The Propagation of Innovations in Social Networks

1. The Propagation of Innovations in Social NetworksRobert GoldstoneIndiana UniversityDepartment of Psychological and Brain SciencesProgram in Cognitive Science Collaborators Allen Lee Andy Jones Marco Janssen Todd Gureckis Winter Mason Michael Roberts

2. 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

3. Technological advances build on previous advances

4. 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

5. Network Types

6. 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)

7. 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

9. 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 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

10. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Round Round Unimodal Trimodal at Global Maximum Percentage of Participants N e t w o r k F u l l L a t t i c e S m a l l R a n d o m 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.

11. SSEC Model of Innovation Propagation(Self-, Social-, and Exploration-based Choices) • Each agent use one of five strategies • With Bias B1, use agent’s guess from the last round • With B2, use agent’s historically best guess • With B3, use the best guess from neighbors in the last round • With B4, use neighbors’ historically best guess • With B5, 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 =

12. SSEC Model 1 . 0 0 0 . 8 0 0 . 6 0 Percentage of Participants at Global Maximum 0 . 4 0 0 . 2 0 0 . 0 0 1 3 5 7 9 1 1 1 3 1 5 1 3 5 7 9 1 1 1 3 1 5 R o u n d R o u n d Unimodal Trimodal N e t w o r k F u l l L a t t i c e S m a l l R a n d o m B1=10, B2=0, B3=0, B4=10, B5=1 Full network best for Unimodal Small-world best for Trimodal Human Results

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

14. N e t w o r k F u l l L a t t i c e S m a l l R a n d o m Needle Function Human Data SSEC Model Percentage of Participants at Global Maximum R o u n d B1=10, B2=0, B3=0, B4=10, B5=5 Lattice network performs best - It fosters the most exploration, which is needed to find a hidden solution

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

16. Bimodal Function with Equal Peaks 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 Bandwagon effect - Groups tend to congregate at one peak Score (Fitness) Local Maximum Participant’s Guess

17. Information Propagation in a Complex Search Space • http://groups.psych.indiana.edu/ • 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

18. Subject’s Guess 36 out of 49 cells correct 34 out of 49 cells correct 30 out of 49 cells correct Neighbor 1’s Guess Neighbor 2’s Guess Neighbor 3’s Guess Information Propagation in a Complex Search Space 31 out of 49 cells correct Computer’s Mystery Picture

19. Empirical Conclusions Increasing need for exploration • 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) Decentralized Centralized

20. 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

21. 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 • http:/groups.psych.indiana.edu/