Collaborators Ben Ashpole Andy Jones Marco Janssen

Human Collective Behavior as aComplex Adaptive System

Robert GoldstoneIndiana University

Department of PsychologyProgram 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.

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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

Invi

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le50/50 65/35 80/20

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s50/50 Distribution - only Pools 1 and 2

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s65/35 Distribution - only Pools 1 and 2

Pro

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of A

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s80/20 Distribution - only Pools 1 and 2

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)10 20 30 .05 .1 .15 .2

Pow

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Poo

l 1 P

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ize

Poo

l 1 P

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ize

Pow

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10 20 30 .05 .1 .15 .2

Foraging for ResourcesP

ower

More cyclic activity for invisible than visible conditions

Most power at about .02 cycles/second = 50 second cycle

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)

• http://groups.psych.indiana.edu/– On-line experiments served 24 hours/day– Bots as agents-based computational models

EPICURE: Agent-based modelRoberts & 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

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Technological advances build on previous

advances

Network Types

Small World Networks

Constructing a small world network (Watts, 1999)Start with regular graphRewire each edge with probability p

Benefits for information diffusion (Kleinberg, 2000; Wilhite, 2000) Systematic search because regular structureRapid dissemination because short path lengths

Prevalence of small world networks (Barabási & Albert, 1999)

Time remaining: 13

Guess!

ID Guess ScoreYOU 45 36.1Player 1 39 45.7Player 2 95 4.2Player 3 52 29.0

Experiment Interfacehttp://groups.psych.indiana.edu/

Participant’s Guess

Sco

re (

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Unimodal

Trimodal

31

Participant’s 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

Percentage of Participants

at Global Maximum

Unimodal Trimodal

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.

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Round

FullLatticeSmallRandom

Network

SSEC Model of Innovation Propagation

(Self-, Social-, and Exploration-based Choices)

•Each agent use one of three strategies– With Bias B1, use agent’s guess from the last round

– With B2, use the best guess from neighbors in the last round

– With B3, randomly explore

€

p Cx( ) =BxSxBnSn

n

∑Probability of choosing strategy x =

Where Sx= Score obtained from Strategy x

Next guess =

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Gx + N(μ = 0,σ = D)Add random drift to guess based on Strategy x

SSEC ModelUnimodal Trimodal

1 3 5 7 9 11 13 15Round

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Percentage of Participants

at Global Maximum

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Percentage of Participants at Global Maximum

1412108642

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1412108642

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Network

B1=10, B2=10, B3=1

Full network best for Unimodal

Small-world best for Trimodal

HumanResults

Participant’s Guess

Sco

re (

Fit

ness

)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

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

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Lattice network performs best - It fosters the most exploration, which is needed to find a hard-to-find solution

FullLatticeSmallRandom

Network

Unimodal

Adding links and social information always helps Unimodal

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N=15, B2=1-B1, B3=0.1, D=3

Trimodal

Intermediate level of connectivity is best if use social information

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N=15, B2=1-B1, B3=0.1, D=3

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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

Information Propagation in a Complex Search Space

Computer’s Mystery Picture Subject’s Guess

31 out of 49 cells correct

Neighbor 1’s Guess

36 out of 49 cells correct

Neighbor 2’s Guess

34 out of 49 cells correct

Neighbor 3’s Guess

30 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.

IsoscelesEquilateral

- 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)

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G r, t( )Gmax r( )

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⎦ ⎥ δ r − ra t( )( )α

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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.

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– http:/groups.psych.indiana.edu/