Simulating Superdiversity

Simulating Superdiversity, Bruce Edmonds, Birmingham, January 2017. slide 1
Simulating Superdiversity
Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

Acknowledgements
• This work came out of a long personal
collaboration with David Hales 
• A tiny part of the “SCID” project (the
Social Complexity of Immigration and
Diversity), 2010-2016, funded by the
EPSRC under their “Complexity
Science for the Real World” call 
• In conjunction with the Cathy Marsh
Institute for Social Research and the
Department for Theoretical Physics at
the University of Manchester 

Aims of Talk
• To talk about agent-based social simulation, and
its place in social science
• To illustrate how social simulation might be used
to explore and illustrate issues of diversity
• To show both its power and its difficulties
• To, hopefully, inspire collaboration for the
development of this tool for understanding issues
of diversity

Caveats!
• What will be presented is an abstract simulation
• This should be treated as a kind of “thought
experiment” to suggest ideas, hypotheses etc.
• It has not been checked against any observed
data and so does not tell us about what happens
in observed processes/phenomena
• It is merely to show what sort of thing can be put
into a simulation…
• …with the hope of stimulating collaborations that
might develop a model with a better evidential
grounding from which conclusions might be drawn

Structure of Talk
1. About agent-based social simulation
2. A brief bit of historical simulation context
3. About the simulation model set-up
4. The complexity of simulation outcomes
5. How this kind of simulation might be developed
into something more serious

Agent-Based Simulation
• Is a computer program
• Much like a multi-character game, where each
social actor is represented by a different “agent”
• These agents can each have very different
behaviours and characteristics
• Social phenomena (such as social networks) can
emerge out of the decisions and interaction of
these individual agents (upwards “emergence”)
• But, at the same time, the behaviour of individuals
can be constrained by “downwards” acting rules
and social norms from society and peers
• No particular theoretical assumptions are needed!

System Dynamics, Statistical, or other
Mathematical modelling
Real World Equation-based Model
Actual Outcomes
Aggregated
Actual Outcomes
Aggregated
Model Outcomes

Actual Outcomes
Aggregated
Actual Outcomes
Aggregated
Model Outcomes

Individual- or Agent-based simulation
Real World Individual-based Model
Actual Outcomes Model Outcomes
Aggregated
Actual Outcomes
Aggregated
Model Outcomes

Aggregated
Actual Outcomes
Aggregated
Model Outcomes

Aggregated
Actual Outcomes
Aggregated
Model Outcomes
Agent-

What happens in ABS
• Entities in simulation are decided on
• Behavioural Rules for each agent specified (e.g. sets of
rules like: if this has happened then do this)
• Repeatedly evaluated in parallel to see what happens
• Outcomes are inspected, graphed, pictured, measured
and interpreted in different ways
Simulation

What happens in ABS
Simulation

What happens in ABS
Simulation
Specification (incl. rules)

What happens in ABS
Simulation

What happens in ABS
Simulation
Representations of OutcomesSpecification (incl. rules)

In Vitro vs In Vivo Analogy
• In biology there is a well established distinction
between what happens in the test tube (in vitro) and
what happens in the cell (in vivo)
• In vitro is an artificially constrained situation where
some of the complex interactions can be worked
out…
• ..but that does not mean that what happens in vitro
will occur in vivo, since processes not present in vitro
can overwhelm or simply change those worked out in
vivo
• One can (weakly) detect clues to what factors might
be influencing others in vivo but the processes are too
complex to be distinguished without in vitro
experiments or observation

The Micro-Macro Link
• How do the tendencies, abilities and observed
behaviour of individuals…
• …relate to the measured aggregate properties of
society?
• Social Embedding etc. implies this link is complex
• Averaging assumptions (a general tendency +
random noise) do not capture non-linear interaction
• This is often two-way, with society constraining and
framing individual action as well as individual
constituting society in an emergent fashion
• Somewhat-persistent, complicated meso-level
structures mediate these effects – these might be key
to understanding this

Micro-Macro Relationships
Micro/
Individual data Qualitative, behavioural, social psychological data
Theory,
narrative
accounts
Social, economic surveys; Census
Macro/
Social data
Simulation

