Human Collective Behavior as a Complex Adaptive System Robert Goldstone Indiana University Department of Psychology Program in Cognitive Science Collaborators Ben Ashpole Andy Jones Marco Janssen Allen Lee Winter Mason Michael Roberts

Complex Adaptive Systems Systems made up of many interacting elements Emergent, high-level properties from low-level interactions Decentralized processing Computational and mathematical models that apply across superficially dissimilar systems Applications to many natural systems: plants, animals, minerals.

Collective Behavior as a Complex System Individual versus group perspectives Collective phenomena: creation of currency, transportation systems, rumors, the web, resource harvesting, crowding, scientific communities Compare group behavior experiments with agent-based computational models –Competitive foraging for resources –The dissemination of innovations in a social network –Cooperative path formation

Foraging for Resources Near-optimal harvesting of resources by isolated individuals (Stephens & Krebs, 1986) Group foraging –Ideal Free Distribution model (Fretwell, 1972) Animals are free to move between resource patches Animals have ideal knowledge about resource payoffs Optimal allocation of animals to resources is for the distribution of animals to match the distribution of resources –Near-optimal distributions of cichlids (Godin & Keeleyside, 1984) and ducks (Harper, 1982)

Foraging for Resources Godin and Keeleyside (1984)

Human Group Foraging Experiment (Goldstone & Ashpole, 2004) Java environment for multi-participant interaction –Participants dwell in a common virtual environment comprised of food resources and other participants –Moment-by-moment collection of resource and agent data Experimental manipulations –Resource distribution: 50/50, 65/35, 80/20 –Agent knowledge Visible: every agent sees all food resources and other agents Invisible: agents only see their own location, and food after they have picked it up

Experiment Methods Agents –166 I.U. undergraduates divided into 8 groups –Four directions (up, down, left, right) determined by arrow keys –When an agent lands on food, the food disappears Food distribution –Food dropped once every 4/N seconds, N=# agents –Within pool, Gaussian distribution with mean at pool’s center Six 5-minute sessions

Invisible Visible 50/50 65/3580/20

Proportion of Agents 50/50 Distribution

Proportion of Agents 65/35 Distribution

Proportion of Agents 80/20 Distribution

Proportion of Agents 50/50 Distribution - only Pools 1 and 2

Proportion of Agents 65/35 Distribution - only Pools 1 and 2

Proportion of Agents 80/20 Distribution - only Pools 1 and 2

Systematic Undermatching Invisible Visible Perfect matching s visible =.78, b visible =.01 s invisible =.68, b invisible =.01 F A = Foragers at Patch A F B = Foragers at Patch B N A = Resource amount at Patch A N B = Resource amount at Patch B s = Sensitivity to resource variations Undermatching: S<1 Overmatching: S>1 b = Bias toward Patch A Kennedy & Gray (1993): Mean of 52 slopes was 0.7

Periodic oscillations in populations? Informal observation - cyclic resource use –Underutilization of a resource attracts agents to resource –Crowd of agents leads to poor payoffs at resource –Agents decide at about the same time to try the other resource Fourier analysis to reveal oscillations –Represent time series by sine waves varying in their frequency, amplitude, and phase –Population waves indicated by a high amplitude sinusoid

Time (Seconds)Frequency (cycles/second) Power Pool 1 Population Size Power

Foraging for Resources Power More cyclic activity for invisible than visible conditions Most power at about.02 cycles/second = 50 second cycle

Distribution of Wealth Greater disparity between “Haves” and “Have-nots” for invisible conditions

Concluding Remarks Inefficiencies in food foraging –Scatter (exploration) in populations –Undermatching –Population cycles Importance of knowledge –All inefficiencies were larger in the invisible than visible condition –Knowledge of food restricts exploration and population cycles –Knowledge of other agents curbs impulse to move toward food resources, but buzzarding too (Goldstone, Ashpole, & Roberts, 2005) –On-line experiments served 24 hours/day –Bots as agents-based computational models

Overall Results VisibleInvisible Food Visible Invisible Agents Undermatching Overmatching Slow population cycles Fast population cyclesSlow population cycles No population cycles Population scattered Population concentrated

EPICURE: Agent-based model Roberts & Goldstone (2005; in press) Probabilistic choice of target location based on value Distance - tend to choose close target Inertia - tend to select same target as did previously Visible condition –Density of food around target as an attractant –Density of other agents as a deterrent Invisible condition –Value of target increases at region where food is found –Value decreases to visited cells with no food –Value gradually regenerates over time to previous maximal value

Confirmed Predictions of Forager Model Undermatching for both invisible and visible conditions –No need for bias to spend equal time at pools, unequal competitive ability, or interference to predict undermatching –Spatial turfs: a single agent can efficiently patrol a turf of about 10 squares relatively uninfluenced by food output. –The 80% and 20% pools both have the same spatial extent, and so can support a more similar number of agents than predicted by their output rates Fourier population waves which have the highest amplitude in the 80/20 invisible condition Approximate amount of pool switching and distribution of steps Greater undermatching as the number of agents increases (Gillis & Kramer, 1987) More undermatching for compact resource patches (Baum & Kraft, 1998) More undermatching as travel costs increase (Baum & Kraft, 1998)

