Complex Contagion of Campaign Donations V.A. Traag ∗ Royal Netherlands Institute of Southeast Asian and Caribbean Studies, Leiden, Netherlands e-Humanities Group, Royal Netherlands Academy of Arts and Sciences, Amsterdam, Netherlands and CWTS, Leiden University, Leiden, Netherlands (Dated: April 19, 2016) Money is central in US politics, and most campaign contributions stem from a tiny, wealthy elite. Like other political acts, campaign donations are known to be socially contagious. We study how campaign donations diffuse through a network of more than 50000 elites and examine how connectivity among previous donors reinforces contagion. We find that the diffusion of donations is driven by independent reinforcement contagion: people are more likely to donate when exposed 6 to donors from different social groups than when they are exposed to equally many donors from 1 thesamegroup. Counter-intuitively,beingexposedtoonesidemayincreasedonationstotheother 0 side. Although the effect is weak, simultaneous cross-cutting exposure makes donation somewhat 2 lesslikely. Finally,theindependenceofdonorsinthebeginningofacampaignpredictstheamount r of money that is raised throughout a campaign. We theorize that people infer population-wide p estimates from their local observations, with elites assessing the viability of candidates, possibly A opposing candidates in response to local support. Our findings suggest that theories of complex contagions need refinement and that political campaigns should target multiple communities. 8 1 Keywords: complexcontagion;socialinfluence;campaigndonation ] h I. INTRODUCTION scholarsarguedthatspatialcorrelationsinthegeographi- p caldistributionofdonationssuggesttheyspreadthrough - c No money, no campaign is a truism in US politics. socialnetworks[11,12]. Personalcontactisusuallymost o Financing a campaign is vital for any candidate to get effectiveforrecruitment[13],whilefieldexperimentswith s . elected. Contrary to appearances, most donations come canvassing also show contagious effects for turnout [14]. s c fromindividualsratherthancorporations. WhileObama It is well known that most social contagion processes i in 2008 attracted the most donors ever, reaching over arenotsimpleepidemiccontagionsinwhichasinglecon- s y 300000 people [1], this still pales in comparison to the tactispotentiallysufficientforsuccessfultransmissionof h US population of over 300 million. The elite thus have some virus [15–19]. For social contagion to materialize, p a disproportionately large influence on campaigns and social reinforcement is usually necessary, requiring mul- [ politics generally [2]. tiple exposures to the behaviour before successful trans- 2 The decision to donate or not, is not a purely individ- mission [20]. Many studies have analysed how the net- v ual one and is embedded in a wider social context [3]. work structure affects diffusion of behaviour [17, 21–26], 9 Peoplewhoareaskedtocontributearemuchmorelikely and different positions in the network may play different 7 to do so [4]. Unsurprisingly, the wealthy are the most roles [27] during the adoption life cycle. Nevertheless, 6 likely to donate [4]. Most money comes from large do- littleattentionhasbeenpaidtohowconnectivityamong 7 nations (i.e. $200), which must be registered with the adopters (i.e. donors) may affect contagion probabili- 0 ≥ . FederalElectionCommittee(FEC).TheFECisafederal ties [28]. We here focus on the question how likely some- 1 US agency tasked with the responsibility to administer bodyistoadoptacertainbehaviour(i.e. donating)given 0 and enforce campaign finance legislation, which is a con- the adopters among his or her network neighbours, and 6 tested subject in itself [5]. Exacerbating the inequality payparticularattentiontotheconnectivityamongthese 1 : in donations, the more wealthy and highly educated are adoptingneighbours. Ifsomebodyisexposedtoadopters v alsomorelikelytobeaskedtodonate[6,7]totheextent who are all acquainted with one another, the probability i X that when controlled for this selection bias, the effect ofthatpersonadoptingmaybedifferentfromwhennone r of asking may even disappear [8]. Such selection bias of the adopters know each other. We here introduce two a leads to an even greater inequality in financial contribu- different modes in which structure may affect contagion: