Measuring Social Capital in Real-World Social Networks

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Measuring Social Capital in Real-World Social
Networks

• Markus Mobius (Harvard University and NBER)
• Do Quoc-Anh (Harvard University)
• Tanya Rosenblat (Wesleyan University and CBRSS)
• October 2004

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Social Capital (Putnams Definition)

• Social capital refers to the collective value of
  all social networks who people know and the
  inclinations that arise from these networks to do
  things for each other norms of reciprocity

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Social Capital

• Inclinations to do things for each other can
  arise because of
• innate altruistic preferences
• cooperative behavior in a repeated game
• The goal is to measure both sources depend on
  network structure

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2 Stages

• Stage 1 Measure social network using a
  coordination game.
• Stage 2 Select players based on social distance
  to measure how social preferences vary with
  network structure.

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Social Network

• Residential social network of (569) upper-class
  undergraduates (sophomores, juniors and seniors)
  at a large private university.
• Students are randomly allocated to 12 residential
  houses after their freshman year (as a blocking
  group of 2-8 students).
• Students make long-term friendships within the
  houses (since houses provide meals, entertainment
  and educational activities).
• 2 Houses used for the study

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Methodology

• Need high participation rate in order to get
  meaningful network data.
• In addition to participation fee and experimental
  earnings, conduct a raffle with valuable prizes
  at the end of the study.
• A major publicity campaign that advertises
  experiment (letters in the mail, posters, flyers,
  information table in the dining halls).
• Direct emailing was not allowed until subjects
  signed up and agreed to receive emails.

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Methodology

• Networks are usually measured through surveys
• Instead, use a coordination game with monetary
  payoffs to induce subjects think more carefully
  about their answers
• Subjects name up to 10 friends and some
  dimensions of their friendship (e.g., how much
  time they spend together during the week).

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Network Elicitation Game
Tanya names Alain
Tanya
Alain
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Network Elicitation Game
Tanya gets a prize of 1 if
Tanya
Alain
Tanya
Alain
Alain names Tanya
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Network Elicitation Game
Tanya gets a prize of 1 if
Tanya
Alain
Alain and Tanya get an additional prize if they
agree on how much time they spend together each
week.
Tanya
Alain
Alain names Tanya Alain also gets a prize of 1
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Network Elicitation Game
Tanya
Alain
If T names A and A names T (coordinate) we call
it a link the link is stronger if there is
agreement on the attributes of the relationship.
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Network Elicitation Game
Tanya
Alain
In order to protect students feelings, each
match is paid with 50 probability so if they
get 0, they dont know whether this is because
they were rejected, or because they were
unlucky.
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Network Data

• In addition to the network game
• Know who the roommates are
• Geographical network (where rooms are located in
  the house)
• Data from the Registrars office
• Survey on lifestyle (clubs, sports) and
  socio-economic status

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Network Data Sample Description

• House1 - 46 (259) House2 - 54 (310)
• Sophomores - 31(174) Juniors - 30 (168)
  Seniors - 40 (227)
• Female - 51 (290) Male - 49 (279)
• 5690 one-way relationships in the dataset 4042
  excluding people from other houses
• 2086 symmetric relationships (1043 coordinated
  friendships)

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Symmetric Friendships
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Symmetric Friendships
The agreement rate on time spent together (/- 1
hour) is 80
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Network description

• Cluster coefficient (probability that a friend of
  my friend is my friend) is .5841
• The average path length is 6.5706
• 1 giant cluster and 34 singletons
• If ignore friends with less than 1 hr per week,
  many disjoint clusters (175)

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How does social distance affect social capital?

• Use network data to design a non-anonymous
  experiment to study the role of social distance
  on social capital.

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Social Capital (Putnams Definition)

• Social capital refers to the collective value of
  all social networks who people know and the
  inclinations that arise from these networks to do
  things for each other norms of reciprocity

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Sources of Social Capital
2. Cooperative Social Capital
1. Preference-Based Social Capital
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Sources of Social Capital
1. TYPE TRUST
1. Preference-Based Social Capital
The other player is altruistic and takes my
utility into account.
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Sources of Social Capital
1. TYPE TRUST
1. Preference-Based Social Capital
The other player is altruistic and takes my
utility into account.
Altruism can differ by social distance (feel
differently towards friends, friends of friends,
friends of friends of friends or strangers)
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Sources of Social Capital
2. Cooperative Social Capital
1. TYPE TRUST
1. Preference-Based Social Capital
The other player is altruistic and takes my
utility into account.
The other player fears punishment in future
interactions with me (or other players) if she
does not take my utility into account.
Altruism can differ by social distance (feel
differently towards friends, friends of friends,
friends of friends of friends or strangers)
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Sources of Social Capital
2. Cooperative Social Capital
1. Preference-Based Social Capital
The other player is altruistic and takes my
utility into account.
The other player fears punishment in future
interactions with me (or other players) if she
does not take my utility into account.
Altruism can differ by social distance (feel
differently towards friends, friends of friends,
friends of friends of friends or strangers)
Fear of punishment can differ by social distance
(differently afraid of punishment from friends,
friends of friends, friends of friends of friends
or strangers)
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Experimental Design

• Use Andreoni-Miller (Econometrica, 2002) GARP
  framework to measure altruistic types
• A modified dictator game in which the allocator
  divides tokens between herself and the recipient.
  Tokens can have different values to the allocator
  and the recipient.

