1. Complex Contagion
of
Campaign Donations
CWTS, Leiden, the Netherlands
ICCSS 2016, Evanston, US
June 24, 2016
V.A. Traag

2. Complex contagion
Complex contagion
Contagion of human behaviour typically requires multiple exposures.
Contagion reinforcement
How does the contact structure of adopters reinforces contagion?
Is ego more likely to adopt the behaviour:
• when adopters know each other?
(Cohesive reinforcement)
• or, when adopters do not know each other?
(Independent reinforcement)
.

3. Complex contagion
Cohesive reinforcement
Only adopters from same
(largest) community matter,
ignore adopters from other
(smaller) communities.
Independent reinforcement
Only number of adopting
communities matter, ignore
redundant adopters within
community.
Adopting communities (3)
Adopter degree (4)
Common community
adopter degree (2)

4. Campaign donation
LittleSis (website dedicated to tracking US elite).
• Elite network (n ≈ 50 000, k ≈ 60).
Family, professional, social & colleagues, alumni, club members.
• Campaign donations coupled to network information.
Results for presidential campaign 2008, other campaigns similar.
0
100
200
300
John McCain
Barack Obama
Jan Apr Jul Oct Jan Apr Jul Oct
0
2,000
4,000
6,000
8,000
2007 2008
Announces
Presumptive nominee
Nominated
Announces
Iowa
Super tuesday
Presumptive nominee
Nominated
Elected
No.Donors
a
b

5. Donation probability
0 1 2 3 4 5
0
1
2 ·10−2
† *
†
† ** *
Degree
0 1 2 3 4 5
† ***
***
† ***
*
Common community degree
0 1 2 3 4 5
0
1
2
3
4
5
6
·10−2
†
†
†
**
†
†
†
Communities
0 1 2 3
†
†
**
†
†
†
Source diversity
No Yes
† †
Donated
previously
Donationprobability
a b
c d e
John McCain Barack Obama
χ2-test of consecutive difference: ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001, †p < 0.0001

6. Conditional donation probability
0 1 2 3 4 5
0
2
4
6
8
10
12
14
·10−3
**
** *
*
0 1 2 3 4 5
†
***†
†
0 1 2 3 4 5
0
1
2
3
4
5
6
7
·10−2
***
*
†
Degree
0 1 2 3 4 5
†
***†
**
Communities
a b
c d
Donationprobability
NoYes
Donatedpreviously
John McCain Barack Obama
χ2-test of consecutive difference: ∗p < 0.05, ∗∗p < 0.01, ∗∗∗p < 0.001, †p < 0.0001

7. Logistic regression
Degree
Clustering
−0.0016
−0.22
−0.004
−0.55
General
Donor degree
Donor communities
Donor source diversity
Donors common community
−0.042
0.43
0.25
0.068
−0.032
0.67
0.057
0.098
Not donated previously
−1 0 1 2 3
Donated previously
Donor degree
Donor communities
Donor source diversity
Donors common community
3.5
0.002
0.14
0.17
0.024
3.1
0.015
0.035
0.33
0.033
Effect
Donated previously
a
b
c
John McCain
Barack Obama

8. Additional results
Cross cutting donations
• Exposure to Democratic donors may incite Republication
donations.
2008: Exposure Obama donors increase donations to McCain.
2004: Exposure Bush donors increases donations to Kerry.
• Exposure to both tends to reduce donations, but weak effect.
Macro level
Predict total money raised based on Q1
• Amount is clearly predictive (multiplier 1.8)
• Number of donors not significant
• Number of independent donors significant (multiplier 1.3).

9. Conclusions
Theory
• Use independent sources to infer population estimates (viability).
• Population network externalities ⇒ independent reinforcement.
• Coordination or connections important ⇒ cohesive reinforcement.
• Possibly also negative effects (oppose candidate, public goods).
Consequences
• Recommendations: number of independent friends.
• Independent reinforcement: fast across groups, slow within.
• Cohesive reinforcement: fast within groups, slow across.
• Fundraising: target broad audience, multiple constituencies.

10. Thanks for your attention!
Questions?
Traag VA (2016) Complex Contagion of Campaign Donations.
PLoS ONE 11(4): e0153539. doi:10.1371/journal.pone.0153539
v.a.traag@cwts.leidenuniv.nl Twitter: @vtraag