Simulations can be very complex
• Simulations can be complicated, with lots of detail
happing simultaneously to many agents in parallel
• This is the point of agent-based simulation, since
it allows us to track complicated processes that
we could not hold in our mind
• There may be emergent phenomena – patterns
that appear at the macro level that are not
obviously ‘built into’ the structure but result from
the processes at the micro level
• As well as constraints from the population and
surrounding agents on behaviour of individuals
• This makes the simulations difficult to understand

Understanding Simulations
• Although complex, simulation outcomes can be
inspected in multiple ways at any level of detail
• Any number of experiments on the simulation can
be performed to test understandings
• Population of agents can be measured just as
people can be, (but all of them and without error)
• However other ways can be more helpful, e.g.
– Using different visualisations of the population
– Looking at social networks
– Following individual agents and generating their
‘stories’

Historical Context 1: Schelling’s
Segregation Model
Schelling, Thomas C. 1971.
Dynamic Models of
Segregation. Journal of
Mathematical Sociology 1:143-
186.
Rule: each iteration, each dot
looks at its 8 neighbours and if,
say, less than 30% are the
same colour as itself, it moves
to a random empty square
This was a kind of counter
example – it showed that
segregation could emerge with
low levels of ethnocentrism

Historical Context 2: Axelrod’s Model
of Cultural Change
Axelrod, R (1997) The
dissemination of culture - A
model with local convergence
and global polarization.
Journal of Conflict
Resolution, 41(2):203-226.
Rule: each iteration, each
patch picks a neighbour, if is
sufficiently similar copy one
of their ‘values’
Increasing sized patches
appear different from each
other but uniform inside.
Colours above are a summary,
ethnicity of patches represented
as a string of values

Historical Context 3: Hammond and
Axelrod’s Model of Ethnocentrism
Hammond, RA. & Axelrod, R.
(2006) The Evolution of
Ethnocentrism. Journal of Conflict
Resolution, 50(6):1-11.
Rules: Colours are different
ethnicities: circles cooperate with
same color, squares defect with
same color, filled-in shapes
cooperate with different color,
empty shapes defect with
different color.
If new agents inherit from parents
(with some mutation) then
ethnocentrism evolves over time

This model aims to…
• …go beyond that of a few, pre-defined sets, but
rather allows groupings to emerge and dissolve
• That does not pre-determine what constitutes an
individual’s “in-group” but lets this develop
• That takes seriously the heterogeneity of people
• But also how behaviour and groupings result from
the social embedding of those individuals within
their social environment as a result of their
individual experience and interactions
• To be a starting point for the development of a
more serious model of these issues

Agents in the model have:
• 2 continuous characteristics: their ethnic tag,
and a cultural tag – only difference is that
cultural tag can be changed! No hard-wired
link to behaviour.
• Behaviour is specified as to which action (out
of 3 possible) an agent takes towards: (a) a
member of its in-group (b) a non-member
– 3 possible actions no nothing (Sit), donate
altruistically (Donate), harm other (Fight)
• 2 numbers to determine the extent of their
ethnic- and cultural-tolerance
• Their score in current round of interactions

The meaning of actions
Before the rounds all agents have a score of 0
In the rounds of the interaction phase when paired
• “Bit” (do nothing) no change is made
• “Donate” the agent transfers value to the other at
a cost to itself (value received 0.2 value cost by
sender is 0.1 here)
• “Fight” the agent subtracts value from the other at
a cost to itself (value lost 1.0 value cost by sender
is 0.1 here)
Outcome: an agent may imitate (mutable)
characteristics from one with a higher score

In- and Out-group
• Agents can behave differently towards other
agents, depending on whether other is in their in-
group or not (any of the 3 actions can be their
behaviour to in-group and to out-group)
• Key rule for in-group: the difference in cultural
characteristics is less than their cultural tolerance
AND if the difference in ethnic characteristics is
less than their ethnic tolerance
• Note this is not symmetric: A may consider B as
part of their in-group but not vice versa (e.g.
because B is less tolerant of deviation)

Illustration of characteristics,
tolerances and in-group
Rangeofculturalcharacteristics
Range of ethnic characteristics