Subjects divide 50 tokens which are worth 1
token to the allocator and 3 to the recipient 2
tokens to the allocator and 2 to the recipient 3
tokens to the allocator and 1 to the recipient
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Goals of the Experimental Design
1) Measure Agents Altruistic Type and how their
altruism varies with social distance (when
allocators know the identity of the recipient).
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Goals of the Experimental Design
1) Measure Agents Altruistic Type and how their
altruism varies with social distance (when
allocators know the identity of the recipient).
2) Distinguish between preference-based and
cooperative social capital by varying the degree
to which the recipient finds out about
allocators actions.
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Goals of the Experimental Design
3) Measure Recipients expectations about actions
of allocators to understand to what extent
recipients know about the services of social
capital and how accurately it is alligned with
the decisions of allocators (use this to study
trusting behavior)
1) Measure Agents Altruistic Type and how their
altruism varies with social distance (when
allocators know the identity of the recipient).
2) Distinguish between preference-based and
cooperative social capital by varying the degree
to which the recipient finds out about
allocators actions (use this to study
trustworthiness)
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Experimental Design

• Each allocator participates in 4 treatments in
  random order
• Baseline anonymous allocator and anonymous
  recipient (AA).
• Anonymous allocator and known recipient (AK)
• Known allocator and anonymous recipient (KA)
• Known allocator and known recipient (KK)
• With some uncertainty (always 15 chance that
  allocations are made by computer)

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Sources of Social Capital
2. Cooperative Social Capital
1. Preference-Based Social Capital
The other player is altruistic and takes my
utility into account.
The other player fears punishment in future
interactions with me (or other players) if she
does not take my utility into account.
Anonymous Allocator/Anonymous Recipient (AA),
Anonymous Allocator/Known Recipient (AK)
Known Allocator/Anonymous Recipient (KA), Known
Allocator/Known Recipient (KK)
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Who is the Recipient when known? (AK and KK)
For Allocator choose 5 Recipients (in random
order) 1 direct friend 1 indirect friend of
social distance 2 1 indirect friend of social
distance 3 1 person from the same staircase 1
person from the same house.
Share staircase
Indirect Friend 2 links
Indirect Friend 3 links
Same house
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Experimental Design What Do Recipients Do?

• Recipients make predictions about how much they
  will get from an allocator in a given situation
  and how much an allocator will give to another
  recipient that they know in a given situation.
• One decision is payoff-relevant
• gt The closer the estimate is to the actual
  number of tokens passed the higher are the
  earnings.

Incentive Compatible Mechanism to make good
predictions
Get 15 if predict exactly the number of tokens
that player 1 passed to player 2
For each mispredicted token 0.30 subtracted from
15. For example, if predict that player 1 passes
10 tokens and he actually passes 15 tokens then
receive 15-5 x 0.3013.50.
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Recipients are asked to make predictions in 7
situations (in random order) 1 direct friend 1
indirect friend of social distance 2 1 indirect
friend of social distance 3 1 person from the
same staircase 1 person from the same house 2
pairs chosen among direct and indirect friends
Recipients Expectations
Share staircase
Indirect Friend 2 links
Indirect Friend 3 links
Same house
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Recipients are asked to make predictions in 7
situations (in random order) 1 direct friend 1
indirect friend of social distance 2 1 indirect
friend of social distance 3 1 person from the
same staircase 1 person from the same house 2
pairs chosen among direct and indirect friends
Recipients Expectations
A possible pair
Share staircase
Indirect Friend 2 links
Indirect Friend 3 links
Same house
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Experimental Design

• Within-subject design with randomized order of
  presentation either all choices with will find
  out on one screen followed by will not find
  out screen or will find out/will not find out
  on one screen for each choice.

