=Paper=
{{Paper
|id=Vol-3651/BMDA_paper7
|storemode=property
|title=The Role of Relocation Policies in Urban Segregation Dynamics
|pdfUrl=https://ceur-ws.org/Vol-3651/BMDA-7.pdf
|volume=Vol-3651
|authors=Giovanni Mauro,Luca Pappalardo
|dblpUrl=https://dblp.org/rec/conf/edbt/MauroP24
}}
==The Role of Relocation Policies in Urban Segregation Dynamics==
https://ceur-ws.org/Vol-3651/BMDA-7.pdf
The Role of Relocation Policies in Urban Segregation
Dynamics
Giovanni Mauro1,2,3,∗,† , Luca Pappalardo1,‡
1
Institute of Information Science and Technologies ”Alessandro Faedo” - ISTI-CNR Pisa, Italy
2
Department of Computer Science, University of Pisa, Italy
3
IMT School for Advanced Studies Lucca, Italy
Abstract
This study addresses a gap in the existing literature on the Schelling segregation model by conducting a comprehensive
qualitative assessment of various relocation policies. We introduce novel Schelling models driven by different relocation
policies and analyse their impact on the convergence time and final segregation levels. Our findings demonstrate that all
policies result in segregation levels within bounds established by policies where agents relocate to maximize their happiness.
Notably, a policy ensuring the minimum improvement in agent segregation significantly reduces the model’s convergence
time. These results underscore the potential influence of relocation policies, such as those employed by online recommenders
in real estate platforms, on societal segregation dynamics. The study provides valuable insights into potential strategies for
mitigating and decelerating segregation through tailored recommendations.
Keywords
Segregation, Schelling, Agent-Based Models
1. Introduction the agents’ behaviour, for example associating to each
agent an income status [5] or treating the problem with a
In 1971, Thomas Schelling proposed the very first agent- reinforcement learning approach [6]. Other works anal-
based model to explain how individual actions could re- yse what happens to the model if the environmental con-
sult in a global phenomena like segregation [1, 2, 3, 4]. figuration, like city size or shape change [7, 8, 9, 10, 11],
In Schelling’s simple spatial proximity model, a division or if the dynamics take place on a network-like structure
between the two groups of the population emerged as [12, 13]. In two of these works [12, 9], the agent picks the
a result of a homophily tendency of the agents that, he cell that maximizes its happiness. Other works included
claimed, in real life can happen along many dimensions real-world segregation data along with strategies to vali-
such as ethnicity, language, income, and class affiliation date simulated behaviour with observations [14, 15, 16]
[4]. Agents of two types are placed randomly on a two- or implement agent behaviours based on psychological
dimensional grid (city), with each agent having a prefer- and sociological theories [17, 18, 19, 20]. A recent empir-
ence for living next to people of his type. When an agent ical study suggests a link between experienced income
is surrounded by too many agents of a different kind it segregation and an individual’s tendency to explore new
becomes unhappy and moves to an empty cell that satis- places and visitors from different income groups [21].
fies its preferences. Schelling observed that even when Gambetta et al. [22] show that imposing mobility con-
agents are tolerant (low homophily threshold), the city straints to agents in the Schelling model strongly affects
gets segregated in a few simulation steps. convergence time and the final segregation level.
Several variants and enhancements of the Schelling While previous research has explored various aspects
model have been proposed so far. Some of them modify of urban segregation using models like the Schelling
model, there is still a gap in understanding how different
Published in the Proceedings of the Workshops of the EDBT/ICDT 2024 strategies or guidelines, known as ”relocation policies,”
Joint Conference (March 25-28, 2024), Paestum, Italy directly influence the dynamics of urban segregation.
∗
Corresponding author.
† These policies could include government initiatives, al-
Conceptualized the research, conducted the experiments, made the
plots, wrote the code and the paper. gorithms employed by real estate platforms like Idealista,
‡
Conceptualized the research, supervised the experiments and wrote Booking, or Airbnb 1 , or other mechanisms that shape
the paper. the distribution of people across neighbourhoods.