tions[4]. Thewealthyandhighlyeducatedarealsomore cohesive reinforcement and independent reinforcement. likelytotrytopersuadeothers [9],whiletheinfluenceis If contagion is more likely when adopting neighbours stronger from people who are emotionally close [6]. Re- know each other we will speak of cohesive reinforce- search shows that individuals sitting on the same board ment. In this case, ego (the focal node) is embed- donate to similar candidates, and that this effect also ded in a well-knit cohesive environment of adopters. extends to members of interlocking boards [10]. Some Suchanenvironmentissupportiveandenablespeopleto take risky actions, knowing they are supported by their friends [29]. It is also frequently a normative environ- ment and part of the social influence is simply adhering ∗ [email protected] to group norms [30–32]. Failing to heed to the group’s 2 norms may lead to being ostracised, pressuring people rectly on having worked at the same firm, being alumni to adopt the behaviour and follow the group norms [33]. ofthesamecollegeoruniversity,orbeingamemberofthe Inthecaseofcohesivereinforcementcontagionwouldbe sameorganizationorclub. Assuch,itisamultiplexnet- especiallylikelyifadopterscomefromthesamegroupof work, which may have effects on the interplay between people. Take for example protesting: when four friends structure [42, 43] and dynamics [44]. As we will show participate but do not know each other, we may be less later, the multiplexity indeed has an impact on the way inclined to join than when these four friends know each donations diffuse. The LittleSis database also records other and we can participate as a group [34]. Such co- whodonatedhowmuchtowhomatwhattime. Westudy hesive reinforcement may also play a role in collective how the probability to donate depends on donors in the action more generally. (network) neighbourhood. In complex contagions, the If contagion is more likely when adopting neighbours probability to donate depends on the number of donors don’t know each other, we will speak of independent re- in the network neighbourhood which we call the donor inforcement. In this setting, adopters from the same degree. If contagion is reinforced through cohesion, only group do not reinforce social contagion. In some way, donorswhoarepartofthesamecommunityarerelevant. signalsfromthesamegroupareredundant,whichiscon- Inparticular, themaximumnumberofdonorswhocome sistent with the strength of weak ties [35]: news passes from the same community should be pertinent, which throughweaklinks,crossinggroupboundaries. Informa- we call the common community donor degree. If con- tionfrommultiplesourcesisgenerallymorecredible[36], tagion takes places through independent reinforcement, butonlyiftheyareindependent[37,38]. Indeed,ifmulti- only independent exposures are considered. We oper- plesourcesarenotindependent,theyareessentiallyseen ationalise this by counting the number of communities as a single independent source, and are no more persua- from which at least one member has donated, which we sive than a single source [38]. Take for example informa- call the donor communities. Alternatively, we count the tionpertainingtohealth: iffourfriendsinformusthata types of sources that have donated (family, professional, diet works well, this is more credible when these friends social, colleague, fellow alumni, fellow (club)member), do not know each other and reached this conclusion in- which we call source diversity. We discount any effect of dependently from one another than when they all know multiple exposures from similar sources. Notice this is each other (e.g. from a diet club), and have influenced a measure of multiplex exposure: we count the number each other in believing that the diet works. of layers on which a node is exposed. These measures Weanalyseanetworkofover50000elitescoupledwith are illustrated in Fig. 1, and are defined formally in Ap- donation data to investigate the dynamics of this com- pendix A. We take a quarter as a unit of time, since the plex contagion. Overall, the elite studied here follows daily dynamics exhibit clear dependencies on the (quar- the classical definition of the “power elite” as conceptu- terlyormonthly)FECreportdeadlines(Fig.2),asfound alisedbyMills[39]: theyaremostlypeopleinpositionsof previously [45]. We pool data for all