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

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 diffusion (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

Participant’s Guess Score (Fitness)

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 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

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 groups explore search space, but also exploit best solution quickly when it is found. Full Lattice Small Random Network

SSEC Model of Innovation Propagation (Self-, Social-, and Exploration-based Choices) Each agent use one of three strategies –With Bias B 1, use agent’s guess from the last round –With B 2, use the best guess from neighbors in the last round –With B 3, 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 =10, B 3 =1 Full network best for Unimodal Small-world best for Trimodal Human Results

Participant’s Guess Score (Fitness) Needle Fitness function One broad 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 hard-to-find solution Full Lattice Small Random Network

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 =10, B 3 =5 Full Lattice Small Random Network

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

Trimodal, Full Network Best with combination of self- and social-obtained information N=15, B2=1-B1, B3=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 N=15, B2=1-B1, B3=0.1, D=3

Unimodal Adding links and social information always helps Unimodal N=15, B2=1-B1, B3=0.1, D=3

Trimodal Intermediate level of connectivity is best if use social information N=15, B2=1-B1, B3=0.1, D=3

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

Conclusions For both human participants and the SSEC model, more information is not always better –Full access to all neighbors’ information can lead to premature convergence on local maxima – Unimodal: Full Network best – Trimodal: Small world network best – Needle: Lattice best –Harder problem spaces require more exploration Before designing a social network, first characterize the problem space (Bavelas, 1950; Lazer & Friedman, under review) Increasing need for exploration

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

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

Activity leads to more Activity

Group Path Formation Experiment Goldstone, Jones, & Roberts (in press) Interactive, multi-participant experiment –34 Groups of 7-12 subjects –Instructed to move to randomly selected cities to earn points Points earned for each destination city reached –Points deducted for each traveled spot Travel cost for each spot inversely related to number of times spot was previously visited by all participants Steps on a spot also diffuse to neighboring spots Influence of previous steps decays with time Cost of each spot visually coded by brightness –6 configurations of cities –5-minutes of travel for each configuration

Participants see themselves as green triangles. Navigate by changing heading direction with left and right arrows Cities shown in blue, destination in green Other participants shown as yellow dots The brighter a path, the lower its cost

Video Viewer

- Isosceles triangle shows more pro-Steiner deviation from bee-line pathways compared to equilateral triangle. - The largest distance savings of MST over spanning tree is for equilateral triangle - Having a large advantage of an optimal path is no guarantee that a group will find it. Isosceles Equilateral

- Small rectangle shows more pro-Steiner deviation than large rectangle, despite having the same proportions. - Deviations from bee-line path may be produced if two paths are close enough to influence one another. Large rectangleSmall rectangle

- If include Steiner point, all other paths deviate toward the Steiner path. TriangleTriangle with Steiner point

Does not take into account intended destination   For every trip of each participant, integrate deviations from bee-line paths  Asymmetries in paths: deviations from bee-line paths preferred at end of trip than at beginning (Bailenson, Shum, & Uttal, 1998, 2000)

-Greater pro-Steiner deviations from bee-line paths for Isosceles - Asymmetries in paths: deviations from bee-line paths preferred at end of trip than at beginning (Bailenson, Shum, & Uttal, 1998, 2000)

- Walkers move to destinations, affecting their environment locally as they walk, facilitating subsequent travel for others. - Walkers compromise between taking the shortest way to their destination and using existing, strong trails. - Agent-based model using the Langevin equation for Brownian motion in a potential. Active Walker Model (Helbing, Keltsch, & Molnár, 1997)

G(r,t)= Ground potential at location r at time t, reflecting comfort of walking G 0 = natural ground condition T(r)= Durability of trails from regrowth I(r) = Intensity of vegetation clearing G max = maximum comfort of a location  = Dirac’s delta function. Only count agents  at location r

Active Walker Model (Helbing, Keltsch, & Molnár, 1997) V tr (r ,t)= trail potential = Attractiveness for agent   (r  ) = visibility at agent’s location Attractiveness based on ground potential and distance of location to agent  Integrate to find spatial average of ground potentials

Active Walker Model (Helbing, Keltsch, & Molnár, 1997) e  (r ,t)= Walking direction of agent  d  = next destination r  = gradient of the trail potential Direction determined by destination and the attractiveness of all locations

Active walker model correctly predicts more pro-steiner deviation for isosceles than equilateral triangle, and greater deviation with passing time. For isosceles, the model correctly predicts the most deviation near the triangle point with the smallest angle.

Active walker model predicts greater deviation from bee-line paths for small than large rectangle.

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 –Coalition formation and coordination –Social dilemmas and common pool resource problems –Group polarization and creation of sub-groups in matters of taste –Social specialization and division of labor –