Envelope-Open giovanni.mauro@phd.unipi.it (G. Mauro); These online real estate platforms are more and more
luca.pappalardo@isti.cnr.it (L. Pappalardo) actively suggesting housing options to users, playing a
GLOBE https://kdd.isti.cnr.it/people/mauro-giovanni (G. Mauro);
pivotal role in influencing urban development [23]. The
https://lucapappalardo.com/ (L. Pappalardo)
Orcid 0000-0001-8067-984X (G. Mauro); 0000-0002-1547-6007 choices individuals make, guided by these platforms or
(L. Pappalardo)
Copyright © 2024 for this paper by its authors. Use permitted under Creative Commons License 1
Attribution 4.0 International (CC BY 4.0). idealista.com, booking.com, airbnb.com
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
other relocation policies, can contribute to scenarios of
either increased or decreased segregation within the city,
or the emergence of other phenomena like gentrifica-
tion [24, 25]. Furthermore, these platforms have been
proven to have a crucial impact on the urban scenario.
For example, in areas with a high AirBnB presence, rents
and transactions substantially rise [26] and racial biases
appear to be reinforced [27].
This work aims to fill the literature gap, underscor- Figure 1: Example of a happy agent (left) and an unhappy
ing the need to systematically measure and understand agent (right) with a homophily threshold ℎ = 3. The dashed
the numerical impact of different relocation policies on square represents the Moore neighbourhood Γ𝐾 of cell 𝐾. On
urban dynamics. It does so by offering relocation sug- the left, three yellow agents are in the neighbourhood of a
gestions to a portion of Schelling model-like agents and yellow agent, so the agent is happy. On the right side, only
scrutinizing how these recommendations affect both con- two agents share the type of the agent in cell 𝐾, making the
vergence time and observed levels of segregation. Our agent unhappy.
findings reveal that policies focused on income (dis)simi-
larity notably increase segregation times, while strategies
encouraging agents to relocate where they would experi- use income data from the 2022 USA Social Security Ad-
ence minimal or maximal happiness expedite segregation ministration report,2 which delineates the US worker
times. Notably, these latter policies establish both lower population percentages within specific income intervals.
and upper bounds for the observed segregation levels of Every agent is assigned an income interval 𝑏 with a prob-
all the analysed policies. ability proportional to the US population within 𝑏, and
the assigned income 𝑤 is picked uniformly at random
within 𝑏. The majority agents are the richest 40% ones;
2. Policy-driven segregation model the minority agents are the poorest 60% ones. Note that
Schelling’s classical model illustrates how urban segre- the income assignment changes at each simulation, en-
gation may emerge due to individual preferences for hancing the robustness of our results. Figure 2 shows
similar neighbours. The city is represented as a grid the income distribution: as expected, a few agents have
where agents of two types (initially placed randomly) a high income, while a heavy tail of agents have a low
inhabit cells or leave them unoccupied (approximately income.
20% remain empty). The parameter ℎ controls agents’
homophily tendencies. At each simulation step, an agent 1.75M
in position 𝐾 evaluates its Moore neighbourhood [28] Γ𝐾 1.5M
Income (USD)
– the surrounding eight adjacent cells in a square forma- 1.25M
tion. If an agent has fewer than ℎ neighbours of its type, 1.0M
it becomes unhappy and relocates to a random, empty 0.75M
cell. Figure 1 schematizes the Moore neighbourhood of a 0.5M
happy cell (left) and unhappy cell (right). The simulation 0.25M
terminates when all agents are happy. 0.0M
0 500 1000 1500 2000
Schelling’s analysis reveals striking outcomes: even Agents (ranked)
with a low ℎ value (e.g., ℎ = 3, indicating agents are Figure 2: Income distribution of the agents in the model. On
happy with only 3/8 of their neighbours sharing their the x-axis, the agents are ranked by associated income. The
type), the city segregates rapidly, maintaining an aver- y-axis represents the income. A few agents have a high income
age segregation level higher than the agents’ minimum (around 1 million dollars), and the majority of the agents have
requirement. a low income.
