From Self-Orientation to Social Orientation: A Behavioral Extension of Schelling’s Segregation Model

From Self-Orientation to Social Orientation: A Behavioral Extension of Schelling’s Segregation Model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article From Self-Orientation to Social Orientation: A Behavioral Extension of Schelling’s Segregation Model Unjong Yu, Kyuho Jin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7780879/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted 16 You are reading this latest preprint version Abstract Schelling’s segregation model demonstrates how simple local rules can generate large-scale social patterns, yet it assumes agents act myopically and ignore the broader consequences of their moves. We extend this framework by introducing social orientation as a behavioral microfoundation, reflecting humans’ communal nature. Socially oriented agents follow boundedly rational heuristics that account for the satisfaction of prospective neighbors within a two-step horizon of observability, in addition to their own. We formalize this through three relocation rules—negative externality avoiding (NEA), positive externality favoring (PEF), and positive externality optimizing (PEO)—each capturing a different balance between minimizing disruption and promoting stability. Agent-based simulations reveal that these rules, while maintaining satisfaction, consistently reduce segregation, accelerate the attainment of global stability, and lower relocation moves per agent, thereby reducing social costs. These results provide a stronger behavioral foundation for segregation modeling and show how locally rational, socially sensitive decision-making can scale into equilibria that are not just welfare-enhancing but also yield more integrated and resilient communities. Physical sciences/Mathematics and computing Physical sciences/Physics Schelling’s segregation model Microfoundation Social orientation Externality Observability Bounded rationality Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 INTRODUCTION Schelling’s segregation model, first introduced in the late 1960s through a checkerboard thought experiment 1 , 2 , remains one of the most striking illustrations of how simple micro-level rules can yield surprising macro-level patterns. With only minimal assumptions about agents’ preferences—namely, that they are content with some diversity but dissatisfied with being in a minority—Schelling showed that large-scale segregation can emerge even when no agent desires it. This counterintuitive finding helped launch a broader research agenda on self-organization and unintended consequences, influencing not only economics and sociology but also the study of complexity and emergent order across the natural and social sciences 3 , 4 . Yet despite its enduring influence, the model’s stark simplicity leaves open important questions about the robustness of its insights under more realistic assumptions. Subsequent work has examined the model’s generalizability by relaxing its assumptions, particularly those concerning agents’ microfoundations 5 – 9 . One microfoundation that has been relatively overlooked is that humans are inherently social beings. At their core, people are homo sociologicus 10 , 11 —defined by a fundamental inclination to form and belong to groups, with decisions shaped by communal considerations. From this perspective, a neighborhood is not merely a physical residence but also functions as a social community that builds and sustains mutually beneficial social capital through repeated interactions 12 – 19 . Accordingly, frequent turnover of neighbors signals the erosion of such capital, diminishing the neighborhood’s value as a social group and reducing it to little more than a residence 17 , 18 , 20 – 23 . For socially oriented agents, neighborhoods that risk this kind of degeneration after their move are correspondingly less attractive relocation options. Consequently, they avoid moves that generate negative externalities—destabilizing the community, particularly by prompting prospective neighbors to leave—even if such moves would satisfy them. Instead, they choose moves that generate positive externalities, thereby stabilizing the community and sustaining social capital. By contrast, agents in Schelling’s original model are essentially homo economicus and abstract away from these dynamics 24 , 25 . They evaluate neighborhoods myopically, moving into any vacant site that meets their threshold in the moment, without regard for the destabilizing externalities of relocation. In doing so, they treat satisfaction as purely individualistic and assume away interdependent neighborhood social dynamics—a stylized simplification that diverges from real-world decision-making. To address this gap, we extend Schelling’s model by introducing a "social orientation" to its microfoundations, complementing the original focus on self-orientation. In our formulation, socially oriented agents seek both self-serving and community-preserving locations; they select sites where their move not only satisfies their own preferences but also minimizes dissatisfaction (and thus disruption) and/or enhances the satisfaction (and thus stability) of the prospective neighborhood. In essence, these agents aim to reduce negative externalities and/or increase positive ones. This orientation reflects the valuation of neighborhoods not merely as locations, but as cohesive social communities that foster a shared identity 17 , 18 , 26 . We operationalize this behavior through three heuristic relocation rules based on the prospective neighbors’ satisfaction: Negative Externality Avoiding Rule (NEA) : Agent relocates to a site that satisfies their threshold and does not dissatisfy any currently satisfied neighbors, choosing randomly among such sites. Positive Externality Favoring Rule (PEF) : Agent relocates to a site that satisfies their threshold and generates non-negative externalities by increasing (or at least not reducing) the number of satisfied neighbors, choosing randomly among such sites. Positive Externality Optimizing Rule (PEO) : Agent relocates to a site that satisfies their threshold, generates non-negative externalities by increasing (or at least not reducing) the number of satisfied neighbors and minimizes the number of unsatisfied neighbors, with ties broken at random. All these rules begin with the agent’s own satisfaction—a self-oriented criterion—but then extend it with a layer of social orientation, each in a different way. NEA focuses on avoiding negative externalities by preventing moves that would cause currently satisfied neighbors to become dissatisfied, while still permitting unsatisfied neighbors either to become satisfied or to relocate. This reflects the view that satisfied neighbors are key contributors to the cultivation and maintenance of social capital. PEF , in contrast, aims to increase—or at least not reduce—the total number of satisfied neighbors. The emphasis here is on aggregate numbers, so some switches between satisfied and unsatisfied neighbors may occur, provided the overall count of satisfied neighbors is maintained or improved. In contrast to the previous two rules, PEO maximizes positive externalities by considering both satisfied and unsatisfied neighbors: it is similar to PEF but adds the condition of minimizing the number of unsatisfied neighbors. In doing so, PEO can increase the number of satisfied neighbors, subject to minimizing the number of unsatisfied ones. Notably, deeper insight into these rules can be gained by viewing them through the lens of Pareto efficiency 27 , 28 , a widely used concept in economics. Among them, NEA is strictly Pareto-improving, as it satisfies the moving agent without making others worse off. By contrast, PEF and PEO relax this criterion by focusing on aggregate satisfaction, aligning more with a utilitarian logic than with strict Pareto improvement. Whereas NEA favors stability by preserving satisfied neighbors, PEF and PEO are expected to reduce turnover more proactively by converting unsatisfied neighbors into satisfied ones. Implementing this microfoundation requires refining two implicit assumptions of the original model. The first concerns agents’ observability. In Schelling’s formulation, agents consider only their immediate neighbors, leaving the scope of perception irrelevant. By contrast, socially oriented agents must anticipate how their relocation affects not only themselves but also the satisfaction of prospective neighbors. This requires observing neighbors of neighbors—a form of two-step observability, or horizon of observability, which has empirical support in studies of social influence and network perception 29 . The second refinement concerns agents’ bounded rationality 30 – 33 . In the original model, agents resemble automata, following simple threshold rules with no capacity for foresight. In our extension, by contrast, agents more closely approximate rational decision makers in that they can evaluate prospective neighborhoods and select sites that optimize future social spillovers. Yet their rationality remains bounded by limited information and computational constraints: they cannot access global knowledge or compute system-wide optima 34 , 35 . Instead, they rely on local heuristics 36 , 37 —such as the relocation rules we propose—behaving as greedy searchers within their horizon of observability 38 , 39 . These two behavioral refinements underpin social orientation by allowing agents to anticipate the communal consequences of their moves while remaining subject to realistic cognitive and informational limits. They also make the model more realistic and provide the foundation for our simulation analysis of how social orientation alters segregation dynamics. More broadly, modeling social orientation refines theoretical understanding and highlights implications for the stability and diversity of social systems. In the following section, we outline how these rules are implemented in our extended Schelling model. Our aim is to examine how social orientation alters relocation behavior and, in turn, shapes dynamical outcomes including segregation. To this end, we adapt the classic model to incorporate agents who follow NEA, PEF, PEO, or Schelling’s original relocation rule. We then outline the modeling framework, agent decision rules, and simulation design used to compare these approaches. METHODS To evaluate the role of social orientation in segregation dynamics, we extend Schelling’s original agent-based model of residential mobility. As noted, our extension is based on two behavioral refinements–two-step observability and bounded rationality–allowing agents to anticipate potential neighborhood instability based on local information and avoid moves that could generate dissatisfaction among the prospective neighbors. We systemically assess how individual-level social orientation shapes macro-level outcomes of segregation, satisfaction, and convergence speed. Relocation rules We consider three socially oriented relocation rules, with Schelling’s original rule¹ serving as a benchmark. The NEA , PEF , and PEO rules extend the model by incorporating agents’ socially oriented behavior to account for externalities. The stepwise procedures for each rule are summarized below: Negative Externality Avoiding (NEA) Rule Step 1. Randomly select one dissatisfied agent. Step 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not cause any currently satisfied neighbors to become unsatisfied. Step 3. If more than one such site exists, randomly choose one from this set. Step 4. Relocate the agent to this site. Positive Externality Favoring (PEF) Rule Step 1. Randomly select one dissatisfied agent. Step 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not reduce the number of currently satisfied neighbors. Step 3. If more than one such site exists, randomly choose one from this set. Step 4. Relocate the agent to this site. Positive Externality Optimizing (PEO) Rule Step 1. Randomly select one dissatisfied agent. Step 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not reduce the number of currently satisfied neighbors. Step 3. Among these sites, choose the site that leaves the fewest neighbors unsatisfied after relocation. Step 4. If more than one such site exists, randomly choose one from this set. Step 5. Relocate the agent to this site. NEA is primarily concerned with avoiding the turnover of currently satisfied neighbors, while giving little attention to unsatisfied neighbors. As a by-product, the rule may cause unsatisfied neighbors either to become satisfied or to relocate. In this sense, NEA aims to avoid the negative externalities associated with an agent’s relocation. PEF , by contrast, seeks to increase—or at least not decrease—the number of currently satisfied neighbors, without regard for the switching of unsatisfied neighbors so long as the overall number of satisfied neighbors increases in the prospective neighborhood. Accordingly, PEF is more concerned with generating positive externalities from an agent’s move. PEO integrates both perspectives by addressing positive and negative externalities simultaneously. Like PEF, it permits positive externalities by allowing unsatisfied neighbors to become satisfied, but it goes further by minimizing