Fundamental Building Blocks of Social Structure

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Fundamental Building Blocks of Social Structure

• Honoring Peter Killworths contribution to social
  network theory
• Southampton, Sept. 28, 2006

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The network scale-up team

• Peter D. Killworth (SOC)
• Christopher McCarty (U Florida)
• Gene A. Shelley (Georgia State U)
• Eugene Johnsen (UC-Santa Barbara)
• H. Russell Bernard (U Florida)

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Some background Ill have a go at that
(Scripps, 1972).

• I asked everyone on a ship to rank order their
  interactions with all the others.
• I came to the physics department coffee break and
  asked "anybody here want to know the social
  structure of a vessel that gets all your data?"
• The ocean-going physicists in the room knew they
  weren't supposed to talk to people like me and
  didn't even look up.

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• Peter hadnt gotten the memo about social
  scientists and said he thought it might be fun.
• And thats what its been, for 34 years and
  40-odd papers later

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How to get at the structure of these data? Lets
try this

• Peter applied an algorithm from F.S. Actons
  (then) recent book Numerical Methods that
  (Usually) Work ...
• The algorithm had been developed to solve the a
  traffic problem How to get from point A to point
  B fastest, irrespective of the number of red
  lights on the path.
• Visualizing the messy result.

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The prison studies

• We combined numerical methods with ethnography.
• The cliques always made sense, until one day
• Three numerically tied inmates whose connections
  made no apparent sense different crimes, North
  and South, rural and urban, Black and White.
• Finally, finally an artifact .

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Peter This is too easy.

• We discovered that physicists dont apply their
  models to social structure and anthropologists
  dont test the error bounds of their instruments.
  
• We were half-way on this one, so we started the
  accuracy studies.

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How to study accuracy?

• We studied people whose real communication could
  be unobtrusively monitored and whose members we
  could ask questions like "So, in the last day,
  week, month, who did you talk to in this
  group?"
• Deaf people on TTYs
• Ham radio operators in a local network
• An early e-mail group
• An office
• A fraternity

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Half of what people tell you is incorrect

• People dont recall behaviors that did occur and
  recall behaviors that didn't occur.
• People arent lying. Theyre just terrible
  behaviorscopes.

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Extending (or redefining) the problem

• We asked are the instruments for gathering data
  about human behavior producing accurate
  measurements of human behavior?
• Others used our data and asked what do those
  instruments produce a valid measurement of?
• Answer If you ask people who they interact with,
  people retrieve who they usually interact with
  and report who they ought to interact with, given
  everything they already know about their place in
  the social structure.

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Next, the small world

• Milgrams famous small-world experiment told us
  that there are 5.5 links between any two white
  people in the U.S. and exactly one more link
  between any white and any black person in the
  U.S.
• But these numbers do not tell us anything about
  the structure of the society.

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Peter Lets find out how the SW actually
operates

• Show people a list of SW targets, complete with
  the information about location, occupation,
  hobbies, and organizations.
• ask people to tell us their first link in a
  small-world experiment.
• Repeat 500 times and analyze the information
  needed by people to make their choice of a first
  link.

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The reverse small world experiments

• We ran six of these experiments in the U.S., in
  Micronesia and in Mexico.
• Things that people in the US find useful to the
  task (name, location, occupation, hobbies,
  organizations) are the same things that people in
  other cultures need to know to place someone in
  their network.
• For both of us, the cross-cultural regularity
  discovered in this series of experiments is among
  the most exciting results of our work.

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• We created a similarity matrix between targets
  how many people used the same choice for a given
  pair of targets?
• A 2-d MDS shows the enduring influence of Gerhard
  Mercator on schooling.

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Finding the distribution c

• Our real objective, though, is to understand the
  basic components of social structure.
• One quantity that seems important is the number
  of people whom people know.
• We call this c

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Network size Its just one number

• From the first, Peter pushed us all to learn more
  about the basic quanta
• How does network size vary, within and across
  cultures?
• Whats the distribution look like?
• Our first estimate, in 1978, for average network
  size in the U.S. was 250.

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Peter You have to start somewhere.

• And what was that 250?
• It was the number of people on whom the people of
  Morgantown, West Virginia who sat through this
  grueling, 8-hour experiment could call on to be
  first links if Milgram had shown up and asked
  them to participate in a small world experiment.

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Deriving c from an assumption

• Let t be the size of a population, and let e be
  the size of some subpopulation within it.
• We assume that the fractional size
• p e/t
• of that subpopulation also applies to any
  individuals network, other things being equal.
• That is, everyones network in a society
  reflects the distribution of subpopulations in
  that society.

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The scale-up method to estimate c

• To test this, we ask a representative sample of
  people to tell us how many people they know in
  many subpopulations whose sizes are known
• e.g., diabetics, gun dealers, postal workers,
  women named Nicole, men named Michael

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People answer accurately

• Now, assuming that people can and do answer our
  question accurately

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A maximum likelihood estimate of an individuals
network size
    
where there are L known subpopulations. (Here i
is the individual, who knows mij in subpopulation
j.) Network size is (the sum of all the people
you say you know in some subpopulations of known
size, divided by the total size of those
subpopulations) times the population within which
the subpopulations are embedded.
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The estimates of c are reliable

• This doesnt deal with the big IF, but across 7
  surveys in the U.S., average network size 290
  (sd 232, median 231).
• The 290 is not an average of averages. Its a
  repeated finding.
• And its almost certainly not an artifact of the
  method.

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Reliability I

• In one survey, we estimated c by asking people
  how many people they know in each of 17 relation
  categories people who are in their immediate
  family, people who are co-workers, people who
  provide a service and summing.
• The summation method (due to Chris McCarty)
  produced a mean for c of 290.