This paper aims to evaluate the impact of diverse re-
location policies within the classical Schelling model in
terms of convergence time and final segregation level. Simulation starts with agents randomly spread on the
In our model, each simulation takes place on a 50 × 50 grid (see Figure 3, left). Each cell can either be occupied
grid where 75% of its cells are randomly populated with by only one majority agent (yellow), occupied by a mi-
𝑀 agents. The agents are categorised into two groups: nority agent (red) or be empty (white). At the end of
majority agents (60%) and minority agents (40%). At the the simulation, the grid appears spatially clustered as in
beginning of the simulation, each agent is associated Figure 3. Even if agents are tolerant (e.g., they are happy
with a fixed income 𝑤. To this purpose, as in [5], we 2
www.ssa.gov/cgi-bin/netcomp.cgi?year=2022
when just 3/8 of neighbours are similar to them), the city The Moore [28] neighbourhood centered at a cell 𝐾 =
ends up segregated. (𝑥𝐾 , 𝑦𝐾 ) is defined as:
Start occupancy End occupancy
Γ𝐾 = {(𝑥, 𝑦) ∶ |𝑥 − 𝑥𝐾 | ≤ 1, |𝑦 − 𝑦𝐾 | ≤ 1} (3)
We compute the number of agents in the Moore neigh-
bourhood of cell 𝐸 that are of the same type of agent in
cell 𝐽 as:
Σ(𝐽 , 𝐸) = ∑ 𝐶(𝐽 , 𝐸 ′ ) (4)
𝐸 ′ ∈Γ𝐸
where 𝐶(𝐽 , 𝐸 ′ ) denotes the equality of agents between
cell 𝐽 and cell 𝐸 ′ :
Figure 3: Example of a Starting (left) and final (right) distri-
bution of the agents when our model terminates. White cells
are empty; the majority type agents occupy yellow cells, and 1 if 𝑡𝑦𝑝𝑒(𝐽 ) = 𝑡𝑦𝑝𝑒(𝐸 ′ )
𝐶(𝐽 , 𝐸 ′ ) = { (5)
the minority type agents occupy red cells. The grid dimension 0 otherwise
is 25 × 25 for visualisation purposes.
where 𝑡𝑦𝑝𝑒(𝐾 ) returns the type of the agent in cell
𝐾. For each agent, 𝑎, its segregation score indicates the
In contrast with the original Schelling model, and fol-
number of agents of the same type of 𝑎 in its Moore
lowing the idea proposed by Gambetta et al. [22], each
neighbourhood divided by 8 (the maximum number of
cell 𝐴 is associated with a relevance score 𝑟, represent-
Moore neighbours):
ing the cell attractiveness. We assume a core-periphery
structure to model the distribution of relevance across Σ(𝐾 , 𝐾 )
the grid cells [29] (see Figure 4) and use a radial distri- 𝑠(𝑎) = (6)
8
bution where the relevance value of each cell decreases
with its distance from the grid centre 𝐶: The average segregation score of the grid, ⟨𝑆⟩, is the
average of the segregation score of all the agents:
1
𝑟(𝐴) ∝ (1)
𝑑(𝐴, 𝐶) ∑ 𝑠(𝑎)
√ ⟨𝑆⟩ = 𝑎∈𝑀 (7)
|𝑀|
0 The richness 𝑊𝐾 of a Moore neighbourhood Γ𝐾 with
1
2 1.0 𝑚 agents is the average income of the agents in the cells
3
4 within Γ𝐾 :
5 0.9
6 1
7 0.8 𝑊𝐾 = ⋅ ∑ 𝑤 (8)
8 𝑚 𝑋 ∈Γ 𝑋
9 𝐾
10 0.7
11 where 𝑤𝑋 denotes the income of the agent in cell 𝑋.
12
13 0.6 The similarity between two Moore neighbourhoods is
14 assessed in terms of average income similarity, i.e. the
15 0.5
16 square root of the absolute difference between the aver-
17
18 0.4 age incomes of the two neighbourhoods.
19
20
21 0.3 𝑠𝑖𝑚(Γ𝐾 , Γ𝐽 ) = |𝑊𝐾 − 𝑊𝐽 | (9)
22 √
23
24 Finally, 𝑡𝑎𝑢(𝐾 ) represents the consecutive time steps
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 during which a cell 𝐾 has been empty, starting from the
Figure 4: Cell’s relevance distribution. Central cells have a last step and moving backwards.
higher relevance than peripheral ones. The visualized grid
(25 × 25) is smaller than the actual one for visualisation.