the number of unsatisfied neighbors rather than merely avoiding turnovers. Table 1 summarizes these distinctions. Table 1 Comparison of social oriented rules. NEA focuses narrowly on avoiding the turnover of satisfied neighbors, thereby minimizing negative externalities but disregarding unsatisfied ones. PEF, in contrast, prioritizes generating positive externalities by permitting unsatisfied neighbors to become satisfied, even if some turnover occurs. PEO integrates both perspectives: like PEF, it allows for positive spillovers, but it further minimizes the number of unsatisfied neighbors, making it the most balanced rule in terms of managing both positive and negative externalities. Rule Primary Focus Treatment of Neighbors Externality Orientation NEA Avoid turnover of currently satisfied neighbors Ignores unsatisfied neighbors; some may become satisfied or move out as a side effect Minimizes negative externalities (avoids new dissatisfaction) PEF Increase or at least not decrease the number of satisfied neighbors Allows unsatisfied neighbors to switch to satisfied; unconcerned with turnover if satisfaction increases overall Generates positive externalities (permits satisfaction gains) PEO Balance positive and negative externalities Like PEF, permits unsatisfied → satisfied switches, but also minimizes the number of unsatisfied neighbors Addresses both: permits positive externalities while minimizing negative ones It is worth noting that although the two-step observability in our model is farther-sighted than in the original, the three proposed rules still operate as local heuristics, since agents cannot anticipate consequences beyond their perceptual horizon. This property aligns with our goal of enhancing realism by modeling agents as boundedly rational actors who rely on such heuristics. Taken together, these rules allow us to explore a spectrum of socially oriented decision-making—from simple harm-avoidance to active community optimization. By doing so, we can systematically assess how these behavioral refinements impact macro-level outcomes. Formally, when considering a move to site \(\:i\) , an agent with two-step observability computes for each neighbor \(\:j\) the fraction of same-type neighbors as $$\:{h}_{j}\left(i\right)=\frac{1}{\left|N\left(j\right)\right|}\sum\:_{k\in\:N\left(j\right)}1\{{x}_{j}\left(i\right)={x}_{k}\left(i\right)\}$$ where \(\:N\left(j\right)\) denotes the set of neighboring agents of \(\:j\) , and \(\:{x}_{m}\left(i\right)\in\:\{-1,\:+1\}\) represents the occupant of site \(\:m\) after the focal agent is hypothetically relocated to site \(\:i\) . The indicator function \(\:1\{{x}_{j}\left(i\right)={x}_{k}\left(i\right)\}\) equals 1 if neighbor \(\:j\) and their neighbor \(\:k\) are of the same type following the relocation, and 0 otherwise. Accordingly, \(\:{h}_{j}\left(i\right)\) captures the updated fraction of same-type neighbors for each \(\:j\) , incorporating the agent’s prospective move. This assumption aligns with Friedkin’s empirical observation of the “horizon of observability,” which suggests that an individual’s social vision is limited and typically extends only to indirect social ties 29 . Consequently, agents can consider the broader consequences of their relocation on local neighborhood stability. Simulation design The model is implemented on a two-dimensional square lattice with periodic boundary conditions, so that agents at the edges are connected to those on the opposite side. Each cell can be occupied by a single agent or left vacant, and agents belong to one of two groups of equal size. A fixed vacancy ratio (20% unless otherwise noted) provides sufficient mobility for agents to relocate. At initialization, agents and vacancies are randomly assigned to sites on the grid. Time advances in asynchronous sequential updates, so that only one agent moves per step. The process continues until either (i) all agents are satisfied, or (ii) no further moves are possible because dissatisfied agents cannot find admissible sites. Outcome measures We track three primary outcomes. First, segregation is measured using the standard adjacency-based segregation index¹³: $$\:S=\frac{1}{2N}\sum\:_{i,j}{A}_{ij}{T}_{i}{T}_{j}$$ where \(\:N\) is the number of agents, \(\:A\) represents the adjacency matrix of the neighborhood structure, and \(\:{T}_{i}\:\) denotes the type of agent at site \(\:i\) (+ 1 or − 1 for occupied sites, 0 for vacancies). The segregation measure \(\:S\) takes positive values when the system exhibits segregation and negative values when it is integrated. The maximum value of S is \(\:{\Delta\:}/2\) in a \(\:{\Delta\:}\) -regular network as \(\:N\to\:\infty\:\) and the proportion of vacant site \(\:V=0\) . Notably, \(\:S\) is closely related to the energy \(\:E\) of the spin-glass model, satisfying the relation \(\:S=-E/N\) 40, 41 . Second, overall satisfaction is measured as the proportion of agents who meet their threshold condition at the end of the simulation. Third, stability is assessed by recording the number of relocation steps until equilibrium. Computational implementation The model was implemented in Python 3.12 using standard scientific libraries (NumPy, pandas, and matplotlib). Random number generation was controlled by fixed seeds for reproducibility. For each parameter configuration, we conducted 10,000 independent replications to account for stochastic variability. RESULTS Our simulations reveal that social orientation non-trivially alters the dynamics of Schelling’s segregation model. Under the original rule, the model reproduces Schelling’s classic finding: even moderate individual preferences lead to considerable segregation. By contrast, socially oriented relocation consistently reduces segregation and accelerates convergence to equilibrium (i.e., global stability) with fewer relocation steps, all while preserving full satisfaction. These results suggest that incorporating social orientation aligns individual-level decision-making with macro-level outcomes that enhance social integration, stability, and collective welfare. We present the results in three parts, focusing respectively on satisfaction outcomes, segregation outcomes, and equilibrium dynamics. Baseline parameters Unless otherwise specified, all simulations were conducted on a 32 × 32 grid with periodic boundary conditions, Moore neighborhoods, a vacancy ratio of 0.2, and a satisfaction threshold of 0.5. Each reported value represents the mean of 10,000 independent replications, with standard errors shown where applicable. These baseline settings provide a consistent reference point for evaluating how socially oriented relocation rules shape segregation outcomes. Baseline results are summarized in Table 2 . Table 2. Baseline simulation results under socially oriented relocation rules. Rule Satisfaction (%) Segregation Index (S) Convergence Steps Moves per Agent Schelling 100.0 (0.0) 2.384 (0.001) 7.759 (0.017) 0.558 (0.001) NEA 100.0 (0.0) 2.191 (0.001) 5.684 (0.011) 0.490 (0.001) PEF 100.0 (0.0) 2.187 (0.001) 5.797 (0.011) 0.497 (0.001) PEO 100.0 (0.0) 2.079 (0.001) 5.380 (0.011) 0.468 (0.000) Simulations were conducted on a 32 × 32 grid with periodic boundary conditions, Moore neighborhoods, a vacancy ratio of 0.2, and a satisfaction threshold of 0.5. Each entry represents the mean of 10,000 replications, with standard errors in parentheses. Socially oriented relocation yields lower segregation, full satisfaction, and faster convergence, reducing both equilibrium time and moves per agent. Satisfaction outcomes We first examine overall satisfaction levels across the three relocation rules. In all simulations, the system converges to complete satisfaction (a final satisfaction value of 1). This indicates that the rules do not impede the attainment of full satisfaction. Accordingly, our subsequent analysis focuses on segregation outcomes under a ceteris paribus condition with respect to satisfaction. Segregation outcomes We next compare segregation outcomes across relocation rules based on the probability distributions of segregation outcomes ( Figure 1 ). Each strategy was simulated 10,000 times, with kernel density estimation (KDE) applied for line smoothing. The results show that the original Schelling rule produces the highest level of segregation, whereas PEO yields the lowest. NEA and PEF fall in between, with PEF resulting in slightly lower segregation than NEA, although the difference is marginal. Overall, socially oriented rules substantially reduce segregation relative to the original Schelling rule. The particularly low segregation under PEO underscores the advantage of simultaneously considering both satisfied and unsatisfied neighbors in relocation decisions. Next, we investigate segregation outcomes as a function of the fraction of socially oriented agents in the population ( Figure 2 ). The share of agents following the three rules varies from 0 to 1, with the remainder following the original Schelling rule. (Final segregation indices across baseline conditions are reported in Table 1.) Figure 2 shows that, consistent with expectations, segregation decreases steadily as the fraction of socially oriented agents increases, yielding more integrated equilibria across replications. Among the tested rules, PEO is the most effective at reducing segregation. While NEA and PEF yield similar outcomes, PEF holds a slight but statistically significant advantage over NEA. Overall, the results indicate that even when only a fraction of agents adopt these rules, the system becomes more integrated, demonstrating that partial incorporation of social orientation is sufficient to improve macro-level outcomes. Figure 3 illustrates representative simulation snapshots, showing the final grids at convergence. To identify typical outcomes, we conducted 10,000 simulations and averaged the segregation values at equilibrium. For each rule, we then selected the run with a final segregation value closest to this average, ensuring that the displayed grids reflect characteristic results. Consistent with Figure 1 the socially oriented rules yield visibly lower segregation than the original Schelling rule. Taken together, these findings demonstrate that social orientation systematically reduces segregation while preserving complete satisfaction, offering a simple yet powerful behavioral refinement that aligns individual mobility decisions with collective welfare and social stability. Equilibrium dynamics Finally, we examine how social orientation affects convergence to equilibrium, or global stability. From this perspective, the speed of convergence is vital for both socially oriented agents and society as a whole for two reasons. First, once achieved, global stability fosters and reinforces mutually beneficial social capital at both the individual and societal levels. Second, it reflects the resilience of the system to exogenous shocks. Figure 4 plots the number of simulation steps required for convergence as a function of the fraction of socially oriented agents. Under all three socially oriented rules, the number of steps decreases as the proportion of socially oriented agents increases. The rules are largely indistinguishable up to a fraction of 0.8, after which convergence accelerates most under PEO, followed by NEA and then PEF. This ordering is slightly different from the segregation results in Figure 1. Overall, the findings suggest that socially oriented behavior not only promotes more integrated equilibria but also accelerates convergence toward them. This has significant implications for social planners, as faster attainment of stability both strengthens social cohesion–and thus social capital–while mitigating social costs. Figure 5 reports the number of relocation moves per agent required for the system to stabilize. (Because the total number of moves naturally declines as the vacancy ratio increases, moves per agent provide a more meaningful measure when the vacancy ratio varies.) The results show that the number of moves per agent decreases with the fraction of socially oriented agents under all rules. Among them, PEO requires the fewest relocation steps per agent, followed by NEA and then PEF. While earlier results suggest that social integration enhances both integration and system-wide stability, these findings further imply that social-oriented behavior also can reduce the considerable social costs of unnecessary moves–whether psychological, social, or economic–when moving entails nontrivial costs. Together, these results demonstrate that social orientation reduces segregation, accelerates convergence to equilibrium, and lowers relocation moves per agent, thereby reducing social costs and promoting both welfare and stability. Robustness checks To assess the robustness of our findings, we conducted additional simulations varying vacancy ratios (0.05–0.30), grid size (32 × 32 to 100 × 100), and neighborhood type (Von Neumann). At low vacancy ratios (≤0.10), some inconsistencies emerged: complete satisfaction was not always achieved, although the proportion of unsatisfied agents remained marginal (below 0.001) ( Figure 6a ). Moreover, the number of steps to equilibrium was higher under socially oriented rules than under the original Schelling rule—for NEA and PEF at a vacancy ratio of 0.05, and for PEO up to 0.125 ( Figure 6b ). These results indicate that socially oriented rules require an adequate number of vacant sites to operate effectively, thereby defining a boundary condition for their applicability. Nonetheless, across all other parameter ranges of grid size and neighborhood type, the qualitative patterns remain unchanged: socially oriented relocation consistently reduces segregation, maintains complete satisfaction, and accelerates convergence relative to the original Schelling rule. Together, these findings affirm the robustness of our results. Summary of results Across all baseline simulations, social orientation consistently reshaped the dynamics of Schelling’s segregation model. Compared with the original Schelling relocation, socially oriented relocation produced lower segregation without hampering full satisfaction and faster convergence to equilibrium (i.e., global stability). These effects were robust across replications and parameter settings except lower vacancy ratios, underscoring that a simple behavioral refinement—agents avoiding moves that might destabilize others—can transform macro-level outcomes. Together, the results highlight social orientation as a powerful microfoundation linking individual decision-making to collective outcomes. Specifically, our findings show that incorporating social orientation into Schelling’s framework not only reduces segregation but also accelerates stabilization, offering a simple yet powerful behavioral refinement that lowers social costs and fosters more resilient, integrated communities. These findings motivate the broader theoretical and empirical implications we discuss in what follows. DISCUSSION Our results show that introducing social orientation into Schelling’s segregation model reshapes its macro-level dynamics. Unlike the original rule, which reproduces considerable segregation, socially oriented relocation reduces segregation, maintains satisfaction, and accelerates the attainment of global stability. These outcomes demonstrate how locally rational behaviors that preserve social capital by considering others’ satisfaction can scale into welfare-enhancing equilibria that also produce more integrated and resilient communities. Theoretical implications. Our findings extend Schelling’s original insight that simple local rules can produce complex social outcomes. In contrast to the destabilizing dynamics of Schelling’s other-ignorant relocation rule, social orientation establishes conditions under which individual rationality, collective welfare, and social integration are mutually aligned. This provides a stronger microfoundation for segregation models by showing how boundedly rational, socially sensitive agents can generate more integrated equilibria. More broadly, our results contribute to theories of self-organization and emergent order by demonstrating how realism-based local decision-making heuristics can reshape global outcomes. Applications to empirical contexts. These insights are relevant across multiple domains. In urban settings, residents naturally avoid neighborhoods prone to instability, and our results suggest that socially oriented preferences can counteract destabilizing forces such as segregation or rapid gentrification by fostering more resilient communities. In organizational contexts, similar dynamics apply to team formation and group stability: members who avoid moves likely to unsettle colleagues can strengthen cohesion and reduce turnover. Taken together, these parallels illustrate how social orientation provides a unifying principle across domains where individual mobility decisions aggregate into collective outcomes. Suggestions for policy makers and social planners. Our findings suggest several avenues for fostering stability and integration. Policy makers can encourage such outcomes by improving transparency (e.g., publishing neighborhood stability indicators), designing incentives that reward community-preserving moves, and providing institutional support such as vacancy buffers or coordinated relocation programs. Social norms and community engagement can further reinforce stability by embedding social orientation as a shared value. Taken together, these measures align individual mobility choices with key societal outcomes such as reduced segregation, collective welfare, and stability. This alignment, in turn, lowers social costs and fosters more resilient and integrated communities. Limitations and future directions. Our study abstracts from several real-world complexities that warrant future work. First, we focus on binary group membership and a uniform satisfaction threshold, whereas empirical settings often involve multiple identities, heterogeneous preferences, and evolving tolerance. Second, while we model two-step observability, actual perception of neighborhood stability may vary across individuals and contexts 42 , 43 . Third, we assume simple greedy search behavior, though more sophisticated heuristics could further influence dynamics. Future research could also integrate network structures beyond grids, such as small-world or scale-free networks, to examine how social orientation operates under different topologies 44 , 45 . Finally, empirical validation using residential mobility data or organizational turnover patterns would be a critical step in testing the model’s applicability. CONCLUSION By extending Schelling’s segregation model with social orientation, we show that individual-level tendencies to preserve social capital and community can reduce segregation and facilitate the attainment of global stability. These results provide a stronger behavioral foundation for models of segregation and highlight how social orientation, combined with bounded rationality under local observability, shapes collective patterns. Beyond theoretical insight, the findings suggest that fostering socially oriented behaviors—whether in urban mobility or organizational settings—may promote more integrated, resilient, and sustainable communities. Declarations Data availability All simulation codes developed and used in this study are publicly available to enable replication, validation, and extension of the results at https://github.com/kyuhojin/schelling-social-orientation.git. Acknowledgements The authors acknowledge the support of the Gwangju Institute of Science and Technology (GIST) for providing research facilities. Research funding This work was supported by GIST Research Project grant funded by the GIST in 2025. Author contributions U.Y. and K.J. jointly conceived and conceptualized the research, conducted the simulations, performed the data analysis, and developed the code. K.J. designed the figures and generated the plots, wrote the original draft, and directed and supervised the research. Both authors reviewed and edited the manuscript, contributed to the scientific discussion, and approved the final version of the paper. Competing interests The authors declare no competing interests. Additional Information Correspondence and requests for materials should be addressed to Kyuho Jin. The authors declare no competing interests. References Schelling, T. C. Models of segregation. The American Economic Review 59 , 488–493 (1969). Schelling, T. C. Dynamic models of segregation. Journal of Mathematical Sociology 1 , 143–186 (1971). Wilensky, U. & Rand, W. An introduction to agent-based modeling: modeling natural, social, and engineered complex systems with NetLogo . (MIT Press, 2015). Smaldino, P. E. Modeling social behavior : mathematical and agent-based models of social dynamics and cultural evolution . (Princeton University Press, 2023). Bruch, Elizabeth E. & Mare, Robert D. Neighborhood Choice and Neighborhood Change1. American Journal of Sociology 112 , 667–709, doi:10.1086/507856 (2006-11). Xie, Y., Zhou, X., Xie, Y. & Zhou, X. Modeling individual-level heterogeneity in racial residential segregation. Proceedings of the National Academy of Sciences 109 , doi:10.1073/pnas.1202218109 (2012-7-17). Liu, Z., Li, X., Khojandi, A. & Lazarova-Molnar, S. in 2019 Winter Simulation Conference (WSC). 285-296. Sert, E. et al. Segregation dynamics with reinforcement learning and agent based modeling. Scientific Reports 2020 10:1 10 , 11771, doi:10.1038/s41598-020-68447-8 (2020). Abella, D. et al. Aging effects in Schelling segregation model. Scientific Reports 2022 12:1 12 , 19376, doi:10.1038/s41598-022-23224-7 (2022-11-12). Dahrendorf, R. Out of Utopia: Toward a Reorientation of Sociological Analysis. American Journal of Sociology 64 , doi:10.1086/222419 (1958-9-1). Boudon, R. The logic of social action : an introduction to sociological analysis . (Routledge & Kegan Paul, 1981). Coleman, J. S. Social Capital in the Creation of Human Capital. American Journal of Sociology 94 , S95-S120 (1988). Adler, P. S. & Kwon, S.-W. Social Capital: Prospects for a New Concept. Academy of Management Review 27 , 17-40 (2002). Putnam, R. D. Bowling alone : the collapse and revival of American community . (Simon & Schuster, 2000). Portes, A. Social capital: Its origins and applications in modern sociology. Annual Review of Sociology 24 , 1-24 (1998). Lewicka, M. Place attachment: How far have we come in the last 40 years? Journal of Environmental Psychology 31 , 207–230, doi:10.1016/j.jenvp.2010.10.001 (2011). Forrest, R. & Kearns, A. Social cohesion, social capital and the neighbourhood. Urban studies 38 , 2125-2143 (2001). Kearns, A. & Parkinson, M. The significance of neighbourhood. Urban studies 38 , 2103-2110 (2001). Sampson, R. J. Great American city : Chicago and the enduring neighborhood effect . (The University of Chicago Press, 2011). Braakmann, N. Residential turnover and crime—Evidence from administrative data for England and Wales. The British Journal of Criminology 63 , 1460-1481 (2023). Sampson, R. J., Raudenbush, S. W. & Earls, F. Neighborhoods and violent crime: A multilevel study of collective efficacy. science 277 , 918-924 (1997). Sharp, G. & Warner, C. Neighborhood structure, community social organization, and residential mobility. Socius 4 , 2378023118797861 (2018). Agha, A., Hwang, S. W., Palepu, A. & Aubry, T. The role of housing stability in predicting social capital: Exploring social support and psychological integration as mediators for individuals with histories of homelessness and vulnerable housing. American Journal of Community Psychology 74 , 173-183 (2024). Henrich, J. et al. In search of homo economicus: behavioral experiments in 15 small-scale societies. American economic review 91 , 73-78 (2001). Persky, J. Retrospectives: The ethology of homo economicus. Journal of Economic Perspectives 9 , 221-231 (1995). Mahmoudi Farahani, L. The value of the sense of community and neighbouring. Housing, theory and society 33 , 357-376 (2016). Pareto, V. Manuale di economia politica con una introduzione alla scienza sociale . Vol. 13 (Società editrice libraria, 1919). Arrow, K. J. Social choice and individual values . 2nd. edn, (Wiley, 1963). Friedkin, N. E. Horizons of Observability and Limits of Informal Control in Organizations. Social Forces 62 , 54-77 (1983). Simon, H. A. A behavioral model of rational choice. The quarterly journal of economics , 99-118 (1955). Simon, H. A. Models of man, social and rational : mathematical essays on rational human behavior in a social setting . (Wiley, 1957). Simon, H. A. Models of bounded rationality . (MIT Press, 1982). Conlisk, J. Why bounded rationality? Journal of economic literature 34 , 669-700 (1996). Kempe, D., Kleinberg, J. & Tardos, É. in Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. 137–146 (2003). Bharathi, S., Kempe, D. & Salek, M. 306–311 (Springer). Tversky, A. & Kahneman, D. Availability: A heuristic for judging frequency and probability. Sognitive psychology 5 , 207-232 (1973). Miller, J. H. & Page, S. E. Complex Adaptive Systems: An Introduction to Computational Models of Social Life . (Princeton University Press, 2009). Berg, N., Abramczuk, K. & Hoffrage, U. in Simple heuristics in a social world (Oxford University Press, 2012). Steinbacher, M. et al. Advances in the agent-based modeling of economic and social behavior. SN Business & Economics 1 , 99 (2021). Jin, K. & Yu, U. Entropy profiles of Schelling’s segregation model from the Wang–Landau algorithm. Chaos: An Interdisciplinary Journal of Nonlinear Science 32 , 113103 (2022). Domic, N. G., Goles, E. & Rica, S. Dynamics and complexity of the Schelling segregation model. Physical Review E 83 , 056111 (2011). Christakis, N. A. & Fowler, J. H. The spread of obesity in a large social network over 32 years. New England journal of medicine 357 , 370-379 (2007). Christakis, N. A. & Fowler, J. H. Social contagion theory: examining dynamic social networks and human behavior. Statistics in medicine 32 , 556-577 (2013). Fagiolo, G., Valente, M. & Vriend, N. J. Segregation in networks. Journal of economic behavior & organization 64 , 316-336 (2007). Henry, A. D., Prałat, P. & Zhang, C.-Q. Emergence of segregation in evolving social networks. Proceedings of the National Academy of Sciences 108 , 8605-8610 (2011). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 07 Nov, 2025 Reviews received at journal 06 Nov, 2025 Reviews received at journal 02 Nov, 2025 Reviews received at journal 01 Nov, 2025 Reviews received at journal 27 Oct, 2025 Reviewers agreed at journal 27 Oct, 2025 Reviews received at journal 27 Oct, 2025 Reviewers agreed at journal 26 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers invited by journal 23 Oct, 2025 Editor assigned by journal 23 Oct, 2025 Editor invited by journal 15 Oct, 2025 Submission checks completed at journal 08 Oct, 2025 First submitted to journal 08 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7780879","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":538848386,"identity":"3ca8d820-06f4-407f-916e-8e9ac2b83cb9","order_by":0,"name":"Unjong Yu","email":"","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Unjong","middleName":"","lastName":"Yu","suffix":""},{"id":538848387,"identity":"852dd33d-df10-4aaa-9e85-b521a91ab4da","order_by":1,"name":"Kyuho Jin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYBACCQYGNgYGHgkGfgbGBogQD7FaJBuAWg4QrwUIDEDKidIiOSPH7MEHGYs84/OLmz9/YLCTZ+A5+wCvFmmJHHPDGTwSxWY3HrZJHGBINmzgbTfAq0VOIsdMmodHInHbjYNtQIcxJzDws+F3GFzL5hkHmz8cYKgnrEUapmUDf2MD0GGHExh42/Brkex5ViYJ9EvijBuMbRJnDI4btvEcw69F4njyNomPPXWJ/f3HH3+oqKiW5+dJw6+FQSCBgYGxB6QZyGAwgEUTPsB/AEj8gDFGwSgYBaNgFGABAH5lP1sHQsgeAAAAAElFTkSuQmCC","orcid":"","institution":"Gwangju Institute of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Kyuho","middleName":"","lastName":"Jin","suffix":""}],"badges":[],"createdAt":"2025-10-04 15:53:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7780879/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7780879/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-32159-8","type":"published","date":"2025-12-11T15:57:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95228522,"identity":"e74ede11-852e-4ad4-90b9-c5bbea0cf407","added_by":"auto","created_at":"2025-11-05 16:33:52","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":679460,"visible":true,"origin":"","legend":"","description":"","filename":"SegregationandSocialOrientationsubmissionrevised2.docx","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/c19b193adba6ac8202fb6ab3.docx"},{"id":95227348,"identity":"8d4fdc3a-0c94-4309-9674-7ad0d3b4d3a1","added_by":"auto","created_at":"2025-11-05 16:32:24","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4417,"visible":true,"origin":"","legend":"","description":"","filename":"47ee7455e0cc41b38520eb4055f8771e.json","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/2fd7d10313042a35de064ec7.json"},{"id":95228497,"identity":"570a176d-ccff-4b49-b045-a798cce79725","added_by":"auto","created_at":"2025-11-05 16:33:50","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":106262,"visible":true,"origin":"","legend":"","description":"","filename":"47ee7455e0cc41b38520eb4055f8771e1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/dd0b48380cf8cf500bc2b190.xml"},{"id":95201997,"identity":"2ff84ad6-dba2-4e2f-a0af-1f259faa8979","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":82089,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/968ae00afba0d348203b84ba.png"},{"id":95201993,"identity":"f9d6088c-4005-45ee-8218-bb442c62292a","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":68103,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/fd858754368182185b50f83c.png"},{"id":95202001,"identity":"a3731b6b-8f8f-4659-8e8b-fa48b79c4007","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":179923,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/d8283524d90d550183268e7d.png"},{"id":95228629,"identity":"9f4b2228-e713-4d04-a60e-2d333e266ffb","added_by":"auto","created_at":"2025-11-05 16:34:00","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77009,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/62205a0a3922d22b4ba8d877.png"},{"id":95201994,"identity":"47d06ffe-f195-4a4c-bbdd-dabdc0357790","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":70874,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/6895651a04d772b31213ab22.png"},{"id":95202008,"identity":"e523f18a-80ef-4178-8649-1caca731e198","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"jpeg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":168319,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/611d8a2f9349f3a37eab50e8.jpeg"},{"id":95202000,"identity":"028ab3dc-011e-4509-98bb-8623695615f5","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":25246,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/eca10c546f85ece4664644a7.png"},{"id":95229112,"identity":"3b191deb-8b8f-4f37-bec9-4f0040c9a90d","added_by":"auto","created_at":"2025-11-05 16:34:28","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":20319,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/02cd4f6369f686849522fe1c.png"},{"id":95202009,"identity":"7eabfc27-b91a-44bd-9fb4-2297cacacb20","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33658,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/5eafc7619d5d839c0341e69e.png"},{"id":95202011,"identity":"d353bd71-4b1a-4c2d-b5f3-e2fbd747a7db","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":17097,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/370fec6272d3fe65a67f28dd.png"},{"id":95202002,"identity":"f51430c8-b96f-4b3a-a86c-93c48342360d","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":19613,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/8cb4ce2a0f44a448f913e480.png"},{"id":95202007,"identity":"1f88bd57-5743-4130-8963-df14234cd567","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":36443,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/25447aa9a938cd2953b24f50.png"},{"id":95227513,"identity":"b598f91d-4aea-4d90-b063-3fd9e5d70fd9","added_by":"auto","created_at":"2025-11-05 16:32:35","extension":"xml","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104670,"visible":true,"origin":"","legend":"","description":"","filename":"47ee7455e0cc41b38520eb4055f8771e1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/30db27cf5e537d3a9316a27a.xml"},{"id":95202013,"identity":"0be2e1f2-e3d8-4221-a481-e525c0bbbab3","added_by":"auto","created_at":"2025-11-05 12:35:14","extension":"html","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":116983,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/ced0ae1a591c19396e283e39.html"},{"id":95201988,"identity":"8e40917a-2295-4eb5-be99-a8aec608a15a","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":82089,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSegregation outcomes across relocation rules. \u003c/strong\u003eProbability distributions of each strategy. The original Schelling rule produces the highest segregation, while socially oriented rules reduce segregation, with PEO yielding the lowest levels and highlighting the benefit of accounting for both satisfied and unsatisfied neighbors. Lines are smoothed using kernel density estimation (KDE).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/d6a86854f2a0d6a410f01579.png"},{"id":95227739,"identity":"c5b5647e-46ba-4df0-8973-f000fbf1a81b","added_by":"auto","created_at":"2025-11-05 16:32:50","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":68103,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSegregation as a function of the fraction of socially oriented agents. \u003c/strong\u003eThe fraction of agents following socially oriented rules ranges from 0 to 1, with the remainder following the original Schelling rule. Equilibrium satisfaction is reached in all cases. Segregation decreases steadily as the share of socially oriented agents increases, indicating that even partial adoption of socially oriented relocation improves integration. Shaded regions denote 95% confidence intervals.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/fb7a5f794763907e44339782.png"},{"id":95228895,"identity":"1a521efc-564e-4c52-afff-7f61fb6e1187","added_by":"auto","created_at":"2025-11-05 16:34:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":162434,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRepresentative grids at equilibrium. \u003c/strong\u003eInitial configuration and final grids under each relocation rule. To identify representative outcomes, 10,000 simulations were conducted, and for each condition the run with final segregation closest to the mean was selected. Consistent with Figure 1, socially oriented rules yield visibly lower segregation than the original Schelling rule.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/33db13e0f30ee433b2be898a.png"},{"id":95201989,"identity":"1ed79f63-efc2-4fa1-94df-1d1fbbb4da49","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":77009,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConvergence to equilibrium under socially oriented relocation rules. \u003c/strong\u003eThe fraction of agents following socially oriented rules ranges from 0 to 1, with the remainder following the original Schelling rule. The number of simulation steps required for convergence decreases as the fraction of socially oriented agents increases. Up to a fraction of 0.8, the three rules (NEA, PEF, and PEO) exhibit similar dynamics. Beyond this point, convergence accelerates fastest under PEO, followed by NEA and then PEF. Shaded regions indicate 95% confidence intervals. Overall, the results indicate that socially oriented relocation not only promotes more integrated equilibria but also accelerates convergence toward them, with implications for social cohesion and resilience.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/32d1341c30fc39b1f0029e80.png"},{"id":95201995,"identity":"d0e12711-a567-4c91-99aa-003f1e580249","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":70874,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelocation moves per agent required for equilibrium. \u003c/strong\u003eThe fraction of agents following socially oriented rules ranges from 0 to 1, with the remainder following the original Schelling rule. The figure shows the average number of relocation moves per agent required for the system to stabilize. Shaded regions denote 95% confidence intervals. Results indicate that the number of moves per agent decreases with the fraction of socially oriented agents across all rules. Among them, PEO requires the fewest moves, followed by NEA and then PEF. These findings suggest that, in addition to promoting integration and stability, socially oriented relocation can reduce the social, psychological, and economic costs of unnecessary moves when moving entails nontrivial costs.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/fe60f208400cd4ee8493856d.png"},{"id":95201999,"identity":"6db83f91-4d21-4831-9bb2-82bfdf98c99c","added_by":"auto","created_at":"2025-11-05 12:35:13","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":168319,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRobustness checks against vacancy ratios. \u003c/strong\u003e(a) Proportion of satisfied agents at equilibrium across vacancy ratios. At very low vacancy ratios (≤0.10), complete satisfaction is not always achieved, although the proportion of unsatisfied agents remains below 0.001. (b) Steps to equilibrium across vacancy ratios. At low vacancy ratios, socially oriented rules require more steps than the original Schelling rule (notably NEA and PEF at 0.05, and PEO up to 0.125). At higher vacancy ratios, however, socially oriented rules converge more quickly, consistent with the main results. The shaded areas around each line represent 95% confidence intervals.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/c6d7a5694e5bef481511c501.jpeg"},{"id":98243627,"identity":"d24c1a6f-ed24-497c-8545-f4e2637ac12e","added_by":"auto","created_at":"2025-12-15 16:09:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1657688,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7780879/v1/f4bcce47-ca82-431b-b659-b0a486dc19bb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"From Self-Orientation to Social Orientation: A Behavioral Extension of Schelling’s Segregation Model","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eSchelling\u0026rsquo;s segregation model, first introduced in the late 1960s through a checkerboard thought experiment\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, remains one of the most striking illustrations of how simple micro-level rules can yield surprising macro-level patterns. With only minimal assumptions about agents\u0026rsquo; preferences\u0026mdash;namely, that they are content with some diversity but dissatisfied with being in a minority\u0026mdash;Schelling showed that large-scale segregation can emerge even when no agent desires it. This counterintuitive finding helped launch a broader research agenda on self-organization and unintended consequences, influencing not only economics and sociology but also the study of complexity and emergent order across the natural and social sciences\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Yet despite its enduring influence, the model\u0026rsquo;s stark simplicity leaves open important questions about the robustness of its insights under more realistic assumptions.