quarters. power,suchaspoliticians,businessleaders,lobbyistsand topbureaucrats,althoughtherearealsosomeexceptions, such as academics and public intellectuals, but they are A. Contagion of donation relatively few. We examine whether contagion is driven by cohesive reinforcement or independent reinforcement. Themainquestionweaddressinthissectioniswhether We further study cross-cutting exposure [40, 41]: how contagionisdrivenbycohesivereinforcementorbyinde- exposuretoDemocraticdonorsaffectsdonationstoaRe- pendent reinforcement. We first analyse whether dona- publican candidate and vice versa. Finally, we examine tion is more likely when exposed to donors by studying whetherthemicroleveleffectcanbeextrapolatedtothe the effect of the donor degree. We then compare this to macrolevelbyusingthenetworkstructuretopredictthe theeffectofthenumberofindependentdonors. Thisen- total amount of money raised. We report results for the tails comparing the effect of the (common community) presidential election cycle of 2008 (January 1, 2007 to donor degree to the effect of donor communities and December 31, 2008) for the Republican and Democratic source diversity. We first study this question by report- candidateinthemainpaper. Resultsforothercampaigns ing the immediate effects of exposure. However, these andfordonationstotheDemocraticandRepublicanNa- effects may be biased due to homophily—as we will ex- tional Committees can be found in Appendix B. plain later—and we therefore check our findings by con- trolling for previous donations. Finally, we corroborate our results using logistic regression in order to consider II. RESULTS all factors simultaneously. The probability to donate in the next quarter clearly We use data gathered by LittleSis, a website that depends on the donor degree (Fig. 3(a)). A person ex- tracksUSelites,forconstructinganetworkbetweenelites posedtoasingledonoris1.7timesmorelikelytodonate (see Appendix A). We construct the elite network based than a person not exposed to any donor (χ2 = 71.6, on direct family, professional and social relations (which p = 2.68 10 17 for Democrats, results for Republi- − × constitute only a small fraction of relations), and indi- cans are comparable). The marginal effect of exposure 3 much stronger effects. Exposure to a single donor com- munity makes donation 2.27 times more likely (χ2 = 320.5,p=1.15 10 71). Anadditionaldonorcommunity Common community makesdonation×2.2−3timesmorelikelyagain(χ2 =244.9, donor degree (2) p=3.45 10 55, Fig. 3(c)). The marginal effect dimin- − × ishes: three donor communities make donation only 1.56 times more likely (χ2 = 32.3, p = 1.32 10 8), still − × high compared to the effect of donor degree. Overall, the probability to donate after exposure to two donor communities is of the same order as the maximum effect of donor degree (either overall or common community). Indeed, when controlling for donor communities, donor degree shows no significant effect. Independence mea- sured in terms of source diversity shows even stronger Donor communities (3) effects(Fig.3(d)). Exposuretoasingletypeofsourcein- creasesthelikelihoodofdonation2.56times(χ2 =467.2, Donor degree (4) p=1.31 10 103). Asecondtypeofsourceincreasesthe − likelihood×of donation a further 2.77 times (χ2 = 404.2, p = 6.57 10 90). While exposure from a third type − × of source increases the likelihood of donation again 2.19 times (χ2 = 37.8, p = 7.92 10 10), the effect weak- − × ensthereafter. Inshort, thereisevidenceofindependent reinforcement. One of the notorious problems of studying social con- tagion is the problem of homophily [46]. People with similar preferences are more likely to be connected [47], so that exposure to donors does not necessarily causally affect donation, but may simply reflect an underlying similarity in preferences. Such homophilic links may Fig. 1. Network neighbourhood example. The fo- have consequences for how phenomena diffuse over net- cal node in the centre (square) is related to all the other works[48–51]. Homophilycanalsocreateaselectionbias nodes (shown in light lines), who may be connected to each (treatment bias) as exposure to donors also depends on other (shown in dark lines). The neighbourhood can be di- underlying preferences, meaning that donors are more vided into communities (shown in shades of green). Filled likely to be