2.1. Relocation policies
The distance between any two cells 𝐾 and 𝐽 on the An agent moves to an empty cell when it is unhappy, i.e.,
grid, represented by coordinates (𝑥𝐾 , 𝑦𝐾 ) and (𝑥𝐽 , 𝑦𝐽 ), is the number of neighbours of its type is smaller than a ho-
computed as their Euclidean distance: mophily threshold ℎ = 3. In the original Schelling model,
when unhappy, an agent moves to a random empty cell
𝑑(𝐾 , 𝐽 ) = √(𝑥𝐾 − 𝑥𝐽 )2 + (𝑦𝐾 − 𝑦𝐽 )2 (2)
(random policy). In our model, we introduce more so- • Distance-relevance: the score of a cell is directly
phisticated relocation policies. proportional to the cell’s relevance and inversely
When an agent leaves its cell 𝐴 because unhappy, our proportional to the distance between the starting
model assigns to an empty cell 𝐵 a score proportional to and arriving cell [22]:
a policy 𝒫, sorts the cells in decreasing order, and selects
the top 𝑘 cells. The unhappy agent uniformly randomly 𝑟(𝐵)2
𝑝(𝐵) ∝ (15)
picks one of these 𝑘 cells. We set 𝑘 = 30 to emulate real- 𝑑(𝐴, 𝐵)2
world practices in online real estate platforms, typically This policy encapsulates a fundamental principle
suggesting 30 results per page. 3 of human mobility, as postulated by the Grav-
We investigate six main policies: ity model, wherein individuals seek to minimize
travel time while being drawn toward significant
• Similar neighbourhood: the score of a cell 𝐵 is
locations [30].
calculated as:
In Figure 3, we presented the initial (left) and final
𝑝(𝐵) ∝ 𝑠𝑖𝑚(Γ𝐴 , Γ𝐵 ) (10)
(right) configurations resulting from the execution of the
The more the neighbourhood of a cell 𝐵 is similar model, where all agents follow the baseline random policy.
to the neighbourhood of the original cell 𝐴, in Starting from the same initial configuration, Figure A1
terms of average income of the agents, the higher reports the final configurations of simulations in which
the score of cell 𝐵. all agents follow the other six policies
• Different neighbourhood: the score of a cell 𝐵
is computed as 2.2. Experimental settings
1 In our experiments, we vary the adoption rate 𝑝 ∈
𝑝(𝐵) ∝ (11)
𝑠𝑖𝑚(Γ𝐴 , Γ𝐵 ) [0, 100], a parameter representing the percentage of
agents following the suggested policy. At the beginning
The score of the cell 𝐵 is inversely proportional of the simulation, each agent has a probability 𝑝 to follow
to the economic similarity between the starting the policy during all steps of the simulation, and thus
and ending neighbourhoods. a probability 1 − 𝑝 to follow the random policy. Each
• Minimum improvement: the agents may move agent will be categorised as policy-follower or not at
only to cells it would be happy. Among these cells, the beginning of the simulation based on probability 𝑝.
the score of each cell 𝐵 is inversely proportional The baseline of our experiments is the classical Schelling
to the number of agents of the same class of the model, where all agents follow the random policy (this,
agent in the starting cell 𝐴: 𝑝 = 0).
1 We perform 100 simulations for each configuration
𝑝(𝐵) ∝ , if Σ(𝐴, 𝐵) ≥ ℎ (12) of the model. Each configuration combines the values
Σ(𝐴, 𝐵)
of two parameters: the policy 𝒫 and the adoption rate
• Maximum improvement: the agents may move 𝑝. Each simulation uses a different random spatial dis-
only to cells it would be happy. Among these cells, tribution of agents on the grid and a different random
the score of each cell 𝐵 is directly proportional income assignment taken from the income distribution.
to the number of agents of the same class of the Each simulation terminates when all agents are happy or
agent in the starting cell 𝐴 after a maximum of 300 simulation steps. For each simu-
lation, we calculate the convergence time, 𝑛, the number
𝑝(𝐵) ∝ Σ(𝐴, 𝐵), if Σ(𝐴, 𝐵) ≥ ℎ (13) of steps needed to reach an equilibrium state, and the
• Recently emptied: we assign a higher score to final segregation level, ⟨𝑆⟩, at the end of the simulation.
the empty cells that have been emptied for the
lower amount of time in the last steps:
3. Results
1
𝑝(𝐵) ∝ (14) The analysis of convergence time as 𝑝 varies uncovers
𝜏 (𝐵)
intriguing patterns (see Figure 5).