\u003c/p\u003e\u003cp\u003eSubsequent work has examined the model\u0026rsquo;s generalizability by relaxing its assumptions, particularly those concerning agents\u0026rsquo; microfoundations\u003csup\u003e\u003cspan additionalcitationids=\"CR6 CR7 CR8\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. One microfoundation that has been relatively overlooked is that humans are inherently social beings. At their core, people are \u003cem\u003ehomo sociologicus\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e\u0026mdash;defined by a fundamental inclination to form and belong to groups, with decisions shaped by communal considerations. From this perspective, a neighborhood is not merely a physical residence but also functions as a social community that builds and sustains mutually beneficial social capital through repeated interactions\u003csup\u003e\u003cspan additionalcitationids=\"CR13 CR14 CR15 CR16 CR17 CR18\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. Accordingly, frequent turnover of neighbors signals the erosion of such capital, diminishing the neighborhood\u0026rsquo;s value as a social group and reducing it to little more than a residence\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. For socially oriented agents, neighborhoods that risk this kind of degeneration after their move are correspondingly less attractive relocation options. Consequently, they avoid moves that generate negative externalities\u0026mdash;destabilizing the community, particularly by prompting prospective neighbors to leave\u0026mdash;even if such moves would satisfy them. Instead, they choose moves that generate positive externalities, thereby stabilizing the community and sustaining social capital. By contrast, agents in Schelling\u0026rsquo;s original model are essentially \u003cem\u003ehomo economicus\u003c/em\u003e and abstract away from these dynamics\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. They evaluate neighborhoods myopically, moving into any vacant site that meets their threshold in the moment, without regard for the destabilizing externalities of relocation. In doing so, they treat satisfaction as purely individualistic and assume away interdependent neighborhood social dynamics\u0026mdash;a stylized simplification that diverges from real-world decision-making.\u003c/p\u003e\u003cp\u003eTo address this gap, we extend Schelling\u0026rsquo;s model by introducing a \"social orientation\" to its microfoundations, complementing the original focus on self-orientation. In our formulation, socially oriented agents seek both self-serving and community-preserving locations; they select sites where their move not only satisfies their own preferences but also minimizes dissatisfaction (and thus disruption) and/or enhances the satisfaction (and thus stability) of the prospective neighborhood. In essence, these agents aim to reduce negative externalities and/or increase positive ones. This orientation reflects the valuation of neighborhoods not merely as locations, but as cohesive social communities that foster a shared identity \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. We operationalize this behavior through three heuristic relocation rules based on the prospective neighbors\u0026rsquo; satisfaction:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eNegative Externality Avoiding Rule (NEA)\u003c/b\u003e: Agent relocates to a site that satisfies their threshold and does not dissatisfy any currently satisfied neighbors, choosing randomly among such sites.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePositive Externality Favoring Rule (PEF)\u003c/b\u003e: Agent relocates to a site that satisfies their threshold and generates non-negative externalities by increasing (or at least not reducing) the number of satisfied neighbors, choosing randomly among such sites.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePositive Externality Optimizing Rule (PEO)\u003c/b\u003e: Agent relocates to a site that satisfies their threshold, generates non-negative externalities by increasing (or at least not reducing) the number of satisfied neighbors and minimizes the number of unsatisfied neighbors, with ties broken at random.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eAll these rules begin with the agent\u0026rsquo;s own satisfaction\u0026mdash;a self-oriented criterion\u0026mdash;but then extend it with a layer of social orientation, each in a different way. \u003cb\u003eNEA\u003c/b\u003e focuses on avoiding negative externalities by preventing moves that would cause currently satisfied neighbors to become dissatisfied, while still permitting unsatisfied neighbors either to become satisfied or to relocate. This reflects the view that satisfied neighbors are key contributors to the cultivation and maintenance of social capital. \u003cb\u003ePEF\u003c/b\u003e, in contrast, aims to increase\u0026mdash;or at least not reduce\u0026mdash;the total number of satisfied neighbors. The emphasis here is on aggregate numbers, so some switches between satisfied and unsatisfied neighbors may occur, provided the overall count of satisfied neighbors is maintained or improved. In contrast to the previous two rules, \u003cb\u003ePEO\u003c/b\u003e maximizes positive externalities by considering both satisfied and unsatisfied neighbors: it is similar to PEF but adds the condition of minimizing the number of unsatisfied neighbors. In doing so, PEO can increase the number of satisfied neighbors, subject to minimizing the number of unsatisfied ones.\u003c/p\u003e\u003cp\u003eNotably, deeper insight into these rules can be gained by viewing them through the lens of Pareto efficiency\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, a widely used concept in economics. Among them, NEA is strictly Pareto-improving, as it satisfies the moving agent without making others worse off. By contrast, PEF and PEO relax this criterion by focusing on aggregate satisfaction, aligning more with a utilitarian logic than with strict Pareto improvement. Whereas NEA favors stability by preserving satisfied neighbors, PEF and PEO are expected to reduce turnover more proactively by converting unsatisfied neighbors into satisfied ones.\u003c/p\u003e\u003cp\u003eImplementing this microfoundation requires refining two implicit assumptions of the original model. The first concerns agents\u0026rsquo; observability. In Schelling\u0026rsquo;s formulation, agents consider only their immediate neighbors, leaving the scope of perception irrelevant. By contrast, socially oriented agents must anticipate how their relocation affects not only themselves but also the satisfaction of prospective neighbors. This requires observing neighbors of neighbors\u0026mdash;a form of two-step observability, or horizon of observability, which has empirical support in studies of social influence and network perception\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The second refinement concerns agents\u0026rsquo; bounded rationality\u003csup\u003e\u003cspan additionalcitationids=\"CR31 CR32\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. In the original model, agents resemble automata, following simple threshold rules with no capacity for foresight. In our extension, by contrast, agents more closely approximate rational decision makers in that they can evaluate prospective neighborhoods and select sites that optimize future social spillovers. Yet their rationality remains bounded by limited information and computational constraints: they cannot access global knowledge or compute system-wide optima\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Instead, they rely on local heuristics\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e\u0026mdash;such as the relocation rules we propose\u0026mdash;behaving as greedy searchers within their horizon of observability\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThese two behavioral refinements underpin social orientation by allowing agents to anticipate the communal consequences of their moves while remaining subject to realistic cognitive and informational limits. They also make the model more realistic and provide the foundation for our simulation analysis of how social orientation alters segregation dynamics. More broadly, modeling social orientation refines theoretical understanding and highlights implications for the stability and diversity of social systems.\u003c/p\u003e\u003cp\u003eIn the following section, we outline how these rules are implemented in our extended Schelling model. Our aim is to examine how social orientation alters relocation behavior and, in turn, shapes dynamical outcomes including segregation. To this end, we adapt the classic model to incorporate agents who follow NEA, PEF, PEO, or Schelling\u0026rsquo;s original relocation rule. We then outline the modeling framework, agent decision rules, and simulation design used to compare these approaches.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003eTo evaluate the role of social orientation in segregation dynamics, we extend Schelling\u0026rsquo;s original agent-based model of residential mobility. As noted, our extension is based on two behavioral refinements\u0026ndash;two-step observability and bounded rationality\u0026ndash;allowing agents to anticipate potential neighborhood instability based on local information and avoid moves that could generate dissatisfaction among the prospective neighbors. We systemically assess how individual-level social orientation shapes macro-level outcomes of segregation, satisfaction, and convergence speed.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eRelocation rules\u003c/h2\u003e\u003cp\u003eWe consider three socially oriented relocation rules, with Schelling\u0026rsquo;s original rule\u0026sup1; serving as a benchmark. The \u003cb\u003eNEA\u003c/b\u003e, \u003cb\u003ePEF\u003c/b\u003e, and \u003cb\u003ePEO\u003c/b\u003e rules extend the model by incorporating agents\u0026rsquo; socially oriented behavior to account for externalities. The stepwise procedures for each rule are summarized below:\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eNegative Externality Avoiding (NEA) Rule\u003c/h3\u003e\n\u003cp\u003eStep 1. Randomly select one dissatisfied agent.\u003c/p\u003e\u003cp\u003eStep 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not cause any currently satisfied neighbors to become unsatisfied.\u003c/p\u003e\u003cp\u003eStep 3. If more than one such site exists, randomly choose one from this set.\u003c/p\u003e\u003cp\u003eStep 4. Relocate the agent to this site.\u003c/p\u003e\n\u003ch3\u003ePositive Externality Favoring (PEF) Rule\u003c/h3\u003e\n\u003cp\u003eStep 1. Randomly select one dissatisfied agent.\u003c/p\u003e\u003cp\u003eStep 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not reduce the number of currently satisfied neighbors.\u003c/p\u003e\u003cp\u003eStep 3. If more than one such site exists, randomly choose one from this set.\u003c/p\u003e\u003cp\u003eStep 4. Relocate the agent to this site.\u003c/p\u003e\n\u003ch3\u003ePositive Externality Optimizing (PEO) Rule\u003c/h3\u003e\n\u003cp\u003eStep 1. Randomly select one dissatisfied agent.\u003c/p\u003e\u003cp\u003eStep 2. Identify all vacant sites where (i) the agent would be satisfied, and (ii) the move would not reduce the number of currently satisfied neighbors.\u003c/p\u003e\u003cp\u003eStep 3. Among these sites, choose the site that leaves the fewest neighbors unsatisfied after relocation.\u003c/p\u003e\u003cp\u003eStep 4. If more than one such site exists, randomly choose one from this set.\u003c/p\u003e\u003cp\u003eStep 5. Relocate the agent to this site.\u003c/p\u003e\u003cp\u003e\u003cb\u003eNEA\u003c/b\u003e is primarily concerned with avoiding the turnover of currently satisfied neighbors, while giving little attention to unsatisfied neighbors. As a by-product, the rule may cause unsatisfied neighbors either to become satisfied or to relocate. In this sense, NEA aims to avoid the negative externalities associated with an agent\u0026rsquo;s relocation. \u003cb\u003ePEF\u003c/b\u003e, by contrast, seeks to increase\u0026mdash;or at least not decrease\u0026mdash;the number of currently satisfied neighbors, without regard for the switching of unsatisfied neighbors so long as the overall number of satisfied neighbors increases in the prospective neighborhood. Accordingly, PEF is more concerned with generating positive externalities from an agent\u0026rsquo;s move. \u003cb\u003ePEO\u003c/b\u003e integrates both perspectives by addressing positive and negative externalities simultaneously. Like PEF, it permits positive externalities by allowing unsatisfied neighbors to become satisfied, but it goes further by minimizing the number of unsatisfied neighbors rather than merely avoiding turnovers. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes these distinctions.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003eComparison of social oriented rules.\u003c/b\u003e NEA focuses narrowly on avoiding the turnover of satisfied neighbors, thereby minimizing negative externalities but disregarding unsatisfied ones. PEF, in contrast, prioritizes generating positive externalities by permitting unsatisfied neighbors to become satisfied, even if some turnover occurs. PEO integrates both perspectives: like PEF, it allows for positive spillovers, but it further minimizes the number of unsatisfied neighbors, making it the most balanced rule in terms of managing both positive and negative externalities.