small world problem
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Small World Problem. Christopher McCarty. Small World Phenomenon. You meet someone, seemingly randomly, who has a connection to someone you know Person you meet on a plane who went to school with a relative Killworth’s example McCarty example - PowerPoint PPT PresentationTRANSCRIPT
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Small World Problem
Christopher McCarty
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Small World Phenomenon
• You meet someone, seemingly randomly, who has a connection to someone you know– Person you meet on a plane who went to school
with a relative– Killworth’s example– McCarty example
• Is this a bizarre coincidence or is there an underlying explanation?
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John Barnes (1969) Networks and Political Process in Social Networks in Urban Situations
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Small World StudyJeffrey Travers and Stanley Milgram (1969) An Experimental Study of the Small
World Problem, Sociometry 32(4): 425-443
• What is the probability that any two randomly selected people know each other?
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Method• 296 respondents in Nebraska and Boston are asked to send a
packet to someone they knew who had the best chance of knowing a target person in Massachusetts
• The target was a Boston stockbroker
• 100 respondents owned stocks, the rest were randomly selected
• There were 453 intermediaries
• There were no incentives
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Method (cont.)
• The profile contained name, address, occupation, place of employment, college, military service, his wife’s maiden name and home town
• Roster included to prevent looping
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Results
• 217 of the 296 sent the packet on
• 64 chains were completed (29 percent) with an average length of 5.2
• 48 percent of the chains passed through 3 people before reaching the target
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Characteristics of intermediaries• There was a division of
labor among the 3
• One person was a clothing merchant and handled chains using residence
• Others were scattered around Boston and used occupation (stockbrokers)
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Future study
• Throughout the article Travers and Milgram suggest a different study where they manipulate the starter and target information
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H. Russell Benard, Peter D. Killworth and Christopher McCarty (1982) Index: An Informant-Defined Experiment
in Social Structure, Social Forces 61(1): 99-133• 50 mythical targets
• Each started with set characteristics
• 50 respondents were instructed to select the person they knew with the best chance of knowing the target
• The respondent had to decide which questions to ask
• As new information was given it was recorded on the target’s profile
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Preset Target Characteristics
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Peter D. Killworth, H. Russell Bernard and Christopher McCarty (1984) Measuring Patterns of Acquaintanceship, Current
Anthropology 25(4): 381-397
• Reverse Small World
• 500 mythical targets, 400 around the world and 100 in the U.S.
• Distributions of 10 areas of the world, occupations, sex, age, education, marital status
• 40 respondents
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Suggests line would asymptote around 250. This is another measure of network size
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Duncan J. Watts and Steven H. Strogatz (1998) Collective Dynamics of ‘Small World’ Networks,
Nature 393(4): 440-442• Mathematical re-examination of the small
world problem
• Highly ordered networks are re-wired to introduce disorder
• These lead to highly clustered networks with small path lengths (small world)
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Peter Sheridan Dodds, Roby Muhamad and Duncan J. Watts (2003) An Experimental Study of Search in Global
Networks, Science 301 (5634): 827-829• Internet based study
• 18 target people from 13 countries
• Different occupations
• 98,847 people registered at web site, about 25% provided personal information
• 61,168 participants from 166 countries
• 24,163 chains – 384 (1.6% completed)
• Average chain length was 4.05
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Results
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Peter D. Killworth, Christopher McCarty, H. Russell Bernard and Mark House (2006) The Accuracy of Smal World Chains in Social
Networks, Social Networks 28: 85-96
• 105 members of survey lab were shown a roster of all other names
• They indicated if they knew each one
• For those they did not know they nominated someone who would have the best chance of knowing them
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Results
• Mean length of shortest actual path was 2.3 (S.D. 0.71)
• 21.7% of the conceptual paths terminated as they included people who did not participate
• Another 23.7% ended up in loops (i chooses j chooses i)
• The remaining 54.6% reach completion with mean 3.23 (S.D. 2.06), 40% longer than actual length