Post on 22-Jan-2016
description
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
0
0.1
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0.6
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0.8
0.9
1
0 5 10 15 20 25
Round
Perf
orm
an
ce
score full 36
Bigger is better
Impact of size
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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0 5 10 15 20 25
Round
Perf
orm
an
ce
score full 36
score full 100
Bigger is better
Impact of size
0
0.1
0.2
0.3
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0.5
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0.7
0.8
0.9
1
0 5 10 15 20 25
Round
Perf
orm
an
ce
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
0
0.1
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0.9
10 10
20
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Round
Perf
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score full
…but not so good in the long haul
Impact of network structure
0
0.1
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0.9
10 10
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Round
Perf
orm
an
ce
score line
score full
Small worlds drive out variety
Heterogeneity
0
20
40
60
80
1000 9
18
27
36
45
54
63
72
81
90
99
10
8
11
7
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6
Round
Nu
mb
er
of
str
ate
gie
s
line
full
LR Performance of random graphs
Random graphs
0.4
0.45
0.5
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
0
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1 4 7 10 13 16 19 22 25 28 31 34 37
Round
Pe
rfo
rma
nc
e
Score line
Impact of structure is contingent on problem space
Search in a "simple" world: linear vs full graph
0
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1 4 7 10 13 16 19 22 25 28 31 34 37
Round
Pe
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Score line
Score full
Velocity increases exploitation and decreases exploration
Impact of velocity on performance
0
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1 10 19 28 37 46 55 64 73 82 91 100
Round
Pe
rfo
rma
nc
e
score full
Velocity increases exploitation and decreases exploration
Impact of velocity on performance
0
0.1
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0.5
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0.7
0.8
0.9
1
1 11 21 31 41 51 61 71 81 91 101
Round
Pe
rfo
rma
nc
e
Asynch10 full
score 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
Per
form
ance
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
Per
form
ance
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
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
e
Synch10 line
Synch10 full
Asynch10 line
Asynch10 full
HeterogeneityHeterogeneity over time for fully connected graph:
synchronous vs asynchronous
0
10
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0 20 40 60 80 100 120 140 160 180 200
Round
He
tero
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ne
ity
Synch10 full
Asynch10 full
HeterogeneityHeterogeneity over time for line: synchronous vs asynchronous
0
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0 20 40 60 80 100 120 140 160 180 200
Round
He
tero
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Synch10 line
Asynch10 line
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