1. Networks of Social Influence Eliot Smith Indiana University, Bloomington March, 2007

2. Social influence: The core of social psychology Definitionally (Allport): Social psychology studies the effect of others (real, imagined, or implied) on our thoughts, feelings, and actions Substantively: Social influence underlies every major topic area: conformity, group decision making, close relationships, persuasion, intergroup relations, negotiation, etc….

3. Typical research approach Micro-level focus on individual cognitive processes –One-shot influence –Experimenter-constructed messages

4. Types of influence Persuasion –Intended by influence source –Via message Conformity –Often not intended by influence source –Multiple motives of influence targets Want to fit in with crowd (identity) See benefits in what others are doing (rewards)

5. Broadening the focus Patterns of influence that emerge when –many people (each acting as source and target of influence) –influence each other over time As in face-to-face groups Emergence: Even complete knowledge of micro-level processes insufficient for prediction and understanding

6. Our project Review, conceptually analyze social influence models that look at multidirectional influence over time Encourage integration of social psychology’s knowledge about micro-level processes with broader context provided by these models –Winter Mason, Frederica (Riki) Conrey, Eliot Smith (Personality and Social Psychology Review, in press)

7. First lesson learned Vast majority of models are from outside social psychology –Economics, sociology, political science, cognitive science, cognitive anthropology, physics, … Many disciplines are interested in social influence processes –Rumor spread, group problem-solving and decision-making, word of mouth about new products, … –Closely related models: disease epidemics

8. Models from other fields –usually more concerned with macro-level outcomes (e.g., % of population who hears rumor) than with micro-process –rarely if ever draw on social psychological theory or findings

9. First question about each model How (and whether) it avoids predicting collapse of attitudes or beliefs to complete uniformity Relevant to exploitation/exploration tradeoff: maintaining diversity allows exploration, sampling of different regions of search space –Hutchins example

10. Abelson’s dilemma Consider 3 assumptions: –Multiple actors (who are all connected) –Influence over many time steps –Assimilative influence, linear in form Linear, assimilative influence means recipient of influence, on average, moves some percentage of the way from original position toward influencer’s position

11. Abelson’s dilemma With those assumptions the inevitable outcome is complete uniformity of attitudes within the range of original attitudes –R. P. Abelson (1964)

12. Abelson’s dilemma But this outcome is not often observed in reality –Minority opinions persist –Attitudes show variation –Groups often polarize Move outside original range of opinions

13. Avoiding Abelson’s dilemma Four distinct ways to avoid collapse Constitute four dimensions on which to place social influence models 1.Patterns of Connectivity 2.Behavior vs. Attitudes 3.Variable Environmental Influences 4.Assimilation vs. Contrast

14. Remainder of talk Briefly describe the four dimensions Give examples of models Describe how each dimension can help avoid Abelson’s collapse, maintain variability and diversity

15. 1. Patterns of connectivity The pathways along which influence flows determine the final outcome for a group –How many buy a product –Strength and certainty of attitudes –Polarization or conformity

19. Patterns of connectivity Models assume different patterns of influence –All-connect –Regular networks –General networks –Dynamic networks (not today)

20. All-connect Each person potentially influences each other A E B CD

21. All-connect Most small group research in social psychology (Levine & Moreland, 1998; Stasser, 1988) –Thinking of group sitting around a table Innovation diffusion models (Granovetter, 1978)

22. Innovation diffusion (Granovetter, 1978) Individuals have different thresholds for adopting innovation (e.g., new product) –Threshold: % of others who must use innovation before the individual will Early adopters (0-1% threshold) start the process off, then those with low thresholds jump on board, and so on All-connect network assumption: each individual knows how many others in whole population have adopted innovation

23. Regular (grid) networks Each person connected to some number of nearest neighbors only –No long-distance links A E B CD

24. Regular (grid) networks Cellular Automata models (Conway, 1990) Dynamic Social Impact Model (Nowak, Szamrej, & Latané, 1990)

25. Dynamic Social Impact Model (Nowak et al., 1990) Individuals have binary (pro/con) attitudes, initially random Fixed locations in rectangular grid Influenced by close others (influence declines as square of distance) Change attitude if total influence to change > total influence to stay

26. Dynamic Social Impact Model Predictions –Initial majority (e.g., 60%) increases (e.g., to 90%) polarization –Minority persists by becoming spatially clustered protected from majority influence by clustering together

27. General networks Each person can have unique pattern of links Number of links may vary (“degree”) Mix of local, longer- range connections A E B CD

28. General networks Bavelas (1950) & Leavitt (1950) Watts & Strogatz (1998) small-world networks Friedkin (1998) sociological model –Preference distribution –Influence networks

29. Collapse to uniformity

31. All-connect network most subject to Abelson’s collapse –Every individual influenced by same overall majority –Rather than influenced by unique set of network neighbors

