What

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Whats good for the group Experimental work on
innovation diffusionRobert GoldstoneIndiana
UniversityDepartment of PsychologyProgram in
Cognitive Science
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Innovation Propagation in Networked Groups

• Importance of imitation
• Cultural identity determined by propagation of
  concepts, beliefs, artifacts, and behaviors
• Requires intelligence (Bandura, 1965 Blakemore,
  1999)
• Sociological spread of innovations (Ryan
  Gross, 1943 Rogers, 1962)
• Standing on the shoulders of giants
• Relation between individual decisions to imitate
  or innovate and group performance
• Imitation allows for innovation spread, but
  reduces group exploration potential
• Innovation leads to exploration, but at the cost
  of inefficient transmission of good solutions

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Technological advances build on previous advances
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Innovation Propagation in Networked
Groups(Mason, Jones, Goldstone, 2005, in press)

• Relation between individual decisions to imitate
  or innovate and group performance
• Imitation allows for innovation spread, but
  reduces group exploration potential
• Innovation leads to exploration, but at the cost
  of inefficient transmission of good solutions

Single-peaked
Score (Fitness)
Three-peaked
Participants Guess
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Mason, Jones, Goldstone (2005, 2008)

• Participants solve simple problem, taking
  advantage of neighbors solutions
• Numeric guesses mapped to scores according to
  fitness function
• Attempt to maximize earned points over 15 rounds
• Network Types
• Lattice Ring of neighbors with only local
  connections
• Fully connected Everybody sees everybody elses
  solutions
• Random Neighbors randomly chosen
• Small world Lattice with a few long-range
  connections
• Fitness Functions
• Single-peaked - a single, gradually increasing
  peak
• Three-peaked - two local maxima and one global
  maxima

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Network Types
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Small World Networks
Constructing a small world network (Watts,
1999) Start with regular graph Rewire each edge
with probability p Benefits for information
diffusion (Kleinberg, 2000 Wilhite, 2000)
Systematic search because regular
structure Rapid dissemination because short path
lengths Prevalence of small world networks
(Barabási Albert, 1999)
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Small World Networks (Watts Strogatz, 1998)
As random rewirings increase, clustering
coefficient and characteristic path length both
decreaseBut, for a large range of rewiring
probabilities, it is possible to have short path
lengths but still clusters
Clustering
Average Path Length
Proportion of Lattice Connections Randomly Rewired
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Experiment Interface
http//groups.psych.indiana.edu/
Time remaining 13
Guess!

• ID Guess Score
• YOU 45 36.1
• Player 1 39 45.7
• Player 2 95 4.2
• Player 3 52 29.0

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Score (Fitness)
Single-peaked
Three-peaked
Participants Guess
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Score (Fitness)
Participants Guess
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Experimental Details

• 56 groups with 5-18 participants per group
• 679 total participants
• Mean group size 12
• Within-group design each group solved 15 rounds
  of 8 problems (4 network types X 2 Fitness
  functions)
• For Trimodal function, global maximum had average
  score of 50, local maxima had average scores of
  40
• Normally distributed noise added to scores, with
  variance of 25
• Average number of network connections for random,
  small world, and lattice graphs 1.3 N
• Characteristic path lengths Full 1, Random
  2.57, Small world 2.61, Lattice 3.08

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Single-peaked
Three-peaked
at Global Maximum
Percentage of Participants
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For single-peaked function, lattice network
performs worst because good solution is slow to
be exploited by group. For three-peaked function,
small-world network performs best because groups
explore search space, but also exploit best
solution quickly when it is found.
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SSEC Model of Innovation Propagation(Self-,
Social-, and Exploration-based Choices)

• Each agent use one of three strategies
• With Bias B1, use agents guess from the last
  round
• With B2, use the best guess from neighbors in the
  last round
• With B3, randomly explore

Probability of choosing strategy x
Where Sx Score obtained from Strategy x
Add random drift to guess based on Strategy x
Next guess
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SSEC Model (Goldstone, Roberts, and Gureckis,
2008 in press)
Single-peaked
Three-peaked
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B110, B210, B31 Full network best for
single-peaked Small-world best for three-peaked
Human Results
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Three-peaked, Small World Network
Best with low noise and social (1 -
self-obtained) information
N15, B21-B1, B30.1, D3
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Three-peaked, Full Network
Best with combination of self- and
social-obtained information
N15, B21-B1, B30.1, D3
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Three-peaked, Comparison of Small World and Full
Networks
Self-obtained information works best with Full
network
N15, B21-B1, B30.1, D3
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Needle Fitness function
One broad local maximum, and one hard-to-find
global maximum
Global Maximum
Score (Fitness)
Local Maximum
Participants Guess
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Needle Function
Percentage of Participants
at Global Maximum
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Lattice network performs best by fostering the
most exploration, which is needed to find a
hard-to-find solution
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Needle Function
Human Data
SSEC Model
Percentage of Participants
at Global Maximum
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B110, B210, B35
Lattice network performs best - It fosters the
most exploration, which is needed to find a
hidden solution
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Single-peaked
Adding links and social information always helps
Unimodal
N15, B21-B1, B30.1, D3
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Three-peaked
Intermediate level of connectivity is best if use
social information
N15, B21-B1, B30.1, D3
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Needle
Even lower degrees of connectivity and more
self-obtained information is good
N15, B21-B1, B30.1, D3
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Conclusions

• For both human participants and the model, more
  information is not always better
• Full access to all neighbors information can
  lead to premature convergence on local maxima
• Harder problem spaces require more exploration,
  and hence more local connectivity patterns (Lazer
  Friedman, in press)
• Optimal performance is an interaction between
  problem space, social network, and personality
  (sheeps versus mavericks) of agents
• An informational social dilemma

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Creature League Task

• Build good teams of creatures by taking into
  account individual traits as well as interactions
  between team members
• 24 rounds of team construction
• A participant can choose their new team from
• their old team incumbent
• their best previous team reinforced memories
• other participants teams social learning
• the entire set of creatures innovation
• Problem difficult manipulated by changing league
  and team size
• Score of team individual creatures values
  interactions between pairs of creatures

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Screenshot
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Point distribution

• (small league size condition)

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Results Score vs. Round

• F(1,958)1015, plt.0001

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Results Score vs. Group Size

• F(1,38)70.5, plt.0001

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Results Score vs. League Size
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Strategies Over Rounds

• Less imitation and innovation over rounds
• More use of ones own current and previous teams
  over rounds

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Results Source vs. Group Size

• More imitation as group size increases
• Less innovation as group size increases

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Results Imitation

• Overall imitation rate (the proportion of rounds
  for all participants in which any copying
  occurred) was 29.3
• Of all imitation, participants copied
• 82.6 were of a participant with the highest
  score
• 92.4 were of a participant with a higher score
  than the imitator

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Coverage vs. Round, by Group Size

• Coverage the proportion of league icons
  represented on any team at the end of a round,
  normalized by group size.
• As group size increases, the group converges
  increasingly rapidly.

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Score vs. Choice Strategy

• Imitation is a good strategy for the individual

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Score vs. Copy Proportion

• As the probability of imitating increases, the
  participants score increases

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Score vs. League Proportion

• As the probability of innovating increases, the
  participants score decreases