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRule\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePrimary Focus\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTreatment of Neighbors\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eExternality Orientation\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNEA\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAvoid turnover of currently satisfied neighbors\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIgnores unsatisfied neighbors; some may become satisfied or move out as a side effect\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMinimizes negative externalities (avoids new dissatisfaction)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003ePEF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIncrease or at least not decrease the number of satisfied neighbors\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAllows unsatisfied neighbors to switch to satisfied; unconcerned with turnover if satisfaction increases overall\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eGenerates positive externalities (permits satisfaction gains)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003ePEO\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBalance positive and negative externalities\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLike PEF, permits unsatisfied \u0026rarr; satisfied switches, but also minimizes the number of unsatisfied neighbors\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eAddresses both: permits positive externalities while minimizing negative ones\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIt is worth noting that although the two-step observability in our model is farther-sighted than in the original, the three proposed rules still operate as local heuristics, since agents cannot anticipate consequences beyond their perceptual horizon. This property aligns with our goal of enhancing realism by modeling agents as boundedly rational actors who rely on such heuristics. Taken together, these rules allow us to explore a spectrum of socially oriented decision-making\u0026mdash;from simple harm-avoidance to active community optimization. By doing so, we can systematically assess how these behavioral refinements impact macro-level outcomes.\u003c/p\u003e\u003cp\u003eFormally, when considering a move to site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e, an agent with two-step observability computes for each neighbor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e the fraction of same-type neighbors as\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{h}_{j}\\left(i\\right)=\\frac{1}{\\left|N\\left(j\\right)\\right|}\\sum\\:_{k\\in\\:N\\left(j\\right)}1\\{{x}_{j}\\left(i\\right)={x}_{k}\\left(i\\right)\\}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\left(j\\right)\\)\u003c/span\u003e\u003c/span\u003e denotes the set of neighboring agents of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{m}\\left(i\\right)\\in\\:\\{-1,\\:+1\\}\\)\u003c/span\u003e\u003c/span\u003e represents the occupant of site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e after the focal agent is hypothetically relocated to site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e. The indicator function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:1\\{{x}_{j}\\left(i\\right)={x}_{k}\\left(i\\right)\\}\\)\u003c/span\u003e\u003c/span\u003e equals 1 if neighbor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e and their neighbor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k\\)\u003c/span\u003e\u003c/span\u003e are of the same type following the relocation, and 0 otherwise. Accordingly, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{h}_{j}\\left(i\\right)\\)\u003c/span\u003e\u003c/span\u003e captures the updated fraction of same-type neighbors for each \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e, incorporating the agent\u0026rsquo;s prospective move.\u003c/p\u003e\u003cp\u003eThis assumption aligns with Friedkin\u0026rsquo;s empirical observation of the \u0026ldquo;horizon of observability,\u0026rdquo; which suggests that an individual\u0026rsquo;s social vision is limited and typically extends only to indirect social ties\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Consequently, agents can consider the broader consequences of their relocation on local neighborhood stability.\u003c/p\u003e\n\u003ch3\u003eSimulation design\u003c/h3\u003e\n\u003cp\u003eThe model is implemented on a two-dimensional square lattice with periodic boundary conditions, so that agents at the edges are connected to those on the opposite side. Each cell can be occupied by a single agent or left vacant, and agents belong to one of two groups of equal size. A fixed vacancy ratio (20% unless otherwise noted) provides sufficient mobility for agents to relocate. At initialization, agents and vacancies are randomly assigned to sites on the grid. Time advances in asynchronous sequential updates, so that only one agent moves per step. The process continues until either (i) all agents are satisfied, or (ii) no further moves are possible because dissatisfied agents cannot find admissible sites.\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eOutcome measures\u003c/h2\u003e\u003cp\u003eWe track three primary outcomes. First, segregation is measured using the standard adjacency-based segregation index\u0026sup1;\u0026sup3;:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:S=\\frac{1}{2N}\\sum\\:_{i,j}{A}_{ij}{T}_{i}{T}_{j}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\)\u003c/span\u003e\u003c/span\u003e is the number of agents, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e represents the adjacency matrix of the neighborhood structure, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\:\\)\u003c/span\u003e\u003c/span\u003edenotes the type of agent at site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e (+\u0026thinsp;1 or \u0026minus;\u0026thinsp;1 for occupied sites, 0 for vacancies). The segregation measure \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e takes positive values when the system exhibits segregation and negative values when it is integrated. The maximum value of S is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Delta\\:}/2\\)\u003c/span\u003e\u003c/span\u003e in a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Delta\\:}\\)\u003c/span\u003e\u003c/span\u003e-regular network as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\to\\:\\infty\\:\\)\u003c/span\u003e\u003c/span\u003e and the proportion of vacant site \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:V=0\\)\u003c/span\u003e\u003c/span\u003e. Notably, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e is closely related to the energy \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e of the spin-glass model, satisfying the relation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S=-E/N\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003e40,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Second, overall satisfaction is measured as the proportion of agents who meet their threshold condition at the end of the simulation. Third, stability is assessed by recording the number of relocation steps until equilibrium.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eComputational implementation\u003c/h3\u003e\n\u003cp\u003eThe model was implemented in Python 3.12 using standard scientific libraries (NumPy, pandas, and matplotlib). Random number generation was controlled by fixed seeds for reproducibility. For each parameter configuration, we conducted 10,000 independent replications to account for stochastic variability.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eOur simulations reveal that social orientation non-trivially alters the dynamics of Schelling\u0026rsquo;s segregation model. Under the original rule, the model reproduces Schelling\u0026rsquo;s classic finding: even moderate individual preferences lead to considerable segregation. By contrast, socially oriented relocation consistently reduces segregation and accelerates convergence to equilibrium (i.e., global stability) with fewer relocation steps, all while preserving full satisfaction. These results suggest that incorporating social orientation aligns individual-level decision-making with macro-level outcomes that enhance social integration, stability, and collective welfare. We present the results in three parts, focusing respectively on satisfaction outcomes, segregation outcomes, and equilibrium dynamics.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eBaseline parameters\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eUnless otherwise specified, all simulations were conducted on a 32 \u0026times; 32 grid with periodic boundary conditions, Moore neighborhoods, a vacancy ratio of 0.2, and a satisfaction threshold of 0.5. Each reported value represents the mean of 10,000 independent replications, with standard errors shown where applicable. These baseline settings provide a consistent reference point for evaluating how socially oriented relocation rules shape segregation outcomes. Baseline results are summarized in \u003cstrong\u003eTable 2\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2. Baseline simulation results under socially oriented relocation rules.\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"493\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRule\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSatisfaction (%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSegregation Index (S)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eConvergence Steps\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMoves per Agent\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003eSchelling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e100.0 (0.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e2.384 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e7.759 (0.017)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e0.558 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003eNEA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e100.0 (0.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e2.191 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e5.684 (0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e0.490 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003ePEF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e100.0 (0.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e2.187 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e5.797 (0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e0.497 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003ePEO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e100.0 (0.0)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e2.079 (0.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e5.380 (0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 99px;\"\u003e\n \u003cp\u003e0.468 (0.000)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eSimulations were conducted on a 32 \u0026times; 32 grid with periodic boundary conditions, Moore neighborhoods, a vacancy ratio of 0.2, and a satisfaction threshold of 0.5. Each entry represents the mean of 10,000 replications, with standard errors in parentheses. Socially oriented relocation yields lower segregation, full satisfaction, and faster convergence, reducing both equilibrium time and moves per agent.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eSatisfaction outcomes\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eWe first examine overall satisfaction levels across the three relocation rules. In all simulations, the system converges to complete satisfaction (a final satisfaction value of 1). This indicates that the rules do not impede the attainment of full satisfaction. Accordingly, our subsequent analysis focuses on segregation outcomes under a \u003cem\u003eceteris paribus\u003c/em\u003e condition with respect to satisfaction.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eSegregation outcomes\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eWe next compare segregation outcomes across relocation rules based on the probability distributions of segregation outcomes (\u003cstrong\u003eFigure 1\u003c/strong\u003e). Each strategy was simulated 10,000 times, with kernel density estimation (KDE) applied for line smoothing. The results show that the original Schelling rule produces the highest level of segregation, whereas PEO yields the lowest. NEA and PEF fall in between, with PEF resulting in slightly lower segregation than NEA, although the difference is marginal. Overall, socially oriented rules substantially reduce segregation relative to the original Schelling rule. The particularly low segregation under PEO underscores the advantage of simultaneously considering both satisfied and unsatisfied neighbors in relocation decisions.\u003c/p\u003e\n\u003cp\u003eNext, we investigate segregation outcomes as a function of the fraction of socially oriented agents in the population (\u003cstrong\u003eFigure 2\u003c/strong\u003e). The share of agents following the three rules varies from 0 to 1, with the remainder following the original Schelling rule. (Final segregation indices across baseline conditions are reported in Table 1.) Figure 2 shows that, consistent with expectations, segregation decreases steadily as the fraction of socially oriented agents increases, yielding more integrated equilibria across replications. Among the tested rules, PEO is the most effective at reducing segregation. While NEA and PEF yield similar outcomes, PEF holds a slight but statistically significant advantage over NEA. Overall, the results indicate that even when only a fraction of agents adopt these rules, the system becomes more integrated, demonstrating that partial incorporation of social orientation is sufficient to improve macro-level outcomes.