Why more contact may increase cultural polarization Presentation prepared for QMSS Seminar Networks and Behavior: Statistical Models and Advances in the

Why more contact may increase cultural

polarizationPresentation prepared for QMSS Seminar

Networks and Behavior: Statistical Models and Advances in the Theory of Action

Andreas Flache, University of GroningenMichael W. Macy, Cornell University

This work has been supported by Innovational Research Incentive (VIDI)

Preprint available at arXive physics/0604196

Flache, Macy. Why more contact may increase cultural polarization

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Cultural diversity and global communication

Two positions Increasingly global communication

homogenizes cultures E.g. Hamelink 1983

Increasingly global communication makes cultural differences and cross-cultural conflict more pronounced E.g. Huntington 1996


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How define cultural diversity for the sake of modeling it? In 1952, Kroeber and Kluckhohn compiled a list

of more than 200 different definitions of culture. Anderson: “culture provides a set of ideas,

values and beliefs that function to provide a basis for interaction and understanding among a collection of people”

Axelrod: culture is “set of individual attributes that are subject to social influence”

Examples Firm: multidisciplinary working team School: multiethnical school class Neighborhood: class + ethnical differences that go

along with differences in ideas, values and beliefs


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Fundamental mechanisms: Why is there cultural diversity

in the first place?

Two powerful and general mechanisms in interpersonal interaction Homophily the more similar people are,

the more they influence each other. Influence the more people influence each

other, the more similar they become.

How can there be stable diversity in a world where nobody is entirely disconnected from influence?


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Computational models of culture formation

Models proposed by Carley, Axelrod, Mark, Latane… Multiple agents

Cultural profiles: vector cultural “attributes” per agent Relations: likelihood of interaction, strength of influence

Homophily the higher the similarity, the more likely the interaction

(relational dynamic). Influence:

if there is interaction, the interactants become more similar (attribute dynamic).

Interaction & influence is restricted to local neighbors


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Profile of an agent:

Cultural overlap between two neighbors: Proportion of features with equal traits

Probability of interaction = overlap

Influence:If interaction, one randomly chosen interactant copies previously dissimilar trait of interaction partner

Axelrod’s original model (slight reformulation)

}1,...,1,0{),,...,,( 21 Qsssss ixiFiii


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Results (replication of Axelrod 1997): the evolution of stable diversity

The “baseline scenario” 5 features, 15 traits, 10x10 agents small neighborhoods, no torus

Stable diversity can be an equilibrium Diversity measured as #cultural regions,

i.e. “Set of contiguous sites with identical culture”

On average about 20 different cultural regions in equilibrium in this scenario


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Why is there stable diversity? Axelrod’s solution: interaction thresholds

Influence stops when individuals are too different

i.e.: zero overlap. preservation of diverse,

isolated “subcultures” Local regions become

homogenous over time Differentiation from

neighboring regions No more influence

between local regions Stable diversity

(Axelrod: “polarization”)

Equilibrium of Axelrod model

(F=5,Q=15, N=10x10

von Neumann neighborhood)


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Modeling globalization: Increasing geographical range of communication

Axelrod (1997): Increasing range less diversity Diversity = #distinct “cultural regions” in equilibrium Initial distribution more similar across local regions (random) more overlap, i.e. smaller chance of getting isolated from neighboring regions

Follow-up studies E.g. Shibani (2001), Greig (2002) Global mass media and larger range of interaction allow local minorities to find support

against local conformity pressures Globalized communication may also increase diversity

Implications of Axelrod’s model for globalizing communication


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What is missing…(1): metric scaling Axelrod etc assume nominal opinion space

Either you agree or you don’t: direction and degree of influence on an issue can not be scaled

Metric scaling may often be more adequate “What should be the age at first marriage” Many traditional opinion formation models use

metric scaling of opinions...(French, Abelson…) And they imply that homogeneity is an almost

inevitable outcome of opinion dynamics


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What is missing… (2): Negativity

Heterophobia and negative influence Axelrod etc assume that agents never change

opinions to decrease similarity Empirical evidence for “negative referents”,

“profiling”

Negativity in our model: Heterophobia

if difference too large, relations become negative Negative influence

If relations are negative, agents increase distance These mechanisms may profoundly change

influence dynamics (Macy et al 2002)


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Our model with metric scaling and negativity

Nowak & Vallacher, 1997 (Hopfield attractor NN) Agent i has “opinion” on K dimensions (-1 ≤sik ≤ 1) Agents i and j are tied by positive or negative

weights (-1≤wij≤1) Opinion of j can attract or repel opinion of i,

depending on wij

i jwij


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Opinion change depends on relations

Effect of sj on si depends on the connection between i and j Positive weights: opinions become more similar Negative weights: opinions become less similar Change in position of i with regard to issue s is

weighted average of distances sj-si modified by “moderation” m

Moderation: degree to which actors weigh small differences in opinion relatively less (m >1 “moderate”)

N

j

mtitjijtiti

ssw

Nss

1

,,,1, )

2(

1


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Relational change depends on opinions

Weight wij increases with agreement in the K states of i and j

Threshold for negative agreement = midpoint of interval (zero).

