The Parable of the Hare and the Tortoise:How "Small Worlds"

Reduce the Long Run Performance of Systems

David Lazer

Program on

Networked Governance

Harvard University

Acknowledgements…

• Allan Friedman

• NSF grant 0131923

Living in the (self-consciously) networked age

• Growth of research on networks across disciplines

• We live in an “smaller world” with ever-accelerating flows of information

• Explosion of consultants, software, etc to make organizations “smaller”

Does connecting people help an organization solve problems?

The problem of parallel problem solving in human systems

• Many agents working on same problem simultaneously

• How is that problem solving aggregated?

Brainstorming

“Laboratories of democracy”

Global diffusion…

(Not) Re-inventing the wheel

Roadmap

• The role of informational diversity in systemic performance

• Networks as architecture for experimentation

• Description of model

• Results

• Conclusion

Role of informational diversity

• Sunstein, Nemeth, etc.Informational diversity provides the

menu of options in the system

• However: pressures toward homogeneity, some of which may increase system performance (e.g., the elimination of bad solutions)

Processes of emulation

• Neo-institutionalism– strong pressures for conformity (DiMaggio and Powell)

• Networks play a key conduit for those pressures (Lazarsfeld, Friedkin, Lazer)

• Convergence often not on system “optimum”, even when emulation is driven by success (Bikhchandani, Hirshleifer, and Welch; Strang and Macy)

Network structure

• Cliquish

• Small world– “six degrees of separation” (Milgram, Watts)

• Birds of a feather (Lazarsfeld and Merton)

• “Scale free” (Barabasi)how does the architecture of the

network affect balance between exploration and exploitation?

Cliques

Small worlds (Milgram, Watts and Strogatts)

Big world Small world

Birds of a feather…

Scale Free networks(Barabasi)

Network structure

• Cliquish

• Small world– “six degrees of separation” (Milgram, Watts)

• Birds of a feather (Lazarsfeld and Merton)

• “Scale free” (Barabasi)how does the architecture of the

network affect balance between exploration and exploitation?

Computational model

• KISS principle– simplest possible model that captures some essence of reality

• Agent-based– decision rules dictating agent behavior based on local conditions (not analytically tractable)

• “Experimentally” manipulate parameters, test for robustness

• Key question: what systemic patterns emerge?

Model

• Problem space– what’s the problem agents are trying to solve?

• Agent decision rules– how do agents seek improvements in performance?

• Agent neighborhood– who do agents see (and emulate)?

Problem space

• Key attribute of problem space is its ruggedness

Easy to find optimum…

Less easy to find optimum…

Problem space

• NK model (Kauffman)• N dimensions (19 in these simulations)• The marginal contribution of each dimension to

performance is contingent on K other dimensions

• K determines the ruggedness of the problem space (5 in most of these simulations)

• Scores are calculated using a rank-preserving monotonic transformation

Decision rule

• Capacity of agents to search problem space must be very limited

Decision rule

• If someone agent can see is doing better than agent at time t, copy best alternative.

• Otherwise, look at impact of randomly changing one dimension. If this is an improvement, move there. If not an improvement, stay at previous solution.

Informational velocity

• Always looking at others?

• If not:– Is communication synchronous (e.g., group

meetings)?– Is communication asynchronous?

Network– determines neighborhood

• Linear (max degrees of separation = population size – 1)

• Fully connected (max degrees of separation = 1)

Basic model parameters

• 100 agents• 200 time steps• 1000 simulations of each experiment

– 20 NK spaces (N = 19, K = 5)– 50 randomly seeded starting points

• Vary size, network structure, velocity, and synchronicity

Code written in Java using the Repast libraries

Findings

• Size

• Network structure

• Velocity

• Synchronicity

Bigger is better

Impact of size

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score full 36

Bigger is better

Impact of size

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score full 36

score full 100

Bigger is better

Impact of size

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score full 36

score full 100

score full 500

The hare and the tortoise:Small worlds are good for a quick fix…

Impact of network structure

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…but not so good in the long haul

Impact of network structure

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score full

Small worlds drive out variety

Heterogeneity

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63

72

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LR Performance of random graphs

Random graphs

0.4

0.45

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0.55

0.6

0.65

0.7

0.75

1 10 100 Probability of connection (density)

[log scale]

Score All random grgraphs graphs Complete graphs only

Small worldsSmall Worlds

0.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0 10 20 30 40 50

# of shortcuts on lattice

Avg

Sco

re

Impact of structure is contingent on problem space

Search in a "simple" world: linear graph

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Score line

Impact of structure is contingent on problem space

Search in a "simple" world: linear vs full graph

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Score full

Velocity increases exploitation and decreases exploration

Impact of velocity on performance

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score full

Velocity increases exploitation and decreases exploration

Impact of velocity on performance

0

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1 11 21 31 41 51 61 71 81 91 101

Round

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Asynch10 full

score full

Synchronicity

. Impact of synchronized communications

00.10.20.30.40.50.60.70.80.9

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Per

form

ance

Asynch10 full

Synchronicity

. Impact of synchronized communications

00.10.20.30.40.50.60.70.80.9

1

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Per

form

ance

Synch10 full

Asynch10 full

Synchronicity

. Impact of synchronized communications

00.10.20.30.40.50.60.70.80.9

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Per

form

ance

Synch10 line

Synch10 full

Asynch10 full

Synchronicity

. Impact of synchronized communications

00.10.20.30.40.50.60.70.80.9

1

0 100 200 300 400 500 600 700 800 900 1000

Round

Pe

rfo

rma

nc

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Synch10 line

Synch10 full

Asynch10 line

Asynch10 full

HeterogeneityHeterogeneity over time for fully connected graph:

synchronous vs asynchronous

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Synch10 full

Asynch10 full

HeterogeneityHeterogeneity over time for line: synchronous vs asynchronous

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Synch10 line

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The Social Structure of Exploration and Exploitation

(March 1991)• Exploration– looking

for new solutions (experimentation)

• Exploitation– taking advantage of what the system knows (emulation)

Illustrations

• Agricultural diffusion

• Creative groups

Technological diffusion

• Diamond, Guns, Germs, and Steel

“…[G]eographic connectedness has exerted both positive and negative effects on the evolution of technology. As a result, in the very long run, technology may have developed most rapidly in regions with moderate connectedness, neither too high nor too low. Technology’s course over the last 1,000 years in China, Europe, and possibly the Indian subcontinent exemplifies those net effects of high, moderate, and low connectedness, respectively.” (p. 416)

Creative groups

• Field work on creative groups suggests curvilinear relationship between performance and connectedness (Leenders)

• Experimental work on problem solving groups (Goldstone)

• Broadway (Uzzi and Spiro)

• Project teams (Binz-Scharf)

Conclusions

• Trade-off between networks that perform well in the short run vs long run– Small, high bandwidth, worlds good for SR, bad in LR

• Tragedy of the network: Trade-off between interests of individuals and system

• Are some networks better than others in both SR and LR?

• Are some networks good “compromises”?

Extensions

• Vary problem space

• Error in copying (crossover)

• Timing of “velocity”

• Assume some heterogeneity in problem space

• Make network endogenous

• Have landscape change

Genetic programming

• Holland, Koza, solution “breeding”

• Performs much better if there are multiple (largely) isolated populations, within which there is great intermixing and competition, between which there is little (> 0)

• Speciation