Ethnic tolerance

Cultural tolerance
Ethnic tolerance

A visualisation of a population

Each
rectangle
represents
an individual

Projections to 1D

Cultural
Picture
only

Ethnic
picture
only

FS
“Fight”
in-
group
“Sit” with
out-
group

Behaviour Rules
• (Interaction) Several times for each agent:
– agent paired with other (in the same patch)
• If other is in its in-group: do in-group action to it
• If other is not in its in-group: do out-group action to it
• (Imitation) Several times for each agent:
– agent paired with other (in the same patch)
• If other agent has a better score than self: imitate all that
agent’s characteristics except ethnicity
• (Noisy change) For each agent:
– with a small probability randomly change strategy
– with a small probability randomly change tolerances
– with a small probability randomly change cultural value

Pairing
Is biased in both interaction and imitation phases
• A parameter can be set so as to make it more
likely an agent will be paired from another in its in-
group during the interaction phase (here 50% of
the time from own group 50% at random)
• Another parameter controls how likely an agent is
to be paired with another of its own group during
the imitation phase (here 10% of the time from
own group, 90% at random)

Summary of Model
• Agents have their own behaviours (Sit, Donate,
Fight), different for in- and out-groups
• They have their own definitions of their in-group
• Ethnic characteristic is fixed, but cultural value
characteristic may change
• Model goes through interaction, imitation and
noisy change phases
• No initial correlation between ethnic, cultural
values and behaviours (behaviours are always
random at the start)
• Key process: imitation of an agent doing better

Example run 1
• Only one patch
• 200 agents
• A continuous range of ethnic characteristics
• Initially random ethnic and cultural characteristics
• Initially wide tolerances

Emergent
cooperative
group based on
culture

Graphs of example run 1

‘Waves’ of
group-based
cooperation

‘Waves’ of
group-based
cooperation
Cultural
distinctions
emerging
but not
increasing
ethnic ones

One cooperative dynamic found
One of the dynamics found in this model is:
1. A group of mutual cooperators happens to form
2. These do very well by mutually donating to each
other and hence increasing their score a lot
3. Other agents imitate these, ‘joining’ their group
and copying their cooperative strategy
4. So the group grows quickly
5. After a while one agent in the group changes its
strategy or group and so gains from

Example run 2
• Only one patch
• 200 agents
• 3 differentiated ethnicities
• Initial cultures correlated with ethnicity
• Initially small tolerances

Cooperation in run 2
• Cooperation does occur, with the strategy to
cooperate being imitated
• But cooperation is defined by culture AND
ethnicity
• However no lasting purely ethnically-based
cooperation lasts in this model

Example run 3
• four patches
• 100 agents per patch
• Initial cultures and space correlated with ethnicity
(so one majority and minority ethnicity in each
patch)
• No migration – 4 independent patches

A Patch

Each ‘spoke’
is a group of
culturally
identical
agents

Colours indicate
behaviour,
shape is
ethnicity

Graphs of run 3

Graphs of run 3
Low
cooperative
dynamics
some
aggressive
action

Example run 4
• four patches
(so one majority and minority ethnicity in each
patch)
• Migration at low rates (0.5%) and comparison
between agents on other patches also at low
rates (1%)

Good
cooperative
dynamics but
presence of
aggressive
strategy but
unexpressed

Example run 5
• 5x5 patches
(so one majority on each patch)
• Migration at low rates (0.5%) and comparison
between agents on other patches also at low
rates (1%)

Graphs for run 5

Graphs for run 5
Cooperative
dynamics but
much greater
variety of
behaviours
and more
expressed
aggression

Summary of model
In this model…
• Groups, in-groups etc. all ‘fuzzy’ and only identifiable from
patterns and processes observed
• Cultural groups strongly emerged even when enthicities
and cultures separated to start with
• Groups are dynamic, new ones forming, growing,
decaying all the time
• Cooperation maintained despite ‘selfish’ motivation to
‘defect’ and be a parasite
• Sometimes ethno-cultural groups
• Migration between patches promotes cooperation
• The more patches and the smaller the numbers on each
patch (also the lower the migration) the greater the variety
of behaviours and the more expressed agressive actions
there were

The End
The Centre for Policy Modelling:
http://cfpm.org
These slides will be available at: http://slideshare.net/BruceEdmonds
Ad for Workshop!
Beyond Schelling and Axelrod:
Computational Models of
Ethnocentrism and Diversity
Manchester
June 7-8th
Google
“Ethnosim2017”

Simulating Superdiversity

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