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 3\u003c/strong\u003e illustrates representative simulation snapshots, showing the final grids at convergence. To identify typical outcomes, we conducted 10,000 simulations and averaged the segregation values at equilibrium. For each rule, we then selected the run with a final segregation value closest to this average, ensuring that the displayed grids reflect characteristic results. Consistent with \u003cstrong\u003eFigure 1\u003c/strong\u003e the socially oriented rules yield visibly lower segregation than the original Schelling rule.\u003c/p\u003e\n\u003cp\u003eTaken together, these findings demonstrate that social orientation systematically reduces segregation while preserving complete satisfaction, offering a simple yet powerful behavioral refinement that aligns individual mobility decisions with collective welfare and social stability.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eEquilibrium dynamics\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eFinally, we examine how social orientation affects convergence to equilibrium, or global stability. From this perspective, the speed of convergence is vital for both socially oriented agents and society as a whole for two reasons. First, once achieved, global stability fosters and reinforces mutually beneficial social capital at both the individual and societal levels. Second, it reflects the resilience of the system to exogenous shocks. \u003cstrong\u003eFigure 4\u003c/strong\u003e plots the number of simulation steps required for convergence as a function of the fraction of socially oriented agents. Under all three socially oriented rules, the number of steps decreases as the proportion of socially oriented agents increases. The rules are largely indistinguishable up to a fraction of 0.8, after which convergence accelerates most under PEO, followed by NEA and then PEF. This ordering is slightly different from the segregation results in Figure 1. Overall, the findings suggest that socially oriented behavior not only promotes more integrated equilibria but also accelerates convergence toward them. This has significant implications for social planners, as faster attainment of stability both strengthens social cohesion\u0026ndash;and thus social capital\u0026ndash;while mitigating social costs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 5\u003c/strong\u003e reports the number of relocation moves per agent required for the system to stabilize. (Because the total number of moves naturally declines as the vacancy ratio increases, moves per agent provide a more meaningful measure when the vacancy ratio varies.) The results show that the number of moves per agent decreases with the fraction of socially oriented agents under all rules. Among them, PEO requires the fewest relocation steps per agent, followed by NEA and then PEF. While earlier results suggest that social integration enhances both integration and system-wide stability, these findings further imply that social-oriented behavior also can reduce the considerable social costs of unnecessary moves\u0026ndash;whether psychological, social, or economic\u0026ndash;when moving entails nontrivial costs.\u003c/p\u003e\n\u003cp\u003eTogether, these results demonstrate that social orientation reduces segregation, accelerates convergence to equilibrium, and lowers relocation moves per agent, thereby reducing social costs and promoting both welfare and stability.\u003c/p\u003e\n\u003ch3\u003e\u003cstrong\u003eRobustness checks\u003c/strong\u003e\u003c/h3\u003e\n\u003cp\u003eTo assess the robustness of our findings, we conducted additional simulations varying vacancy ratios (0.05\u0026ndash;0.30), grid size (32 \u0026times; 32 to 100 \u0026times; 100), and neighborhood type (Von Neumann). At low vacancy ratios (\u0026le;0.10), some inconsistencies emerged: complete satisfaction was not always achieved, although the proportion of unsatisfied agents remained marginal (below 0.001) (\u003cstrong\u003eFigure 6a\u003c/strong\u003e). Moreover, the number of steps to equilibrium was higher under socially oriented rules than under the original Schelling rule\u0026mdash;for NEA and PEF at a vacancy ratio of 0.05, and for PEO up to 0.125 (\u003cstrong\u003eFigure 6b\u003c/strong\u003e). These results indicate that socially oriented rules require an adequate number of vacant sites to operate effectively, thereby defining a boundary condition for their applicability. Nonetheless, across all other parameter ranges of grid size and neighborhood type, the qualitative patterns remain unchanged: socially oriented relocation consistently reduces segregation, maintains complete satisfaction, and accelerates convergence relative to the original Schelling rule. Together, these findings affirm the robustness of our results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003c/strong\u003e\u003cstrong\u003eSummary of results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAcross all baseline simulations, social orientation consistently reshaped the dynamics of Schelling\u0026rsquo;s segregation model. Compared with the original Schelling relocation, socially oriented relocation produced lower segregation without hampering full satisfaction and faster convergence to equilibrium (i.e., global stability). These effects were robust across replications and parameter settings except lower vacancy ratios, underscoring that a simple behavioral refinement\u0026mdash;agents avoiding moves that might destabilize others\u0026mdash;can transform macro-level outcomes. Together, the results highlight social orientation as a powerful microfoundation linking individual decision-making to collective outcomes. Specifically, our findings show that incorporating social orientation into Schelling\u0026rsquo;s framework not only reduces segregation but also accelerates stabilization, offering a simple yet powerful behavioral refinement that lowers social costs and fosters more resilient, integrated communities. These findings motivate the broader theoretical and empirical implications we discuss in what follows.\u0026nbsp;\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eOur results show that introducing social orientation into Schelling\u0026rsquo;s segregation model reshapes its macro-level dynamics. Unlike the original rule, which reproduces considerable segregation, socially oriented relocation reduces segregation, maintains satisfaction, and accelerates the attainment of global stability. These outcomes demonstrate how locally rational behaviors that preserve social capital by considering others\u0026rsquo; satisfaction can scale into welfare-enhancing equilibria that also produce more integrated and resilient communities.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheoretical implications.\u003c/b\u003e Our findings extend Schelling\u0026rsquo;s original insight that simple local rules can produce complex social outcomes. In contrast to the destabilizing dynamics of Schelling\u0026rsquo;s other-ignorant relocation rule, social orientation establishes conditions under which individual rationality, collective welfare, and social integration are mutually aligned. This provides a stronger microfoundation for segregation models by showing how boundedly rational, socially sensitive agents can generate more integrated equilibria. More broadly, our results contribute to theories of self-organization and emergent order by demonstrating how realism-based local decision-making heuristics can reshape global outcomes.\u003c/p\u003e\u003cp\u003e\u003cb\u003eApplications to empirical contexts.\u003c/b\u003e These insights are relevant across multiple domains. In urban settings, residents naturally avoid neighborhoods prone to instability, and our results suggest that socially oriented preferences can counteract destabilizing forces such as segregation or rapid gentrification by fostering more resilient communities. In organizational contexts, similar dynamics apply to team formation and group stability: members who avoid moves likely to unsettle colleagues can strengthen cohesion and reduce turnover. Taken together, these parallels illustrate how social orientation provides a unifying principle across domains where individual mobility decisions aggregate into collective outcomes.\u003c/p\u003e\u003cp\u003e\u003cb\u003eSuggestions for policy makers and social planners.\u003c/b\u003e Our findings suggest several avenues for fostering stability and integration. Policy makers can encourage such outcomes by improving transparency (e.g., publishing neighborhood stability indicators), designing incentives that reward community-preserving moves, and providing institutional support such as vacancy buffers or coordinated relocation programs. Social norms and community engagement can further reinforce stability by embedding social orientation as a shared value. Taken together, these measures align individual mobility choices with key societal outcomes such as reduced segregation, collective welfare, and stability. This alignment, in turn, lowers social costs and fosters more resilient and integrated communities.\u003c/p\u003e\u003cp\u003e\u003cb\u003eLimitations and future directions.\u003c/b\u003e Our study abstracts from several real-world complexities that warrant future work. First, we focus on binary group membership and a uniform satisfaction threshold, whereas empirical settings often involve multiple identities, heterogeneous preferences, and evolving tolerance. Second, while we model two-step observability, actual perception of neighborhood stability may vary across individuals and contexts\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Third, we assume simple greedy search behavior, though more sophisticated heuristics could further influence dynamics. Future research could also integrate network structures beyond grids, such as small-world or scale-free networks, to examine how social orientation operates under different topologies\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. Finally, empirical validation using residential mobility data or organizational turnover patterns would be a critical step in testing the model\u0026rsquo;s applicability.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eBy extending Schelling\u0026rsquo;s segregation model with social orientation, we show that individual-level tendencies to preserve social capital and community can reduce segregation and facilitate the attainment of global stability. These results provide a stronger behavioral foundation for models of segregation and highlight how social orientation, combined with bounded rationality under local observability, shapes collective patterns. Beyond theoretical insight, the findings suggest that fostering socially oriented behaviors\u0026mdash;whether in urban mobility or organizational settings\u0026mdash;may promote more integrated, resilient, and sustainable communities.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll simulation codes developed and used in this study are publicly available to enable replication, validation, and extension of the results at https://github.com/kyuhojin/schelling-social-orientation.git.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the support of the Gwangju Institute of Science and Technology (GIST) for providing research facilities.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResearch funding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by GIST Research Project grant funded by the GIST in 2025.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eU.Y. and K.J. jointly conceived and conceptualized the research, conducted the simulations, performed the data analysis, and developed the code. K.J. designed the figures and generated the plots, wrote the original draft, and directed and supervised the research. Both authors reviewed and edited the manuscript, contributed to the scientific discussion, and approved the final version of the paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u0026nbsp;\u003c/strong\u003eand requests for materials should be addressed to Kyuho Jin.\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSchelling, T. C. Models of segregation. \u003cem\u003eThe American Economic Review\u003c/em\u003e \u003cstrong\u003e59\u003c/strong\u003e, 488\u0026ndash;493 (1969).\u003c/li\u003e\n\u003cli\u003eSchelling, T. C. Dynamic models of segregation. \u003cem\u003eJournal of Mathematical Sociology\u003c/em\u003e \u003cstrong\u003e1\u003c/strong\u003e, 143\u0026ndash;186 (1971).\u003c/li\u003e\n\u003cli\u003eWilensky, U. \u0026amp; Rand, W. \u003cem\u003eAn introduction to agent-based modeling: modeling natural, social, and engineered complex systems with NetLogo\u003c/em\u003e. (MIT Press, 2015).\u003c/li\u003e\n\u003cli\u003eSmaldino, P. E. \u003cem\u003eModeling social behavior : mathematical and agent-based models of social dynamics and cultural evolution\u003c/em\u003e. (Princeton University Press, 2023).