exposed to other donors [46]. This problem nodeshavedonated,andthefocalnodeissurroundedbyfour haspreviouslybeenaddressedbyresortingtopropensity donors, who are in three different communities, with a max- matching methods [46]. While it is impossible to com- imum of two nodes from the same community. The central pletely resolve the confounding of homophily and social question is whether contagion of donation is driven by co- contagioninobservationalstudies[52],contagiouseffects hesive reinforcement—in which case the common community donor degree should have a large effect—or by independent have also been documented in experimental studies [53]. reinforcement—in which case the donor communities should The single best indicator of the underlying preference have a large effect. for donating to a particular campaign is whether that person has previously donated to other Democratic or Republican candidates (Fig. 3(e)). Note that campaigns tomoredonorsdecreases: exposuretotwodonorsmakes often use previous donations to target likely donors [54], donation1.23timesmorelikelythanexposuretoasingle so that controlling for previous donations effectively also donor(χ2 =7.2, p=0.0072); exposuretofurtherdonors controls for selective targeting by campaigns. Previous shows diminishing returns. There is hence a clear effect donation makes it more than 17 times more likely to do- of increasing exposure to donors. The marginal effect is nate again (χ2 = 7801, p 0). We use this measure to ≈ slightlystrongerinthecommoncommunitydonordegree control for homophily. We cannot rule out other hidden (Fig. 3(b)), where exposure to a single donor makes do- homophilythatmightexplainanyremainingnetworkef- nation 1.8 times more likely than exposure to no donors fects [52]. While other relevant co-variates are available (χ2 = 101.8, p = 6.07 10 24). People exposed to two in the data (e.g. date of birth, gender, net worth), they − × donors from the same community are in turn 1.3 times have not been as extensively coded, limiting their use- aslikelytodonatethanpeopleexposedtoasingledonor fulness as control variables. Nevertheless, observing an (χ2 =13.2, p=0.00029). The effect size of the common identicalphenomenon(donationtoapoliticalcandidate) communitydonordegreeisonlyslightlystronger,making isastrongindicatorthatshouldaccountbetterthanany the case for cohesive reinforcement not very strong. other measure for the effects of homophily on donation. The measures for independent reinforcement show If we still see an effect of exposure to other donors af- 4 300 a John McCain 200 Barack Obama 100 s or 0 n o D o. 8,000 b N Elected 6,000 Nominated Presumptivenominee 4,000 Supertuesday Iowa Announces Nominated 2,000 Announces Presumptivenominee 0 Jan Apr Jul Oct Jan Apr Jul Oct 2007 2008 Fig.2. Donor dynamics. Dailydonordynamics(a)areaffectedbyFECdeadlines(rawdataistransparent,smootheddata solid). The cumulative number of donors (b) shows the overall growth. John McCain Barack Obama 10 2 12 ·a − * ** † * b ********* * † † † † 0 y 0 1 2 3 4 5 0 1 2 3 4 5 t bili Degree Common community degree a b 10 2 pro 6 ·c − d † e n 5 o ** ati 4 ** † n † o 3 † D † † † 2 † † 1 † † † † 0 0 1 2 3 4 5 0 1 2 3 No Yes Communities Source diversity Donated previously χ2-testofconsecutivedifference: ∗p<0.05,∗∗p<0.01,∗∗∗p<0.001,†p<0.0001 Fig. 3. Contagion effects. The probability to donate based on (a) donor degree, (b) common community donor degree, (c) donor communities, (d) source diversity and (e) previous donation. ter controlling for previous donations—which is such a (χ2 = 10.3, p = 0.0013), and only 1.35 times for old strong predictor—then this strengthens the hypothesis donors (χ2 = 18.4, p = 1.76 10 5). An additional ex- − × of social contagion. posureincreasesthelikelihoodofdonationafurther1.43 times for new donors (χ2 = 4.65, p = 0.031); for old Weseparatetheeffectsofdonordegreeanddonorcom- donors, additional exposure does not increase the prob- munities by previous donation (Fig. 4). Overall, dona- ability of donation further. The effect is clearly stronger tion is much more likely from old donors (those who for new donors than for old donors. The effect of inde- have previously donated) than from new donors (those pendent reinforcement is again much stronger, although who have not), as said earlier. Exposure to a single asimilardifferencebetweenoldandnewdonorsisappar- donor increases the likelihood 1.53 times for new donors 5 ent. For new donors, the likelihood of donation is 2.24 Cross-cutting exposure timeshigherforasinglecommunityexposure(χ2 =73.4, p = 1.04 10 17), while for old donors this is only 1.58 − In the previous section, we found that exposure to (χ2 =76.