Networks of Social Influence
Eliot Smith
Indiana University, Bloomington
March, 2007
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….
Typical research approach
• Micro-level focus on individual cognitive
processes
– One-shot influence
– Experimenter-constructed messages
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)
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
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)
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
• 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
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
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
Abelson’s dilemma
• With those assumptions the inevitable
outcome is complete uniformity of
attitudes within the range of original
attitudes
– R. P. Abelson (1964)
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
Avoiding Abelson’s dilemma
•
•
Four distinct ways to avoid collapse
Constitute four dimensions on which to
place social influence models
1.
2.
3.
4.
Patterns of Connectivity
Behavior vs. Attitudes
Variable Environmental Influences
Assimilation vs. Contrast
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
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
Patterns of connectivity
•
Models assume different patterns of
influence
–
–
–
–
All-connect
Regular networks
General networks
Dynamic networks (not today)
All-connect
A
B
E
D
C
• Each person
potentially
influences each
other
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)
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
Regular (grid) networks
A
B
E
D
C
• Each person
connected to some
number of nearest
neighbors only
– No long-distance
links
Regular (grid) networks
• Cellular Automata models (Conway,
1990)
• Dynamic Social Impact Model (Nowak,
Szamrej, & Latané, 1990)
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
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
General networks
A
B
E
D
C
• Each person can
have unique pattern
of links
• Number of links may
vary (“degree”)
• Mix of local, longerrange connections
General networks
• Bavelas (1950) & Leavitt (1950)
• Watts & Strogatz (1998) small-world
networks
• Friedkin (1998) sociological model
– Preference distribution
– Influence networks
Collapse to uniformity
• 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
Maintaining diversity
1. Isolation
2. Homophily (network linkages correlate
with attitude similarity)
Isolation
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 preexisting similarity)
• likely the more important process
Homophily
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
Continuous attitudes
2.6
0.6
1.3
1.2
2.0
2.3
1.8
0.8
1.1
1.6
2.8
1.9
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
Discrete behaviors
0.6
2.8
1.3
1.2
1.1
1.6
0.8
2.2
2.8
2.3
1.8
1.9
Discrete behaviors
Maintaining diversity
• Easier for models of discrete behaviors
than for models of continuous attitudes
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
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
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
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
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
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
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
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)
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
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
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)
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
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
Thank You!