1. Why more contact may increase cultural polarization Presentation prepared for QMSS Seminar Networks and Behavior: Statistical Models and Advances in the Theory of Action Andreas Flache, University of Groningen Michael W. Macy, Cornell University This work has been supported by Innovational Research Incentive (VIDI) Preprint available at arXive physics/0604196

2. Flache, Macy. Why more contact may increase cultural polarization2 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

3. Flache, Macy. Why more contact may increase cultural polarization3 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

4. Flache, Macy. Why more contact may increase cultural polarization4 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?

5. Flache, Macy. Why more contact may increase cultural polarization5 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

6. Flache, Macy. Why more contact may increase cultural polarization6 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)

7. Flache, Macy. Why more contact may increase cultural polarization7 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

8. Flache, Macy. Why more contact may increase cultural polarization8 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)

9. Flache, Macy. Why more contact may increase cultural polarization9 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

10. Flache, Macy. Why more contact may increase cultural polarization10 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

11. Flache, Macy. Why more contact may increase cultural polarization11 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)

12. Flache, Macy. Why more contact may increase cultural polarization12 Our model with metric scaling and negativity Nowak & Vallacher, 1997 (Hopfield attractor NN) Agent i has “opinion” on K dimensions (-1 ≤s ik ≤ 1) Agents i and j are tied by positive or negative weights (-1≤w ij ≤1) Opinion of j can attract or repel opinion of i, depending on w ij ij w ij

13. Flache, Macy. Why more contact may increase cultural polarization13 Opinion change depends on relations Effect of s j on s i 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 s j -s i modified by “moderation” m Moderation: degree to which actors weigh small differences in opinion relatively less (m >1 “moderate”)

14. Flache, Macy. Why more contact may increase cultural polarization14 Relational change depends on opinions Weight w ij 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

15. Flache, Macy. Why more contact may increase cultural polarization15 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

16. Flache, Macy. Why more contact may increase cultural polarization16 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

17. Flache, Macy. Why more contact may increase cultural polarization17 Experiment 1: Results Monoculture is unique equilibrium outcome Explanation With continuous opinions, agreement is almost never zero  Influence network remains “compact” (Abelson)  All agents gradually move towards emergent consensus

18. Flache, Macy. Why more contact may increase cultural polarization18 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 Explanation Agents 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

19. Flache, Macy. Why more contact may increase cultural polarization19 Experiment 3:Replication of experiment 2 with variation of contact range Larger contact range increases polarization but only with negativity Explanation: 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

20. Flache, Macy. Why more contact may increase cultural polarization20 A stylized example smoking noyes critical distance disliking  disagreement liking  agreement

21. Flache, Macy. Why more contact may increase cultural polarization21 A stylized example: immediate full contact smoking noyes critical distance disliking  disagreement liking  agreement Tendency towards polarization Macy, Kitts, Flache, Benard (2003)

22. Flache, Macy. Why more contact may increase cultural polarization22 A stylized example: small groups first smoking noyes critical distance disliking  disagreement liking  agreement Local convergence eliminates extremes  cohesion when subgroups merge (Flache et al, in progress)

23. Flache, Macy. Why more contact may increase cultural polarization23 Conditions for the effects of larger range: When number of issues (k) increases Negative ties less likely from random start Effect tends to become negative When moderation (m) increases Large opinion differences weigh relatively more Positive 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

24. Flache, Macy. Why more contact may increase cultural polarization24 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

25. Flache, Macy. Why more contact may increase cultural polarization25 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.

26. Flache, Macy. Why more contact may increase cultural polarization26 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).

27. Flache, Macy. Why more contact may increase cultural polarization27 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

28. Flache, Macy. Why more contact may increase cultural polarization28 Effects of contact with negative influence and fixed categories (k=4) Range at k=4 (one fixed category, three opinions) Inverted U-shaped effect on polarization and segregation, U-shaped effect on diversity. Diversity = #distinct opinions / N Polarization = var pairwise agreement Segregation = degree to which positive ties are within categories and negative ties across categories

29. Flache, Macy. Why more contact may increase cultural polarization29 Effects of contact with negative influence and fixed categories (k=5) 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. Diversity = #distinct opinions / N Polarization = var pairwise agreement Segregation = degree to which positive ties are within categories and negative ties across categories

30. Flache, Macy. Why more contact may increase cultural polarization30 A new view on contacts: timing and structure vs. For example:mixing cultures in schools Period 1 Period 2

31. Flache, Macy. Why more contact may increase cultural polarization31 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.

32. Flache, Macy. Why more contact may increase cultural polarization32 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)

33. Flache, Macy. Why more contact may increase cultural polarization33 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?