resource (habitable land) declined over time. It was observed that with a high degree of intolerance towards members of the out-group, the degree of segregation in an artificial society while increasing initially became unsustainable and the highly segregated clusters eventually disintegrated.

Scaling limits of the Schelling model

The Schelling model of segregation, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous clusters of one type. In this model, vertices in an N-dimensional lattice are initially assigned types randomly. As time evolves, the type at a vertex v has a tendency to be replaced with the most common type within distance w of v. We present the first mathematical description of the dynamical scaling limit of this model as w tends to infinity and the lattice is correspondingly rescaled. We do this by deriving an integro-differential equation for the limiting Schelling dynamics and proving almost sure existence and uniqueness of the solutions when the initial conditions are described by white noise. The evolving fields are in some sense very “rough” but we are able to make rigorous sense of the evolution. In a key lemma, we show that for certain Gaussian fields h, the supremum of the occupation density of $$h-\phi $$ at zero (taken over all 1-Lipschitz functions $$\phi $$) is almost surely finite, thereby extending a result of Bass and Burdzy. In the one dimensional case, we also describe the scaling limit of the limiting clusters obtained at time infinity, thereby resolving a conjecture of Brandt, Immorlica, Kamath, and Kleinberg.

Segregation model for dynamic frequency allocation

We apply the Schelling segregation model to the dynamic frequency allocation. An algorithm is introduced for agents segregation over initially unknown radio channels. We relate the number of algorithm iterations until complete agents' segregation to the number of agents, networks, and the other parameters via numerical experiment.

Examining the Schelling Model Simulation through an Estimation of Its Entropy.

The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.

Axiomatic Theory and Simulation: A Philosophy of Science Perspective on Schelling's Segregation Model

The paper uses Schelling’s famous segregation model and a number of extensions to show how a reconstruction of the theory behind these models along the lines of the ‘non-statement view’ on empirical science can contribute to a better understanding of these models and a more straightforward implementation. A short introduction to the procedure of reconstructing a theory is given, using an extremely simple theory from mechanics. The same procedure is then applied to Schelling’s segregation theory. A number of extensions to Schelling’s model are analysed that relax the original idealisations, such as adding dierent tolerance levels between the two subpopulations, assuming inhomogeneous subpopulations and heterogeneous experiences of neighbourhoods, among others. Finally, it is argued that a ‘non-statement view’ reconstruction of a mental model or a verbally expressed theory are relevant for a useful specification for a simulation model.

An agent-based prediction market: a case study of xFuture in Taiwan

This study adopted an agent-based modelling approach to investigate results of the world's leading Chinese prediction market, xFuture; in particular, Taiwan's 2008 and 2012 presidential elections. Real transaction results of xFuture were used as the base model. We employed double auction mechanism and Schelling's segregation model, and attempted to reconstruct the networking structures of the prediction market in 2008 and 2012. Purpose of this study is to discuss whether networking structures have any deterministic influence on how individual and hence joint belief distribution of participants could be formed. It is found that certain belief distribution properties, including shape, spread and location, could be critical factors for market efficiency/inefficiency. Our analysis suggested that in 2012 xFuture participants' belief distributions for the main candidates were associated with high kurtosis, small variance and approximate means. In other words, it might have a higher probability to deviate from the true outcome.

A Self-adaptive Algorithm for Topology Matching in Unstructured Peer-to-Peer Networks

Peer-to-peer networks are overlay networks that are constructed over underlay networks. These networks can be structured or unstructured. In these networks, peers choose their neighbors without considering underlay positions, and therefore, the resultant overlay network may have a large number of mismatched paths. In a mismatched path, a message may meet an underlay position several times, which causes redundant network traffic and end-to-end delay. In some of the topology matching algorithms called the heuristic algorithms, each peer uses a local search operator for gathering information about the neighbors of that peer located in its neighborhood radius. In these algorithms, each peer also uses a local operator for changing the connections among the peers. These matching algorithms suffer from two problems; neither the neighborhood radius nor the local operator can adapt themselves to the dynamicity of the network. In this paper, a topology matching algorithm that uses learning automata to adapt the neighborhood radius and an adaptation mechanism inspired from the Schelling segregation model to manage the execution of the local operator is proposed. To evaluate the proposed algorithm, computer simulations were conducted and then the results were compared with the results obtained for other existing algorithms. Simulation results have shown that the proposed algorithm outperforms the existing algorithms with respect to end-to-end delay and number of mismatched paths.