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Reliability II Change the data

• We changed reported values at or above 5 to a
  value of 5 precisely. The mean dropped to 206, a
  change of 29.
• We set values of at least 5 to a uniformly
  distributed random value between 5 and 15. We
  repeated this random change only for large
  subpopulations (with gt 1 million).
• The mean increased to 402, a change of 38 -- in
  the opposite direction.

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Reliability III Survey clergy

• We surveyed a national sample of 159 members of
  the clergy people who are widely thought to
  have large networks.
• Mean c 598 for the scale-up method
• Mean c 948 for the summation method

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290 is not a coincidence

• 1. Two different methods of counting produce the
  same result.
• 2. Changing the data produces large changes in
  the results.
• 3. People who are widely thought to have large
  networks do have large networks.

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Something is going on

• This next slide shows the probability, for two of
  our surveys, of knowing no one in each of 29
  populations of known size, by the actual size of
  those populations.
• The two distributions track, except for the
  expected offset.

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The distribution of c

• Here is the graph of the distribution of network
  size

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Reliability vs. validity

• Ok, its reliable. But if the model works, we
  ought to be able to use it to estimate the size
  of populations whose sizes are not known.
• Create a maximum likelihood estimate for the size
  of an unknown subpopulation based on what all
  respondents tell us and our estimates of their
  network sizes.
• Roughly speaking, inverting the previous
  formula.

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Can we predict what we know?

• Test this by predicting the size of 29
  populations of known size.
• The overall result is encouraging

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r .79 but note the outliers
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Over- and under-estimation

• The two largest populations are people who have a
  twin brother or sister and diabetics.
• These are highly underestimated.
• Without these two outliers, the correlation rises
  from r .79 to r .94
• No cheating

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Stigma vs. not newsworthy

• Being a twin or a diabetic is neither
  stigmatizing, nor newsworthy.
• From Gene Shelleys work, we know that personal
  information about close co-workers or business
  associates can take a decade or more to be
  transmitted ... and in the case of being a twin
  or a diabetic, may never be transmitted.

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Another encouraging result

• Charles Kadushin ran a national survey to
  estimate the prevalence of crimes in 14 cities,
  large and small, across the U.S.
• He asked 17,000 people to report the number of
  people they knew who had been victims of six
  kinds of crime and the number of people they knew
  who used heroin regularly.

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• Here are the estimates for the number of heroin
  users in each of the 14 cities, along with the
  estimates from the UCR.

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• The fact that we track well with official
  estimates means only that we have a much, much
  less expensive way to get at these estimates
  not that the estimates are correct.
• And estimates of other crimes in those 14 cities
  did not track so well.

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Reliability, validity, and accuracy

• So, while definitely reliable and perhaps valid,
  our estimate of network size (and its
  distribution) is not sufficiently accurate.

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Compromising assumptions

• 1. Transmission effects Everyone knows
  everything about everyone they know.
• 2. Barrier effects Everyone in the population
  has an equal chance of knowing someone in any
  subpopulation.

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Correlation between the mean number of Native
Americans known and the percent of the state
population that is Native American is 0.58, p
0.0001.
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Network social barriers

• Race (Blacks may know more diabetics than Whites
  do.)
• Gender (men may know more gun dealers than women
  do.)
• Even first names are associated with the barrier
  effect.
• We address the barrier effect by using a random,
  nationally representative sample of respondents.
• However, using the method on specific populations
  may still lead to incorrect estimates.

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The transmission effect

• We asked people things about people they knew
  and then called up those people to see how much
  people really do know about their network members.

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Some things are easy to get right

• 99 know their alters marital status.
• People know how many children 89 of their alters
  have.
• 98 know the employment status of their alters.

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Some things are harder to know

• People say they know the state in which 70 of
  their alters were born, but only 57 of the
  reports (egos and alters) agree on this.
• People dont know the number of siblings their
  alters have 52 of the time.

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Some people withdraw

• Gene Shelley found that people who are HIV
  withdraw from their network in order to limit the
  number of people who know their HIV status.
• Eugene Johnsen confirmed this by showing that
  HIV people have, on average, networks that are
  one-third the global average.

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A theory of transmission bias

• Take another look at the comparison of the data
  from clergy and others
• Its likely that you know at least one
  Christopher (the probability of knowing NO
  Christophers is close to zero).
• Twins are likely to be underreported

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• Peter said Assume that people report correctly
  what they know but that what they know is
  incorrect.
• What would happen to the jaggedy curve if people
  responded honestly to correct information instead
  of honestly to incorrect information?

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How to adjust the x-axis rather than the y-axis
in the diagram?

• Suppose that widows dont tell half the people
  they know about their being a widow.
• The .013 on the x-axis remains the same but the
  number that people would be responding to would
  be .013/2.
• To make the x-axis the effective size of that
  population, we slide it to the left while the
  y-axis remains the same.

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The jaggedy line would go

• Of course, we have no idea what the transmission
  error might be.
• We do know that if the numbers remain the same on
  the y-axis and we make up the effective sizes on
  the x-axis, the jaggedy line would go.

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• Peter did this analytically and computed the
  predicted distribution of c.
• The next slide shows that we may be on the right
  track

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Peters (highly) unusual place in the social
sciences

• No. of articles 154
• In Social Science journals (43)
• Total number of Citations 3194
• In Social Science journals  456  (14 )
• In non-Social Science journals 2738 (86)

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• http//garfield.library.upenn.edu/histcomp/killwor
  th-pd_citing/ (http//tinyurl.com/nmhdc)
• http//garfield.library.upenn.edu/histcomp/killwor
  th-pd_auth/ (http//tinyurl.com/ppr82)