The Propagation of Innovations in Social Networks Robert Goldstone Indiana University Department of Psychological and Brain Sciences Program in Cognitive Science Collaborators Allen Lee Andy Jones Marco Janssen Todd GureckisWinter Mason Michael Roberts

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

Technological advances build on previous advances

Mason, Jones, & Goldstone (in press; 2005) Participants solve simple problem, taking advantage of neighbors’ solutions –Numeric guesses mapped to scores according to fitness function –Attempt to maximize earned points Network Types –Lattice: Ring of neighbors with only local connections –Fully connected: Everybody sees everybody else’s solutions –Random: Neighbors randomly chosen –Small world: Lattice with a few long-range connections Based on Newman and Watts (1999), not Watts and Strogatz (1998) Fitness Functions –Unimodal - a single, gradually increasing peak –Trimodal - two local maxima and one global maxima

Network Types

Small World Networks Constructing a small world network (Watts, 1999) Start with regular graph Rewire each edge with probability p Benefits for information distribution (Kleinberg, 2000; Wilhite, 2000) Systematic search because regular structure Rapid dissemination because short path lengths Prevalence of small world networks ( Barabási & Albert, 1999 )

Small World Networks (Watts & Strogatz, 1998) Proportion of Lattice Connections Randomly Rewired Average Path Length Clustering As random rewirings increase, clustering coefficient and characteristic path length both decrease But, for a large range of rewiring probabilities, it is possible to have short path lengths but still clusters

Time remaining: 13 Guess! IDGuessScore YOU Player Player Player Experiment Interface

Participant’s Guess Score (Fitness) Unimodal Trimodal 31

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. A verage number of network neighbors 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

Percentage of Participants at Global Maximum UnimodalTrimodal For unimodal function, lattice network performs worst because good solution is slow to be exploited by group. For trimodal function, small-world network performs best because group explores search space, but also exploits best solution quickly when it is found. Full Lattice Small Random Network

Unimodal Overall group performance Lattice significantly underperforms other three networks No difference between other three

Unimodal Group convergence Lattice significantly underperforms other three networks Random network slightly less than Full & Small-World

Trimodal Speed of discovery Small-world significantly faster than other three Lattice slower than Full

Trimodal Overall group performance Small-world significantly greater than other three No other significant differences

SSEC Model of Innovation Propagation (Self-, Social-, and Exploration-based Choices) Each agent use one of five strategies –With Bias B 1, use agent’s guess from the last round –With B 2, use agent’s historically best guess –With B 3, use the best guess from neighbors in the last round –With B 4, use neighbors’ historically best guess –With B 5, randomly explore Probability of choosing strategy x = Where S x = Score obtained from Strategy x Next guess = Add random drift to guess based on Strategy x

SSEC Model Unimodal Trimodal Full Lattice Small Random Network B 1 =10, B 2 =0, B 3 =0, B 4 =10, B 5 =1 Full network best for Unimodal Small-world best for Trimodal Human Results

Participant’s Guess Score (Fitness) Needle Fitness function One diffuse local maximum, and one hard-to-find global maximum Global Maximum Local Maximum

Round Percentage of Participants at Global Maximum Needle Function Lattice network performs best - It fosters the most exploration, which is needed to find a hidden solution Human Data SSEC Model B 1 =10, B 2 =0, B 3 =0, B 4 =10, B 5 =5 Full Lattice Small Random Network

N=15, B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Trimodal, Small World Network Best with low noise and social (1 - self-obtained) information

B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Trimodal, Full Network Best with combination of self- and social-obtained information

B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Trimodal, Comparison of Small World and Full Networks Self-obtained information works best with Full network Advantage for Full Network Advantage for Small World

B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Unimodal Adding links and social information always helps Unimodal

B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Trimodal Intermediate level of connectivity is best if use social information

B1=0, B3=0, B4=1-B2, B5=0.1, D=3 Needle Even lower degrees of connectivity and more self-obtained information is good

Participant’s Guess Score (Fitness) Local Maximum Bimodal Function with Equal Peaks Bandwagon effect - Groups tend to congregate at one peak Bandwagonning measure = absolute difference between frequencies of guesses within 1 SD of each peak Full network had most bandwagoning Small world network had least bandwagoning

Information Propagation in a Complex Search Space 15 rounds of picture guessing and feedback –Receive feedback on own picture, and neighbors’ pictures –Neighbors defined by 4 network topologies Strategic choice –Imitate others’ successful pictures –Continue exploring with one’s own picture Preliminary results –Greater perseveration on one’s own solution with multi- dimensional search than single-dimension search –Chunk-by-chunk imitation

Information Propagation in a Complex Search Space Computer’s Mystery Picture Subject’s Guess 31 out of 49 cells correct

Empirical Conclusions More more information is not always better –Interaction between network topology and problem space –Unimodal: Full Network best –Trimodal: Small world network best –Needle: Lattice best Converging results –Centralization beneficial for simple “find the common symbol” tasks; Decentralized networks beneficial for complex tasks (Bavelas, 1950; Leavitt, 1951; Sparrow et al., 2001) –Relatively centralized networks develop when a group is given a relative low-complexity task (Brown & Miller, 2000) Increasing need for exploration DecentralizedCentralized

Theoretical Conclusions For the SSEC model, more information is not always better –As the need for exploration increases, more locally-connected networks have a relative advantage –Converging results For networked agents in a NK model, lattices outperform small-world and fully connected networks because the latter prematurely converge (Lazer & Friedman, under review) The dangers of information cascades (Bikchandani et al., 1992; Strang & Macy, 2001) Need for diversity of strategies in societies (Florida, 2002; Sunstein, 2003) Interaction between network topology and reliance on one’s own versus others’ information –Relying more on others combines effectively with sparser networks, as does relying more on self and fuller networks –Relying on one’s own knowledge and sparser networks are both exploration vehicles. –Optimal combination of exploration depends on problem space. Harder problem spaces require more exploration

Humans Groups as Complex Systems Controlled, data-rich methods for studying human group behavior as complex adaptive systems –Less messy than real world data, but still rich enough to find emergent group phenomena –Bridge between modeling work and empirical tests Future Applications –Resource allocation –Group coordination –Coalition formation –Social dilemmas and common pool resource problems –Group polarization and creation of sub-groups in matters of taste –Social specialization and division of labor –