Emergent Segregation through Homophilic Imitation: The Case of School Choice

Segregation by ethnicity, income and other factors still continues in many areas of life. Its prevalence is usually explained by some variation of Schelling's preference-based segregation model. Here we suggest and test a different individual-level mechanism that potentially generates emergent segregation: homophilic imitation. We assume that people tend to mimic choices of those similar to them. We study this mechanism in the context of school choice. To test our hypothesis we use a model of social decision making that describes how individuals estimate the quality of potential choices from the observed actions of others, and how these estimates can be used to predict further actions. Using methods of Bayesian inference, along with individual-level school choices extracted from Norwegian government register data, we establish how homophily influences choice imitation behaviour, particularly in the context of free school choice policy, which then contributes to segregation.

Dynamics of the Schelling Social Segregation Model in Networks

Thomas C. Schelling introduced a simple mathematical model to address the phenomenon of social segregation as a consequence of a natural evolution of elementary local rules. This model became a good framework to understand how local rules, like the selection of a better neighborhood for life, can produce macro-behaviors, like segregation in a population with different kind of individuals. In this work, with the aid of the Schelling's model, we characterize the dynamical evolution of segregation in random networks; analyze the performance of some segregation indices and the dynamics of this model for various network degrees. Finally, we provide probabilistic arguments to explain quantitatively the behavior of the dynamic of Schelling's segregation model in networks.

Simulation and similarity: using models to understand the world

Contents Preface 1 Introduction 1.1 Two Aquatic Puzzles 1.2 Models of Modeling 2 Three Kinds of Models 2.1 Concrete Model: The San Francisco Bay-Delta Model 2.2 Mathematical Model: Lotka-Volterra Model 2.3 Computational Model: Schelling's Segregation Model 2.4 Common Features of these Models 2.5 Only Three Types of Models? 2.6 Fewer Than Three Types of Model? 3 The Anatomy of Models: Structure & Construal 3.1 Structure 3.1.1 Concrete Structures 3.1.2 Mathematical 3.1.3 Computational 3.2 Model Descriptions 3.3 Construal 3.4 Representational Capacity of Structures 4 Fictions and Folk Ontology 4.1 Against Maths: Individuation, Causes, and Face Value Practice 4.2 A Simple Fictions Account 4.3 Enriching the Simple Account 4.3.1 Waltonian Fictionalism 4.3.2 Fictions without Models 4.4 Why I am not a Fictionalist 4.4.1 Variation 4.4.2 Representational Capacity of Different Models 4.4.3 Making Sense of Modeling 4.4.4 Variation in Practice 4.5 Folk ontology 4.6 Maths, Interpretation, and Folk Ontology 5 Target Directed Modeling 5.1 Model Development 5.2 Analysis of the Model 5.2.1 Complete Analysis 5.2.2 Goal-directed Analysis 5.3 Model/Target Comparison 5.3.1 Phenomena and Target Systems 5.3.2 Establishing the fit between Model and Target 5.3.3 Representations of Targets 6 Idealization 6.1 Three Kinds of Idealization 6.1.1 Galilean idealization 6.1.2 Minimalist idealization 6.1.3 Multiple Models Idealization 6.2 Representational Ideals and Fidelity Criteria 6.2.1 Completeness 6.2.2 Simplicity 6.2.3 1-Causal 6.2.4 Maxout 6.2.5 P-General 6.3 Idealization and Representational Ideals 6.4 Idealization and Target Directed Modeling 7 Modeling Without a Specific Target 7.1 Generalized Modeling 7.1.1 How Possibly Explanations 7.1.2 Minimal Models and First Order Causal Structures 7.2 Hypothetical Modeling 7.2.1 Contingent Non-existence: xDNA 7.2.2 Impossible Targets: Infinite Population Growth and Perpetual Motion 7.3 Targetless Modeling 7.4 A Moving Target: The Case of Three-sex Biology 8 An Account of Similarity 8.1 Desiderata for Model/World Relations 8.2 Model Theoretic Accounts 8.3 Similarity 8.4 Tversky's Contrast Account 8.5 Attributes and Mechanisms 8.6 Feature Sets, Construals, and Target Systems 8.7 Modeling Goals and Weighting Parameters 8.8 Weighting Function and Background Theory 8.9 Satisfying the Desiderata 9 Robustness Analysis and Idealization 9.1 Levins and Wimsatt on Robustness 9.2 Finding Robust Theorems 9.3 Three Kinds of Robustness 9.3.1 Parameter Robustness 9.3.2 Structural Robustness 9.3.3 Representational Robustness 9.4 Robustness and Confirmation 10 Conclusion: The Practice of Modeling References