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Timing - Allocators

• AA and AK
• or
• AA and AA

Session 1 1 decision from 1 pair chosen for
monetary payoff (max 15)
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Timing - Allocators

• AA and AK
• or
• AA and AA

KK and KA or KA and KK
OR
Session 2 (1 week later) 1 decision from 1 pair
chosen for monetary payoff (max 15)
Session 1 1 decision from 1 pair chosen for
monetary payoff (max 15)
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Variable DISTANCE
For Allocator choose 5 Recipients (in random
order) 1 direct friend 1 indirect friend of
social distance 2 1 indirect friend of social
distance 3 1 person from the same staircase 1
person from the same house.
Share staircase
Indirect Friend 2 links
Indirect Friend 3 links
Same house
(Stranger) Dist 0
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Variable DISTANCE
For Allocator choose 5 Recipients (in random
order) 1 direct friend 1 indirect friend of
social distance 2 1 indirect friend of social
distance 3 1 person from the same staircase 1
person from the same house.
Share staircase
Dist 1
Indirect Friend 2 links
Indirect Friend 3 links
Same house
(Stranger) Dist 0
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Variable DISTANCE
Share staircase
Dist 1
Dist 2
Dist 3
Indirect Friend 2 links
Indirect Friend 3 links
Same house
(Stranger) Dist 0
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Variable DISTANCE
Not significant in all specifications
Share staircase
Dist 1
Dist 2
Dist 3
Indirect Friend 2 links
Indirect Friend 3 links
Same house
(Stranger) Dist 0
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Variable STRENGTH
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
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Variable STRENGTH
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
2) The intersection varies between 0 and 10.
Divide this number by 10. This is the index of
network strength.
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Variable STRENGTH
A strong link exists between two people who have
lots of common friends.
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
2) The intersection varies between 0 and 10.
Divide this number by 10. This is the index of
network strength.
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Variable STRENGTH
A strong link exists between two people who have
lots of common friends.
A weak link exists between two people who have
few common friends.
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
2) The intersection varies between 0 and 10.
Divide this number by 10. This is the index of
network strength.
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Variable STRENGTH
A strong link exists between two people who have
lots of common friends.
A weak link exists between two people who have
few common friends.
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
2) The intersection varies between 0 and 10.
Divide this number by 10. This is the index of
network strength.
If STRENGTH is 0 then the two subjects have no
friends in common at all.
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Variable STRENGTH
A strong link exists between two people who have
lots of common friends.
A weak link exists between two people who have
few common friends.
1) Take the set of 10 friends named by player 1
and intersect it with the set of 10 people named
by player 2.
2) The intersection varies between 0 and 10.
Divide this number by 10. This is the index of
network strength.
If STRENGTH is 0 then the two subjects have no
friends in common at all.
Note that this measure is defined even if i and j
are not friends and did not name each other.
Generally, however, we would expect that STRENGTH
decreases with social distance.
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3 situations
Subjects divide 50 tokens that are worth T1 1
token to the allocator and 3 to the
recipient T2 2 tokens to the allocator and 2 to
the recipient T3 3 tokens to the allocator and
1 to the recipient

• Player 1 KNOWS player 2's identity and player 2
  WILL FIND OUT the name of player 1 (cooperative
  preference-based social capital)
• Player 1 KNOWS player 2's identity and player 2
  WILL NOT FIND OUT the name of player 1
  (preference-based social capital)

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Number of Tokens Held
T1 T2 T3
Recipient finds out (preference-based and cooperative) 29 35 40
Recipient does not find out (preference-based) 34 40 43
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Regression
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Player 2 Finds out (Preference Based
Cooperative)
Number of tokens held when recipient is not a
friend.
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Player 2 Finds out (Preference Based
Cooperative)
Always give more to friends
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Player 2 Finds out (Preference Based
Cooperative)
Always give more to friends
Give more to friends of friends except in T3.
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Player 2 Does Not Find Out (Preference-Based)
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Player 2 Does Not Find Out (Preference-Based)
Number of tokens held when recipient is not a
friend.
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Player 2 Does Not Find Out (Preference-Based)
Give more to direct friends only!
Number of tokens held when recipient is not a
friend.
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Player 2 Finds out (Preference Based
Cooperative)
STRENGTH is statistically significant in T1 and
T3.
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Player 2 Finds out (Preference Based
Cooperative)
STRENGTH wipes out the effect of DIST2
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Player 2 Finds out (Preference Based
Cooperative)
DIST 1 and STRENGTH seem to have independent
effects.
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Player 2 Does Not Find Out (Preference-Based)
STRENGTH is statistically significant in T2.
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Player 2 Does Not Find Out (Type Trust)
Player 2 Does Not Find Out (Preference-Based)
DIST 1 and STRENGTH seem to have independent
effects.
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Player 2 Does Not Find Out (Type Trust)
Player 2 Does Not Find Out (Preference-Based)
STRENGTH wipes out the effect of DIST3 in T2
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Unified Regression (fixed effects)
Only Direct Friends Matter
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Unified Regression (fixed effects)
Strength only matters in non-anonymous case
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Alternative Estimation

• Use CES utility
• is the value of my token, is the value of
  the other persons tokens in decision d (d1,2,3)
• m is the number of tokens held
• Constant elasticity of substitution

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Alternative Estimation

• CES predicts
• Each player i chooses tokens held with error
• Estimate and using NLLS (3 data
  points for each )
• Run fixed effects regression as before

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Estimation

• Estimate s using non-linear least squares
  assuming a common sigma for all 5 encounters (15
  decisions)
• For each allocator get a sigma and five different
  s.
• Order allocators based on generosity in Dist1
  case from the least selfish to the most selfish
  (increasing s).

