simulating superdiversity

Simulating Superdiversity, Bruce Edmonds, Birmingham, January 2017. slide 1

Simulating Superdiversity

Bruce EdmondsCentre 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 OutcomesAggregated

Model Outcomes

Actual Outcomes

Aggregated

Model Outcomes

Actual Outcomes

Aggregated

Model Outcomes

Actual Outcomes

Aggregated

Model Outcomes

Actual Outcomes

Aggregated

Model Outcomes

Individual- or Agent-based simulation

Real World Individual-based Model

Actual Outcomes Model Outcomes

Aggregated

Model Outcomes

Aggregated

Model Outcomes

Aggregated

Model Outcomes

Aggregated

Model Outcomes

Aggregated

Model Outcomes

Aggregated

Model 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

What happens in ABS

Simulation

What happens in ABS

Simulation

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 vitrowill occur in vivo, since processes not present in vitrocan 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 vitroexperiments 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

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-

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

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

Range o

f cultura

l chara

ristics

Range of ethnic characteristics

Range o

f cultura

l chara

ristics

Range o

f cultura

l chara

ristics

Range o

f cultura

l chara

ristics

Range o

f cultura

l chara

ristics

Range o

f cultura

l chara

ristics

Range o

f cultura

l chara

ristics

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

Range o

f cultura

l chara

ristics

Cultural tolerance

Ethnic tolerance

A visualisation of a population

rectangle

represents

an individual

Projections to 1D

Cultural

Picture

Ethnic

picture

“Fight”

“Sit” with

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

cooperative

dynamics

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%)

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

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

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