32. Maintaining diversity 1.Isolation 2.Homophily (network linkages correlate with attitude similarity)

33. Isolation

35. Homophily Friends correlate in attitudes, beliefs –Empirically found almost universally Arises from –social influence (transmitted along friendship links) –social selection (choice of friends based on pre- existing similarity) likely the more important process

36. Homophily

37. 2. Modeling attitude vs. behavior Attitude (continuous quantity) allows possibility of graded influence –Linear influence rule, move x% of the way toward influence source --> Abelson collapse Behavior (often discrete quantity), usually threshold for influence –E.g., adopt behavior if majority of neighbors do –Nonlinear rule, collapse not inevitable

38. 2.6 0.8 2.8 1.2 1.8 2.3 2.0 1.3 0.6 1.9 1.1 1.6 Continuous attitudes

39. 0.0 Continuous attitudes

40. 2.8 0.8 2.8 1.2 1.8 2.3 2.2 1.3 0.6 1.9 1.1 1.6 Discrete behaviors

42. Maintaining diversity Easier for models of discrete behaviors than for models of continuous attitudes

43. Attitudes and behavior? Possible to model both attitudes and behaviors –Attitudes are continuous, function as summary of input evaluative information –Behaviors are discrete, are observable to others Influence only from behaviors, not attitudes

44. Attitudes and Behavior? No models in this category yet But social psych research on how attitudes guide behavior should help construct them Would allow for modeling pluralistic ignorance

45. 3. Variable environmental influences Some models consider ONLY social influence –Dynamic Social Impact (Nowak et al.) Information other than social influence –Theory of Reasoned Action Attitude and subjective norm –Swarm intelligence (Kennedy & Eberhart) Try things yourself, hear about what neighbors have tried

48. Information cascade model (Bikhchandani et al., 1992) Biased coin, known to fall one way 2/3 of the time Is it biased toward heads or tails? Each person in turn flips coin privately (evidence), announces guess about coin People can use earlier guesses as well as their own private evidence

49. Information cascade model Person 1: sees H, guesses bias is H Person 2: sees T –Knows H, T have been seen, makes 50-50 guess More interesting: person 2 also sees H –Knows H, H have been seen, guesses coin is H –Now even if person 3 sees T, should guess H! –Same (even stronger) for all later people

50. 4. Assimilation vs. contrast Most models assume purely assimilative influence: move toward others’ positions This is likely when influence is purely informational –Learn about others’ successful problem solutions

51. 4. Assimilation vs. contrast But several processes can generate movement away from others’ positions –Reactance processes Resist threats to behavioral freedom –Social Identity Theory, Optimal Distinctiveness Theory Motive to seek distinctiveness of ingroup from outgroup –Avoiding competition Seek rewards less exploited by others

55. Seceder model (Dittrich et al., 2000) Each person in group has random number between 0 - 100 (attitude, behavior) Each person in turn: –Picks 3 others at random, sees their numbers (e.g., 16, 27, 88) –Identifies the number that is farthest from the mean of the 3 (e.g., 88) –Changes his own number to that (plus random error)

56. Seceder model Model is from physics Parallel to Optimal Distinctiveness Theory –Seek distinctiveness (move away from boring average) –But not all alone! (only go where another is already located) –Joining that person makes region less distinctive

57. Space of social influence models 1.Patterns of Connectivity (All-connect, Grid, Heterogeneous, Dynamic) 2.Behavior vs. Attitudes (Continuous, Discrete, Both) 3.Variable Environmental Influences (Only social influence, Other influences) 4.Assimilation vs. Contrast (Pure assimilation, Contrast possible) 4x3x2x2=48 categories of models in principle

58. Avoiding Abelson collapse 1.Patterns of Connectivity (All-connect, Grid, Heterogeneous, Dynamic) 2.Behavior vs. Attitudes (Continuous, Discrete, Both) 3.Variable Environmental Influences (Only social influence, Other influences) 4.Assimilation vs. Contrast (Pure assimilation, Contrast possible)

59. Methodological note How to model complex patterns of influence among many individuals over time? –Some models use mathematical approach Equations describe patterns of social influence Equations solved or iterated to describe influence over time

60. Methodological note Others use agent-based modeling –Not equations but autonomous agents Interact with each other over time Change attitudes according to stated rules –Much more flexible approach compared to equations –More congenial to thinking about processes that generate influence, rather than numerical law that describes influence outcomes

61. Methodological note Possibly familiar examples: –Axelrod evolution of cooperation –Kalick & Hamilton attractiveness matching in dating relationships Multi-agent approach reviewed by Smith & Conrey, PSPR, 2007

62. Integration Social psychology offers: –Well-supported models of micro-processes of social influence –Evidence at level of individual behavior Other fields offer: –Formal models of macro-level processes –Evidence at level of influence outcomes over multiple actors and many time periods

63. Integration These naturally complement each other –Social psychological models need contextual component (I.e., social networks) to predict large-scale outcomes –Models from other fields need empirically and theoretically grounded assumptions about micro-level patterns of influence

64. Thank You!