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Summary of Results - Allocators

• Give more to direct friends (compared to friends
  of friends, friends of friends of friends and
  unknown recipients)
• For non-anonymous interaction about 20 percent
  more tokens are passed to direct friends and
  about 8 percent more to indirect friends.
• For anonymous interaction about 15 percent more
  tokens are passed to direct friends.
• STRONG links (where two people have lots of
  friends in common) imply more giving across all
  three decisions in the NON-ANONYMOUS condition.
  This effect is large and about as big as the
  direct neighbor effect.
• Women seem to be less generous than men.
• Social distance effects are very similar EXCEPT
  for decision 3 where social network does not
  matter for men but it does matter for women.

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Application to Trust

• One of the services of social capital is trust
• Results on preference-based and cooperative
  social capital measure trustworthiness of
  players.
• Can ask a question about trusting behavior by
  measuring expectations of recipients about the
  behavior of allocators.

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What is Trust some common definitions?

• Firm reliance on the integrity, ability, or
  character of a person (The American Heritage
  Dictionary)
• Assured resting of the mind on the integrity,
  veracity, justice, friendship, or other sound
  principle, of another person confidence
  reliance (Websters Dictionary)
• Confidence in or reliance on some quality or
  attribute of a person (Oxford English Dictionary)

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What is Trust?

• Firm reliance on the integrity, ability, or
  character of a person (The American Heritage
  Dictionary)
• Assured resting of the mind on the integrity,
  veracity, justice, friendship, or other sound
  principle, of another person confidence
  reliance (Websters Dictionary)
• Confidence in or reliance on some quality or
  attribute of a person (Oxford English Dictionary)

Define trust as my belief that another player is
willing to sacrifice her utility to improve my
utility.
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Expectations about Player 1 Player 2 Finds out
(Effort TrustType Trust)
Expected Number of tokens held (Higher than
actual!)
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Expectations about Player 1 Player 2 Finds out
(Effort Trust)
Expectations about Player 1 Player 2 Finds out
(Effort TrustType Trust)
Expect direct and indirect links matter more so
than they do!
Expected Number of tokens held (Higher than
actual!)
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Expectations about Player 1 Player 2 Does not
Find out (Type Trust)
Expect direct and indirect links matter more so
than they do!
Expected Number of tokens held (Higher than
actual!) Higher than non-anonymous!
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Expectations about Player 1 - Player 2 Finds out
(Effort TrustType Trust)
STRENGTH doesnt seem to have an independent
effect!
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Expectations about Player 1 Player 2 Doesnt
Find out (Type Trust)
STRENGTH is very important and wipes out DIST2
effect
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Summary of Results - Recipients

• RECIPIENTS - Confirm by and large the results for
  allocators. However
• - subjects think that baseline giving is LOWER
  but that social distance matters MORE (by about a
  factor of 2) than it actually does
• - there is little difference between
  anonymous/non-anoymous treatment now - that means
  that subjects do not seem to properly factor in
  punishment
• - puzzling that STRONG links result is reversed
  Network strength does matter in the anonymous
  case rather than the non-anonymous one. Theory
  would predict that strength matters more in the
  non-anonymous case because punishment mechanisms
  should work better if subjects have more common
  friends.
• - people are not as good in predicting giving
  between two different people

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Summary of Results - Recipients

• Women believe allocators to be less generous than
  men
• Social distance effects are very similar EXCEPT
  for decision 3 where social network does not
  matter for men but it does matter for women (same
  for allocators).

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Summary

• We find strong evidence for directed altruism.
• Need to add data on general altruism.
• We find also evidence for punishment and that
  punishment amplifies directed altruism.
• Interestingly - we find that STRONG links (where
  two people have lots of friends in common) imply
  more giving across all three decisions in the
  NON-ANONYMOUS condition. This effect is large and
  about as big as the direct neighbor effect.

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Effort Trust Gender Effects
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Type Trust Gender Effects
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Gender Effects Expectations about Player 1
Player 2 Finds out (Effort Trust)
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Gender Effects Expectations about Player 1
Player 2 Doesnt Find out (Type Trust)