\u003c/li\u003e\n\u003cli\u003eBruch, Elizabeth E. \u0026amp; Mare, Robert D. Neighborhood Choice and Neighborhood Change1. \u003cem\u003eAmerican Journal of Sociology\u003c/em\u003e \u003cstrong\u003e112\u003c/strong\u003e, 667\u0026ndash;709, doi:10.1086/507856 (2006-11).\u003c/li\u003e\n\u003cli\u003eXie, Y., Zhou, X., Xie, Y. \u0026amp; Zhou, X. Modeling individual-level heterogeneity in racial residential segregation. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e \u003cstrong\u003e109\u003c/strong\u003e, doi:10.1073/pnas.1202218109 (2012-7-17).\u003c/li\u003e\n\u003cli\u003eLiu, Z., Li, X., Khojandi, A. \u0026amp; Lazarova-Molnar, S. in \u003cem\u003e2019 Winter Simulation Conference (WSC).\u003c/em\u003e 285-296.\u003c/li\u003e\n\u003cli\u003eSert, E.\u003cem\u003e et al.\u003c/em\u003e Segregation dynamics with reinforcement learning and agent based modeling. \u003cem\u003eScientific Reports 2020 10:1\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 11771, doi:10.1038/s41598-020-68447-8 (2020).\u003c/li\u003e\n\u003cli\u003eAbella, D.\u003cem\u003e et al.\u003c/em\u003e Aging effects in Schelling segregation model. \u003cem\u003eScientific Reports 2022 12:1\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 19376, doi:10.1038/s41598-022-23224-7 (2022-11-12).\u003c/li\u003e\n\u003cli\u003eDahrendorf, R. Out of Utopia: Toward a Reorientation of Sociological Analysis. \u003cem\u003eAmerican Journal of Sociology\u003c/em\u003e \u003cstrong\u003e64\u003c/strong\u003e, doi:10.1086/222419 (1958-9-1).\u003c/li\u003e\n\u003cli\u003eBoudon, R. \u003cem\u003eThe logic of social action : an introduction to sociological analysis\u003c/em\u003e. (Routledge \u0026amp; Kegan Paul, 1981).\u003c/li\u003e\n\u003cli\u003eColeman, J. S. Social Capital in the Creation of Human Capital. \u003cem\u003eAmerican Journal of Sociology\u003c/em\u003e \u003cstrong\u003e94\u003c/strong\u003e, S95-S120 (1988).\u003c/li\u003e\n\u003cli\u003eAdler, P. S. \u0026amp; Kwon, S.-W. Social Capital: Prospects for a New Concept. \u003cem\u003eAcademy of Management Review\u003c/em\u003e \u003cstrong\u003e27\u003c/strong\u003e, 17-40 (2002).\u003c/li\u003e\n\u003cli\u003ePutnam, R. D. \u003cem\u003eBowling alone : the collapse and revival of American community\u003c/em\u003e. (Simon \u0026amp; Schuster, 2000).\u003c/li\u003e\n\u003cli\u003ePortes, A. Social capital: Its origins and applications in modern sociology. \u003cem\u003eAnnual Review of Sociology\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 1-24 (1998).\u003c/li\u003e\n\u003cli\u003eLewicka, M. Place attachment: How far have we come in the last 40 years? \u003cem\u003eJournal of Environmental Psychology\u003c/em\u003e \u003cstrong\u003e31\u003c/strong\u003e, 207\u0026ndash;230, doi:10.1016/j.jenvp.2010.10.001 (2011).\u003c/li\u003e\n\u003cli\u003eForrest, R. \u0026amp; Kearns, A. Social cohesion, social capital and the neighbourhood. \u003cem\u003eUrban studies\u003c/em\u003e \u003cstrong\u003e38\u003c/strong\u003e, 2125-2143 (2001).\u003c/li\u003e\n\u003cli\u003eKearns, A. \u0026amp; Parkinson, M. The significance of neighbourhood. \u003cem\u003eUrban studies\u003c/em\u003e \u003cstrong\u003e38\u003c/strong\u003e, 2103-2110 (2001).\u003c/li\u003e\n\u003cli\u003eSampson, R. J. \u003cem\u003eGreat American city : Chicago and the enduring neighborhood effect\u003c/em\u003e. (The University of Chicago Press, 2011).\u003c/li\u003e\n\u003cli\u003eBraakmann, N. Residential turnover and crime\u0026mdash;Evidence from administrative data for England and Wales. \u003cem\u003eThe British Journal of Criminology\u003c/em\u003e \u003cstrong\u003e63\u003c/strong\u003e, 1460-1481 (2023).\u003c/li\u003e\n\u003cli\u003eSampson, R. J., Raudenbush, S. W. \u0026amp; Earls, F. Neighborhoods and violent crime: A multilevel study of collective efficacy. \u003cem\u003escience\u003c/em\u003e \u003cstrong\u003e277\u003c/strong\u003e, 918-924 (1997).\u003c/li\u003e\n\u003cli\u003eSharp, G. \u0026amp; Warner, C. Neighborhood structure, community social organization, and residential mobility. \u003cem\u003eSocius\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 2378023118797861 (2018).\u003c/li\u003e\n\u003cli\u003eAgha, A., Hwang, S. W., Palepu, A. \u0026amp; Aubry, T. The role of housing stability in predicting social capital: Exploring social support and psychological integration as mediators for individuals with histories of homelessness and vulnerable housing. \u003cem\u003eAmerican Journal of Community Psychology\u003c/em\u003e \u003cstrong\u003e74\u003c/strong\u003e, 173-183 (2024).\u003c/li\u003e\n\u003cli\u003eHenrich, J.\u003cem\u003e et al.\u003c/em\u003e In search of homo economicus: behavioral experiments in 15 small-scale societies. \u003cem\u003eAmerican economic review\u003c/em\u003e \u003cstrong\u003e91\u003c/strong\u003e, 73-78 (2001).\u003c/li\u003e\n\u003cli\u003ePersky, J. Retrospectives: The ethology of homo economicus. \u003cem\u003eJournal of Economic Perspectives\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 221-231 (1995).\u003c/li\u003e\n\u003cli\u003eMahmoudi Farahani, L. The value of the sense of community and neighbouring. \u003cem\u003eHousing, theory and society\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, 357-376 (2016).\u003c/li\u003e\n\u003cli\u003ePareto, V. \u003cem\u003eManuale di economia politica con una introduzione alla scienza sociale\u003c/em\u003e. Vol. 13 (Societ\u0026agrave; editrice libraria, 1919).\u003c/li\u003e\n\u003cli\u003eArrow, K. J. \u003cem\u003eSocial choice and individual values\u003c/em\u003e. 2nd. edn, (Wiley, 1963).\u003c/li\u003e\n\u003cli\u003eFriedkin, N. E. Horizons of Observability and Limits of Informal Control in Organizations. \u003cem\u003eSocial Forces\u003c/em\u003e \u003cstrong\u003e62\u003c/strong\u003e, 54-77 (1983).\u003c/li\u003e\n\u003cli\u003eSimon, H. A. A behavioral model of rational choice. \u003cem\u003eThe quarterly journal of economics\u003c/em\u003e, 99-118 (1955).\u003c/li\u003e\n\u003cli\u003eSimon, H. A. \u003cem\u003eModels of man, social and rational : mathematical essays on rational human behavior in a social setting\u003c/em\u003e. (Wiley, 1957).\u003c/li\u003e\n\u003cli\u003eSimon, H. A. \u003cem\u003eModels of bounded rationality\u003c/em\u003e. (MIT Press, 1982).\u003c/li\u003e\n\u003cli\u003eConlisk, J. Why bounded rationality? \u003cem\u003eJournal of economic literature\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 669-700 (1996).\u003c/li\u003e\n\u003cli\u003eKempe, D., Kleinberg, J. \u0026amp; Tardos, \u0026Eacute;. in \u003cem\u003eProceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining.\u003c/em\u003e 137\u0026ndash;146 (2003).\u003c/li\u003e\n\u003cli\u003eBharathi, S., Kempe, D. \u0026amp; Salek, M. 306\u0026ndash;311 (Springer).\u003c/li\u003e\n\u003cli\u003eTversky, A. \u0026amp; Kahneman, D. Availability: A heuristic for judging frequency and probability. \u003cem\u003eSognitive psychology\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 207-232 (1973).\u003c/li\u003e\n\u003cli\u003eMiller, J. H. \u0026amp; Page, S. E. \u003cem\u003eComplex Adaptive Systems: An Introduction to Computational Models of Social Life\u003c/em\u003e. (Princeton University Press, 2009).\u003c/li\u003e\n\u003cli\u003eBerg, N., Abramczuk, K. \u0026amp; Hoffrage, U. in \u003cem\u003eSimple heuristics in a social world\u003c/em\u003e (Oxford University Press, 2012).\u003c/li\u003e\n\u003cli\u003eSteinbacher, M.\u003cem\u003e et al.\u003c/em\u003e Advances in the agent-based modeling of economic and social behavior. \u003cem\u003eSN Business \u0026amp; Economics\u003c/em\u003e \u003cstrong\u003e1\u003c/strong\u003e, 99 (2021).\u003c/li\u003e\n\u003cli\u003eJin, K. \u0026amp; Yu, U. Entropy profiles of Schelling\u0026rsquo;s segregation model from the Wang\u0026ndash;Landau algorithm. \u003cem\u003eChaos: An Interdisciplinary Journal of Nonlinear Science\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e, 113103 (2022).\u003c/li\u003e\n\u003cli\u003eDomic, N. G., Goles, E. \u0026amp; Rica, S. Dynamics and complexity of the Schelling segregation model. \u003cem\u003ePhysical Review E\u003c/em\u003e \u003cstrong\u003e83\u003c/strong\u003e, 056111 (2011).\u003c/li\u003e\n\u003cli\u003eChristakis, N. A. \u0026amp; Fowler, J. H. The spread of obesity in a large social network over 32 years. \u003cem\u003eNew England journal of medicine\u003c/em\u003e \u003cstrong\u003e357\u003c/strong\u003e, 370-379 (2007).\u003c/li\u003e\n\u003cli\u003eChristakis, N. A. \u0026amp; Fowler, J. H. Social contagion theory: examining dynamic social networks and human behavior. \u003cem\u003eStatistics in medicine\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e, 556-577 (2013).\u003c/li\u003e\n\u003cli\u003eFagiolo, G., Valente, M. \u0026amp; Vriend, N. J. Segregation in networks. \u003cem\u003eJournal of economic behavior \u0026amp; organization\u003c/em\u003e \u003cstrong\u003e64\u003c/strong\u003e, 316-336 (2007).\u003c/li\u003e\n\u003cli\u003eHenry, A. D., Prałat, P. \u0026amp; Zhang, C.-Q. Emergence of segregation in evolving social networks. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e \u003cstrong\u003e108\u003c/strong\u003e, 8605-8610 (2011).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Schelling’s segregation model, Microfoundation, Social orientation, Externality, Observability, Bounded rationality","lastPublishedDoi":"10.21203/rs.3.rs-7780879/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7780879/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSchelling\u0026rsquo;s segregation model demonstrates how simple local rules can generate large-scale social patterns, yet it assumes agents act myopically and ignore the broader consequences of their moves. We extend this framework by introducing social orientation as a behavioral microfoundation, reflecting humans\u0026rsquo; communal nature. Socially oriented agents follow boundedly rational heuristics that account for the satisfaction of prospective neighbors within a two-step horizon of observability, in addition to their own. We formalize this through three relocation rules\u0026mdash;negative externality avoiding (NEA), positive externality favoring (PEF), and positive externality optimizing (PEO)\u0026mdash;each capturing a different balance between minimizing disruption and promoting stability. Agent-based simulations reveal that these rules, while maintaining satisfaction, consistently reduce segregation, accelerate the attainment of global stability, and lower relocation moves per agent, thereby reducing social costs. These results provide a stronger behavioral foundation for segregation modeling and show how locally rational, socially sensitive decision-making can scale into equilibria that are not just welfare-enhancing but also yield more integrated and resilient communities.\u003c/p\u003e","manuscriptTitle":"From Self-Orientation to Social Orientation: A Behavioral Extension of Schelling’s Segregation Model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-05 12:35:08","doi":"10.21203/rs.3.rs-7780879/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-07T06:53:35+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-06T12:20:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-03T01:49:03+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-01T08:00:35+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-27T20:46:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"234039727790861403577411707951622589406","date":"2025-10-27T12:48:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-27T10:00:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"285241228827395300743150466442439905443","date":"2025-10-27T02:42:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"287356644855621384338216992659915954420","date":"2025-10-24T10:36:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8510522295643190619463325072457592746","date":"2025-10-24T08:48:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"59429793361339039125443055522466106762","date":"2025-10-23T23:30:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-23T20:32:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-23T20:27:41+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-15T12:32:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-08T07:05:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-08T07:02:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f944ad42-49e0-4379-8cd2-e2a5a85972e2","owner":[],"postedDate":"November 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":57303976,"name":"Physical sciences/Mathematics and computing"},{"id":57303977,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-12-15T16:02:13+00:00","versionOfRecord":{"articleIdentity":"rs-7780879","link":"https://doi.org/10.1038/s41598-025-32159-8","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-12-11 15:57:51","publishedOnDateReadable":"December 11th, 2025"},"versionCreatedAt":"2025-11-05 12:35:08","video":"","vorDoi":"10.1038/s41598-025-32159-8","vorDoiUrl":"https://doi.org/10.1038/s41598-025-32159-8","workflowStages":[]},"version":"v1","identity":"rs-7780879","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7780879","identity":"rs-7780879","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}