Enabling Digital Earth simulation models using cloud computing or grid computing – two approaches supporting high-performance GIS simulation frameworks

Geospatial simulation models can help us understand the dynamic aspects of Digital Earth. To implement high-performance simulation models for complex geospatial problems, grid computing and cloud computing are two promising computational frameworks. This research compares the benefits and drawbacks of both in Web-based frameworks by testing a parallel Geographic Information System (GIS) simulation model (Schelling's residential segregation model). The parallel GIS simulation model was tested on XSEDE (a representative grid computing platform) and Amazon EC2 (a representative cloud computing platform). The test results demonstrate that cloud computing platforms can provide almost the same parallel computing capability as high-end grid computing frameworks. However, cloud computing resources are more accessible to individual scientists, easier to request and set up, and have more scalable software architecture for on-demand and dedicated Web services. These advantages may attract more geospatial scientists to utilize cloud computing for the development of Digital Earth simulation models in the future.

Expanding a System of Systems Model with the Schelling Segregation Model

ABSTRACTThe Schelling segregation model is a well‐established representation of social issues in a neighbourhood. On the basis of the systems approach, a model of system of systems (SoS) that is validated through comparison with the Schelling model and applies to more neighbourhoods is proposed. The systems model of an SoS empirically demonstrates the potential for conflict to arise as the autonomy of systems within a geographically distributed SoS increases. The results may contribute to future international policy as well as ecological management. Copyright © 2012 John Wiley & Sons, Ltd.

The Schelling Model of Ethnic Residential Dynamics: Beyond the Integrated - Segregated Dichotomy of Patterns

The Schelling model of segregation is an agent-based model that illustrates how individual tendencies regarding neighbors can lead to segregation. The model is especially useful for the study of residential segregation of ethnic groups where agents represent householders who relocate in the city. In the model, each agent belongs to one of two groups and aims to reside within a neighborhood where the fraction of 'friends' is sufficiently high: above a predefined tolerance threshold value F. It is known that depending on F, for groups of equal size, Schelling's residential pattern converges to either complete integration (a random-like pattern) or segregation. The study of high-resolution ethnic residential patterns of Israeli cities reveals that reality is more complicated than this simple integration-segregation dichotomy: some neighborhoods are ethnically homogeneous while others are populated by both groups in varying ratios. In this study, we explore whether the Schelling model can reproduce such patterns. We investigate the model's dynamics in terms of dependence on group-specific tolerance thresholds and on the ratio of the size of the two groups. We reveal new type of model pattern in which a portion of one group segregates while another portion remains integrated with the second group. We compare the characteristics of these new patterns to the pattern of real cities and discuss the differences.

UML for ABM

Although the majority of researchers interested in ABM increasingly agree that the most natural way to program their models is to adopt OO practices, UML diagrams are still largely absent from their publications. In the last 15 years, the use of UML has risen constantly, to the point where UML has become the de facto standard for graphical visualization of software development. UML and its 13 diagrams has many universally accepted virtues. Most importantly, UML provides a level of abstraction higher than that offered by OO programming languages (Java, C++, Python, .Net ...). This abstraction layer encourages researchers to spend more time on modeling rather than on programming. This paper initially presents the four most common UML diagrams - class, sequence, state and activity diagrams (based on my personal experience, these are the most useful diagrams for ABM development). The most important features of these diagrams are discussed, and explanations based on conceptual pieces often found in ABM models are given of how best to use the diagrams. Subsequently, some very well known and classical ABM models such as the Schelling segregation model, the spatial evolutionary game, and a continuous double action free market are subjected to more detailed UML analysis.