Networks of Social Influence

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Networks of Social Influence

• Eliot Smith
• Indiana University, Bloomington
• March, 2007

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Social influenceThe 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.

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Typical research approach

• Micro-level focus on individual cognitive
  processes
• One-shot influence
• Experimenter-constructed messages

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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)

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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

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Our project

• Review, conceptually analyze social influence
  models that look at multidirectional influence
  over time
• Encourage integration of social psychologys
  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)

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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

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• 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

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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

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Abelsons 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
  influencers position

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Abelsons dilemma

• With those assumptions the inevitable outcome is
  complete uniformity of attitudes within the range
  of original attitudes
• R. P. Abelson (1964)

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Abelsons 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

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Avoiding Abelsons dilemma

• Four distinct ways to avoid collapse
• Constitute four dimensions on which to place
  social influence models
• Patterns of Connectivity
• Behavior vs. Attitudes
• Variable Environmental Influences
• Assimilation vs. Contrast

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Remainder of talk

• Briefly describe the four dimensions
• Give examples of models
• Describe how each dimension can help avoid
  Abelsons collapse, maintain variability and
  diversity

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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

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Patterns of connectivity

• Models assume different patterns of influence
• All-connect
• Regular networks
• General networks
• Dynamic networks (not today)

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All-connect

• Each person potentially influences each other

A
B
E
C
D
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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)

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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

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Regular (grid) networks

• Each person connected to some number of nearest
  neighbors only
• No long-distance links

A
B
E
C
D
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Regular (grid) networks

• Cellular Automata models (Conway, 1990)
• Dynamic Social Impact Model (Nowak, Szamrej,
  Latané, 1990)

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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 gt
  total influence to stay

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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

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General networks

• Each person can have unique pattern of links
• Number of links may vary (degree)
• Mix of local, longer-range connections

A
B
E
C
D
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General networks

• Bavelas (1950) Leavitt (1950)
• Watts Strogatz (1998) small-world networks
• Friedkin (1998) sociological model
• Preference distribution
• Influence networks

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Collapse to uniformity
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• All-connect network most subject to Abelsons
  collapse
• Every individual influenced by same overall
  majority
• Rather than influenced by unique set of network
  neighbors

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Maintaining diversity

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

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Isolation
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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

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Homophily
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2. Modeling attitude vs. behavior

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

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Continuous attitudes
2.6
0.6
1.3
1.2
0.8
2.0
1.1
1.6
2.3
2.8
1.8
1.9
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Continuous attitudes
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
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Discrete behaviors
0.6
2.8
1.3
1.2
1.1
1.6
0.8
2.2
2.8
2.3
1.9
1.8
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Discrete behaviors
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Maintaining diversity

• Easier for models of discrete behaviors than for
  models of continuous attitudes

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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

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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

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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

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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

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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

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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

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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

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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)

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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

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Space of social influence models

• Patterns of Connectivity
• (All-connect, Grid, Heterogeneous, Dynamic)
• Behavior vs. Attitudes
• (Continuous, Discrete, Both)
• Variable Environmental Influences
• (Only social influence, Other influences)
• Assimilation vs. Contrast
• (Pure assimilation, Contrast possible)
• 4x3x2x248 categories of models in principle

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Avoiding Abelson collapse

• Patterns of Connectivity
• (All-connect, Grid, Heterogeneous, Dynamic)
• Behavior vs. Attitudes
• (Continuous, Discrete, Both)
• Variable Environmental Influences
• (Only social influence, Other influences)
• Assimilation vs. Contrast
• (Pure assimilation, Contrast possible)

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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

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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

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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

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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

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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

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Thank You!