THE EMERGING SCIENCE OF
NETWORKS
Duncan Watts
Yahoo! Labs
The Small-World Problem
• “Six degrees of separation between us and
everyone else on this planet”
– John Guare, 1990
– First mentioned in 1920’s by Karinthy
– 1950’s Pool and Kochen first math investigation
• Milgram’s Small-World Experiment 1960’s
• Watts and Strogatz (1998)
– showed that “small-world” property was exhibited by
many real world networks, including social networks
– more generally showed that “complex networks” have
interesting mathematical and dynamical properties
Network Science
• Twelve years later we have a good understanding of
how the small world phenomenon works
• Also starting to understand other characteristics of
large-scale networks
• New theories, better models, faster computers, and
mountains of digital data all contributing factors
• Result has been called “Science of Networks”
– 2005 NAS report on Network Science
– Thousands of papers, dozens of books, numerous
conferences, funding programs, etc.
Network Science and The Internet
• The Internet is a fascinating social and
economic phenomenon in its own right
• But it also presents an historically
unparalleled opportunity to study social
and economic phenomena
– Like the telescope for social science
• Four examples drawn from past decade
that illustrate what is possible
Columbia Small-World Project
Milgram 1960’s
• One target, 300 “letter
chains” - 64 reached
target
WEB EDITION, 2002
• 18 targets around world,
24,163 chains, 61,168
hands, 166 countries
• 400 reached targets
• 40% to Cornell!
• Surprisingly, chains were
about the same length
• But no “hubs”
• Also discovered “bored at
work” network
• What else could we do with
them?
Music Lab:
A “Macro-Sociological” Experiment
CULTURAL MARKETS:
• “Hits” are many X more successful
than average
• Success seems obvious in
retrospect, but hard to predict
• Can inequality and unpredictability
be explained by social influence?
• Want to run an experiment
• Requires 1,000s of participants
• Solution: A “virtual lab”
– Expose some people to
influence, while others decide
independently
– Measure effects on individual
and collective behavior
MUSIC LAB FINDINGS
• Individuals are influenced by observations of the
choices of others
– The stronger the social signal, the more they are influenced
• Collective decisions are also influenced
– Popular songs are more popular (and unpopular songs are less popular)
– However, which particular songs become popular becomes harder to predict
• The paradox of social influence:
– Individuals have more information on which to base choices
– But collective choice (i.e. what becomes popular) reveals less and less about
individual preferences
• Music Lab not just about Music:
– Really about any sort of behavior in which we are influenced by others
– Markets construct preferences as well as reveal them
INFLUENCE & TWITTER
• Music Lab showed importance of influence
• But influence in real life diffuses through networks
• Twitter is ideally suited to study diffusion
– Fully-observable network of “who listens to whom”
– Every tweet corresponds to a “cascade” of information
– URL shorteners enable us to track each cascade
– No matter how small or large
• Objective is to predict cascade size as function of
– # Followers, # Friends, # Reciprocated Ties
– # Tweets, Time of joining
– Size of previously triggered cascades
Cascades on Twitter
•
•
•
•
•
Two months data
Late 2009
1.6M users
posted 39M bit.ly
URL’s
Hence 39M
cascades total
Average cascade
size 1.14
–
•
Median
cascade size 1
Large cascades
extremely rare
“ORDINARY INFLUENCERS”
FINDINGS:
• Large cascades are rare, hence:
– Probably impossible to predict them or how they will start
– Better to trigger many small cascades
• Highly visible users tend to be more influential
- But only on average – lots of randomness
- Also from a marketing perspective, prominent users may also
be expensive
• “Ordinary Influencers” are promising
– May influence less than one other person on average
– But may also be relatively cheap
– Targeting thousands or millions of unexceptional individuals
may be more effective than targeting a few exceptional users
Networked Experiments on
Amazon’s Mechanical Turk
• Created in 2005 Mechanical Turk has developed into
a popular “crowd-sourcing” site
• Can also be viewed as platform for recruiting and
paying participants in behavioral experiments
– Networked experiments require synchronous play
Collaborative Learning
In Networks
• Groups of 16 players searching a landscape for “oil”
• Payoff determined by hidden “fitness landscape”
• Each can see their own performance, along with three of their
neighbors, on some network
Communication Networks
Greatest Average Betweenness
Smallest Average Betweenness
Smallest Maximum Closeness
Greatest Maximum Closeness
Greatest Average Clustering
Smallest Average Clustering
Greatest Maximum Betweenness
Greatest Variance in Constraint
All Individuals in all networks have 3 neighbors,
All Individuals have the same view of the world
Short Paths Speed Learning
Clustering Reduces Exploration
When Do Networks Matter?
• At first, seems clear why path length and clustering
affect performance
– Better efficiency improves learning speed
• But previous theoretical work had predicted the
opposite result: less efficient networks should perform
better on complex problems
• And another recent experiment on cooperation found
that network structure had no effect on behavior at all
• Raises general theoretical question of when networks
matter and when they don’t
– More experiments will probably be required to guide theory
Advantages of the Virtual Lab
• Fast, Cheap, and Under Control
– Can now run up to 20 sessions in a week with up to 36 players per
session
– Roughly $1 per player-hour (comp with ~ $10 for physical lab)
– Hypothesis-Testing loop shrunk from years to week
• Participant pool still not representative, but more diverse
than college students
• Some subjects have played over 50 games
– Longstanding panels open new research opportunities
The Future?
• In past ten years, we have moved beyond the
simple mathematical models of the 1990’s
–
–
–
–
Small World Exp mapped networks on a global scale
Music Lab was a “macro-sociological” experiment
Twitter study measured influence in the wild
AMT closest we have come to a virtual lab
• Still far from the big questions of social science
– Systemic risk, wealth inequality, economic development
• But every year, new things become possible…
Thank You!