The Paths that Groups Make

Robert GoldstoneIndiana University

Department of PsychologyProgram in Cognitive Science

Collaborators

Ben Ashpole Andy Jones Marco Janssen

Allen Lee Winter Mason Michael Roberts

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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

• Concrete and abstract path forging and following– Collective path formation

– The dissemination of innovations in a social network

Group Choice• Collective Behavior as a Complex System

• People in groups often times make similar choices– People in a group are similar

– Normative conformity (Deutsch & Gerard, 1955)

– Early choosers change the environment for later choosers

• Taking advantage of predecessors’ choices– Advantages to choosing popular choices: VHS, Microsoft, QWERTYIOP

– Standing on the shoulders of giants: Moore’s law

– Evolution of path systems: activity facilitates further activity

Technological advances build on previous advances

Emergence of Path Systems

• What trails do people spontaneously create?

• Dwight Eisenhower’s “grassroots” architectural philosophy

• Previous paths are attractive: easier, low cognitive cost

“Traveler, there is no path.

Paths are made by walking.”

-- Antonio Machado

Activity leads to more Activity

Comparison to optimal path systems• Minimal Steiner Tree (MST) = the set of paths that

connects a set of nodes using the minimal amount of total path length

• Steiner points = nodes added to original set of nodes– Always have 3 pathways, with each pair of adjacent pathways at

120o angle (Fermat, 17th century)

• Applications in integrated circuit design, airport hub locations, internet routing, cable layout

• Finding MST solutions is an NP-hard problem– Yet soap film naturally approximate MST solutions– Can people approximate MSTs too?

Minimal Steiner Trees

Minimal Spanning Tree Minimal Steiner Tree

Minimal Spanning Tree

Minimal Steiner Tree

Soap Film MSTs

Group Path Formation Experiment• 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

- 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 rectangle Small rectangle

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

Triangle

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Triangle with Steiner point

- Rotated obtuse shows more pro-Steiner deviation for long path than canonical obtuse.

- People may be influenced by canonical directions, with horizontal paths more salient/attractive than angled paths (Regier & Carlson, 2001)

Canonical Obtuse Rotated Obtuse

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Does not take into account intended destination

For every trip of each participant, integrate deviations from bee-line paths

-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)

-Greater pro-Steiner deviations for long path of rotated obtuse angle than canonical obtuse.

- Asymmetries in paths: deviations from bee-line paths preferred at end of trip than at beginning

- 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)

Active Walker Model (Helbing, Keltsch, & Molnár, 1997)

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dG r, t( )dt

=1

T r( )G0 r( ) −G r, t( )[ ] + I r( ) 1−

G r, t( )Gmax r( )

⎡

⎣ ⎢

⎤

⎦ ⎥ δ r − ra t( )( )α

∑

G(r,t)= Ground potential at location r at time t, reflecting comfort of walking

G0 = natural ground condition

T(r)= Durability of trails from regrowth

I(r) = Intensity of vegetation clearing

Gmax = maximum comfort of a location

= Dirac’s delta function. Only count agents at location r

Active Walker Model (Helbing, Keltsch, & Molnár, 1997)

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Vtr rα , t( ) = d∫2re

- r -rασ rα( )G r, t( )

Vtr(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)

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eα rα , t( ) =dα − rα +∇ rαVtr rα , t( )dα − rα +∇ rαVtr rα , t( )

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.

Model predicts greater deviation from bee-line paths if Steiner point is included as a destination.

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

Active walker model does not predict an influence of rotation on bee-line path deviations

Incorporating Rotational Sensitivity by changing distance function:

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D(r,rα ) = rx − rα x( )s+ ry − rα y( )

s ⎡ ⎣ ⎢

⎤ ⎦ ⎥

1

sS=1, not 2

Model can predict path asymmetries, but predicts them in opposite direction as actual results. It predicts great deviation from bee-line paths going from yellow to blue (or red) rather than going from blue to yellow.

Modeling human-like asymmetries: increase visibility, , as distance to destination decreases

Original Model Revised Model

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rα ,q( ) =σ rα( )

1+ e2D (dα , rα )

⎛

⎝ ⎜

⎞

⎠ ⎟

Conclusion• Group behavior from a complex adaptive

systems perspective– People take advantage of trails left by others

• Group behavior, to a first approximation, is well modeled by an Active Walker Model– Accounts for differences in scales and topologies of destinations,

influence of time, and approximate distribution of steps– Can fix discrepancies: direction of asymmetries, rotation

invariance– Essential insight: people’s movements are a compromise between

going to their destinations and going where the path is attractive

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/