The rationale behind this policy is to assume that The baseline random model typically converges in
a reasonable choice for an RS, is to suggest users around 27 steps. In accordance with the suggestion of
occupy locations that were already in conditions Gambetta et al. [22] the more the users follow a dis-
of being inhabited and that were recently free. tance relevance policy, the more the segregation process
3
is slowed down (hence, the higher 𝑛). The two policies
see idealista.com
300 a different economic composition significantly amplifies
270
240 segregation, especially when influencing the majority of
210 min. improv. random
the population.
180 max. improv. sim. neigh. Conversely, four policies lead to a reduction in ⟨𝑆⟩: re-
150 rec. emptied diff. neigh.
n
dist. rel.
120 cently emptied, distance-relevance, similar neighbourhood
90 and especially minimum improvement. The recently emp-
60 tied policy shows a negligible reduction until only 60% of
30 the population adopts it but becomes increasingly effec-
0
0 10 20 30 40 50 60 70 80 90 100 tive with an increased adoption. The distance-relevance
p (%) policy substantially decreases ⟨𝑆⟩. However, the policy
Figure 5: Average convergence time 𝑛 across 100 simulations that most effectively reduces final observed segregation
of models with a growing percentage 𝑝 of users accepting the levels is minimum improvement: even with a small per-
suggestion of the RS. centage of agents following this policy, the average ⟨𝑆⟩
reduction is substantial.
rooted in the neighbourhood income similarity, similar 4. Discussion
neighbourhood and different neighbourhood substantially
increase convergence time. In particular, the model is Our study explores the intricate relationship between
not able to reach a stable equilibrium if 10% (or more) relocation policies and the dynamics of urban segregation.
agents relocate to a similar neighbourhood. A similar Through a series of simulations, we unveil the impact
result holds for the recently emptied policy. of these policies on both convergence time and the final
Remarkably, the only two policies that effectively expe- level of segregation.
dite segregation, reducing the value of 𝑛 as their adoption The implications of policies grounded in neighbour-
rate 𝑝 increase, are the policies that suggest agents to hood composition, such as the similar neighbourhood and
relocate in places where they would be happy: minimum different neighbourhood, reveal intriguing trends. On the
improvement and maximum improvement. one hand, as one can expct, suggesting agents to relo-
cate to a neighbourhood with a similar income, thereby
0.74 maintaining a comparable average income distribution
0.72 among neighbours, increases convergence times. In fact,
0.70
0.68 if agents adhere strictly to this policy, the model fails to
0.66 converge. On the other hand, it is noteworthy that even
0.64
S
suggesting agents to relocate to a socioeconomically dif-
0.62 min. improv. random ferent neighbourhood slows down segregation times. This
0.60 max. improv. sim. neigh.
0.58 rec. emptied
dist. rel.
diff. neigh. deceleration is most pronounced when between 40% and
0.56 60% of users relocate according to this policy. Interest-
0 10 20 30 40 50 60 70 80 90 100 ingly, having 100% of agents follow this policy produces
p (%)
a similar effect, in terms of convergence time, as only
Figure 6: Average final segregation levels ⟨𝑆⟩ across 100 sim- 10% of agents following it. This dichotomy can also be
ulations of models with a growing percentage 𝑝 of users ac- appreciated in the segregation levels ⟨𝑆⟩ analysis.
cepting the suggestion of the RS. Counterintuitively, a policy that suggests agents re-
locate to a socioeconomically different neighbourhood,
Even more intriguing insights emerge from analysing thus suggesting a mixing, increases the average observed
the final segregation level varying the adoption rate 𝑝 segregation levels as its adoption increases. Surprisingly,
(Figure 6). The final segregation level ⟨𝑆⟩ for the baseline suggesting agents relocate to neighbourhoods with a
random model stabilises around 0.66. Notably, for all similar average income distribution reduces the final ob-
policies, the more users adhere to a policy, the greater served segregation levels.