Weight moves towards level of current agreement with “structural learning rate” λ

)1()1( 11, K

ssww

K

kjktikt

ijttij


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Access structure channels influence

Mutual influence only for local neighbors

Agents are arranged on a circle Parameter range (r)

% of population to which agent has access

Access is symmetrical r=10% r=20% r=50%

Examples for N=20


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Experiment 1: Metric (continuous) scaling, but no negativity

Baseline similar to Axelrod’s high diversity condition

Strongly local interaction: N=100, r = 2% Small number of opinion dimensions: K=1 Fast adaptation (λ=1), linear influence

(m=1) No negativity

just homophily and social influence w restricted to 0..1


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Experiment 1: Results

Monoculture is unique equilibrium outcome

ExplanationWith continuous opinions, agreement is almost never zero Influence network remains “compact” (Abelson) All agents gradually move towards emergent consensus


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Experiment 2: Replication of experiment 1, now with negativity

Polarization is likely equilibrium outcome

Polarization: small number of subgroups with maximal internal agreement and maximal external disagreement

ExplanationAgents who disagree initially with many others move away from their “enemies” towards extreme end of opinion scale

Their “friends” follow them, their enemies move in opposite direction

emergent polarization


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Experiment 3:Replication of experiment 2 with variation of contact range

Larger contact range increases polarization but only with negativityExplanation: highly localized interaction allows equilibria with high diversity due to

gradual shift of opinions from one extreme to the other across space. The more local neighborhoods overlap, the larger is the influence range of

“extremists”, the more difficult it is to obtain coordination on “multiplex” equilibria


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A stylized example

smokingnoye

scritical distance

disliking disagreementliking agreement


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A stylized example: immediate full contact

smokingnoye

scritical distance


Tendency towards polarization

Macy, Kitts, Flache, Benard (2003)


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A stylized example: small groups first

smokingnoye

scritical distance


Local convergence eliminates extremes cohesion when subgroups merge (Flache et al, in progress)


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k=2 moderation=2

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Diversity

Polarization

Variance

k = 2 moderation=1

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Polarization

varianceS

Conditions for the effects of larger range:

•When number of issues (k) increasesNegative ties less likely from random

startEffect tends to become negative

•When moderation (m) increasesLarge opinion differences weigh relatively

morePositive effect (on polarization) prevails

• Inverted U-shape effect of range possible

Range has two opposing effects:•Larger range increases overlap between

neighboring regions pressure towards conformity• ..it also increases influence range of

“extremists” pressure towards polarization

Robustness tests


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Preliminary conclusions Some previous models suggest cultural diversity

can persist despite global interaction range, other’s don’t

All rely on nominal opinion space. Model with continuous opinion space and negative

social influences: Larger contact range may increase cultural polarization

But it also reduces diversity, consistently with Axelrod etc. Depending on moderation and #issues, effect of

increasing range of interaction is increasing polarization decreasing polarization Inverted U-shape


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Another thing that is missing: demographic differences

Demographic differences “fixed categories”, e.g. race, gender, age Can affect “perceived similarity”

see homophily research

Integration into model: make some opinion dimensions fixed and

discreet, e.g. “red” = +1, “blue” = -1. Everything else remains the same.


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The effects of contacts with negative influence and fixed categories

Negative influence, but with fixed categories Diversity declines as range of interaction goes

up, but… Polarization likely at all r, increasingly strong as r

goes up. Fixed categories introduce a tendency towards

polarization from the beginning. Dynamics amplify this tendency.

The larger the range, the stronger are polarization and segregation (at least for k=3).


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Effects of contact with negative influence and fixed categories (k=3)

Range at k=3 (one fixed category, two opinions)

increases polarization and segregation, decreases diversity.

Diversity = #distinct opinions / N

Polarization = var pairwise agreement

Segregation = degree to which positive ties are within categories and negative ties across categories

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Diversity

Polarization

Segregation


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Range at k=4 (one fixed category, three opinions) Inverted U-shaped effect on polarization and

segregation, U-shaped effect on diversity.




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Polarization

Segregation


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Range at k=5 (one fixed category, four opinions) Inverted U-shaped effect on polarization and

segregation only at low range. U-shaped effect on diversity only at low range.




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Polarization

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A new view on contacts: timing and structure

vs.

For example:mixing cultures in schools

Period 1

Period 2


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Initially homogenous subgroups

emergent local consensus extremes moderate integration

Immediate full contact

initial similarities increase, initial dissimilarities increase polarization

A new hypothesis

Theoretical integration of positivity and negativity implies

(under certain conditions):

vs.


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Empirical research Phase 1: test mechanisms in controlled context. Group

discussion experiments (cf. Friedkin): manipulate contact structures measure simultaneous evolution of network (“liking”) and opinions

Phase 2: test selected hypotheses across a range of field contexts. At present we have access to:

2 data sets containing data on class and track composition, opinion and network evolution in ethnically diverse school settings.

2 data sets containing data on task interdependencies, opinion and network evolution in workplace settings.

Use statistical methods based on “actor oriented statistics” (Snijders) to disentangle micromechanisms in evolving networks (Siena)


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More future research Theoretical

Explicate individual incentives E.g. trade-off homophily vs gains from collaboration with

dissimilar others towards analytical models, e.g. stochastic stability

(Young) Apply this to effects of global communication on

cultural convergence (e.g. Axelrod) Empirical

social influence in experiments / online interaction Is there influence? Is it negative?

E.g. world value survey and data on accessibility of internet in different countries or social strata

Is there a relationship between cultural convergence / divergence and access to the internet?

Documents

Why more contact may increase cultural polarization Presentation prepared for QMSS Seminar Networks and Behavior: Statistical Models and Advances in the