the change in ⟨𝑆⟩, indicating that suggesting relocation The analysis of the observed final segregation level
policies other than the random one significantly impacts seems bounded by the outcomes of two extreme poli-
urban segregation. cies: the maximum improvement policy drives the final
Only two policies, different neighbourhood and max- segregation level to its maximum, and the minimum im-
imum improvement amplify final segregation levels as provement policy minimizes it. This distinction becomes
adoption rate 𝑝 increases. In particular, the former leads particularly pronounced when the relocation policies
to the most substantial rise, while even the policy sug- are adopted by many agents (high adoption rate 𝑝). In-
gesting an unhappy user move to a neighbourhood with deed, minimum improvement for 𝑝 = 100% reduces the
distance relevance, 133 steps minimum improvement, 6 steps
final segregation level by 16.67% compared to the base-
line model. Conversely, maximum neighbourhood sig-
nificantly increases the final segregation level by 13.64%.
From a sociological perspective, this observation em-
phasizes how policy choices significantly mould societal
structures. The extremes represented by the accentuated
segregation of the similar neighbourhood or maximum im-
provement policies and the minimized segregation of the
minimum improvement policy delineate the wide spec-
trum of potential societal outcomes based on policy im- recently emptied, 300 steps similar neighborhood, 300 steps
plementations. Recognizing these boundaries provides
crucial insights into the intricate connection between
policy decisions and the resultant societal dynamics. It
clarifies how different policies can influence segregation
levels, thereby guiding more informed and balanced in-
terventions.
5. Conclusion different neighborhood, 17 steps maximum improvement, 4 steps
This paper investigates the effects of different relocation
policies within the Schelling model on convergence time
and final segregation levels. It sheds light on how these
policies influence urban segregation dynamics, paving
the way for future research and the development of more
equitable urban strategies, particularly in understanding
the impact of online real estate platforms on neighbour-
hood demographics.
This work can be improved and extended in several Figure A1: Examples of final configurations produced by each
directions. Inspired by Moro et al. [31], designing a pol- policy on a 25 × 25 grid.
icy that exploits the time series of empty cells could offer
valuable insights. This approach might uncover historical
occupancy patterns, revealing which cells have predom-
inantly housed similar agents or which tend to retain other policies, particularly the minimum improvement
happy occupants for longer durations. Similarly, there is one (top right), which appears to be more mixed.
room to expand the model by training a Machine Learn-
ing (ML) model across multiple model iterations. This Acknowledgments
approach could empower algorithms to predict optimal
cell choices for ensuring an agent’s maximal happiness Questo lavoro è stato finanziato dal PNRR (Piano
probability. Moreover, by considering broader global fac- Nazionale di Ripresa e Resilienza) nell’ambito del pro-
tors, these models might suggest strategies that maintain gramma di ricerca 20224CZ5X4_PE6_PRIN 2022 “URBAI
a stable or reduced average segregation level within the - Urban Artificial Intelligence” (CUP B53D23012770006),
city. Finanziato dall’Unione Europea - Next Generation EU.
This research has also been partially supported by EU
project H2020 SoBigData++ G.A. 871042; and NextGener-
Appendix ationEU—National Recovery and Resilience Plan (Piano
In Figure A1, we present examples of final configurations Nazionale di Ripresa e Resilienza, PNRR), Project “SoBig-
produced by the execution of the model in which the Data.it—Strengthening the Italian RI for Social Mining
100% of agents follow one of the six policies. All the and Big Data Analytics”, prot. IR0000013, avviso n. 3264
simulations starts from the same initial configuration on 28/12/2021.
reported in Figure 3 (left). Authors thank Dino Pedreschi for its precious intu-
It is noticeable that the different neighbourhood and itions as well as Emanuele Ferragina, Giuliano Cornac-
maximum improvement policies, depicted in the last row, chia and Daniele Gambetta for their valuable sugges-
result in a visually less mixed scenario compared to the tions.
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A. Online Resources
The code for replicating and reproducing our model and
experiments is available at
https://github.com/mauruscz/RS-chelling. The simula-
tion has been performed using the Python module MESA
[32].