×05,2.77 10 18). Anadditionalcommunityex- − Democratic donors makes donation to the Democratic × posure for new donors makes donation 3.01 times more candidate much more likely (and similarly so for Repub- likely (χ2 = 111.9, p = 3.80 10 26), while for old − licans), especially for new donors that are exposed to donorsdonationisonly1.04time×smorelikely(χ2 =0.42, multiple independent donors. It is possible that dona- p=0.52). tionisalsoaffectedbytheamountofsupportfortheop- posing party. For example, if somebody is equally much exposed to Democratic and Republican donors, it might Logistic regression confirms that donor communities puthimorherinaratherdifficultposition: should(s)he havethestrongesteffect,andthattheeffectsarestronger support the Democratic or the Republican candidate? for new donors than for old donors (Fig. 5, Tables S1 One possibility is that (s)he donates to neither, to pre- and S2). We also control for overall degree (i.e. not only vent possible conflicts, which was found to be the case including donors), which has a slightly negative effect for voting [40]. In this section we analyse the effects of (θ = 0.0040, t= 11.7, p=1.40 10 31) and cluster- thisso-calledcross-cuttingexposuretothe“other”party − − − × ing of a node, which has a somewhat stronger negative (i.e. the effect of Democratic exposure on Republican effect (θ = 0.55, t = 7.95, p = 1.93 10 15). Hence, donations and vice-versa). − − − × hubs and brokers are less likely to donate overall. When Cross-cutting exposure has a counter-intuitive effect. controlled for all other variables, donor degree actually If there are relatively more Democrats (taking the dif- slightlydecreasesthechancesofdonationforanewdonor ference between the number of Democrats and Republi- (θ = 0.032,t= 2.00,p=0.046),buttheeffectisposi- cans), this not only increases the likelihood of donations − − tiveforolddonors(θ =0.015,t=2.12,p=0.034). Com- to the Democratic candidate, but also to the Republican mon community donor degree does have a positive effect candidate(Fig.6). ExposuretoonemoreDemocratthan on new donors (θ = 0.098, t = 5.40, p = 6.63 10−8) Republican donor increases the likelihood of donations manudltoipldlyidnognothrse(oθd=ds0o.f03d3o,ntat=ion4.0a4b,oupt=1.51.041ti×m×e1s0−a5n)d, WtohRileepuRbelpicuabnlsic1a.n28dtoinmaetsio(nχs2c=on1ti1n.2u,epto=i8n.c3r9ea×se10w−i4t)h. 1.03timesforeachadditionalcommoncommunitydonor further exposure to Democratic donors, none of the re- degree. Donor communities have a much stronger effect mainingconsecutivedifferencesaresignificant. Theeffect on new donors (θ = 0.67, t = 8.55, p = 1.24 10−17), ofrelativelymoreexposuretoRepublicandonorsremains × increasing the odds of donation 1.95 times for each ad- greater,withasingleexposuremakingRepublicandona- ditional community, but have no significant effect on old tions1.46timesmorelikely(χ2 =28.2,p=1.09 10 7). − donors (p = 0.38). Finally, source diversity has no sig- Theeffectseemslesspronouncedfortherelative×number nificant effect for new donors (p = 0.61), but does have of communities in this analysis. a clear positive effect on old donors (θ = 0.33, t = 6.19, However, logistic regression shows that exposure to p = 6.03 10−10), increasing the odds of donation 1.39 Democratic donor communities increases the odds of do- × times. The strongest effect clearly remains previous do- nation to a Republican candidate (θ = 0.62, t = 2.73, nation (θ = 3.13, t = 41.05, p 0), increasing the odds p = 0.0063), and that none of the other Democratic ex- ≈ 23 times. posure measures are significant (Fig. 7). In fact, the effect of Democratic donor communities is higher than RepublicandonorcommunitiesforRepublicandonations In conclusion, we find that the contagion of donation (θ = 0.39, t = 1.47, p = 0.14). The inverse is not ismostlydrivenbyindependentreinforcementcontagion. significant—exposure to Republican communities does For new donors, the number of communities has a much notincreasedonationtotheDemocraticcandidatesignif- largereffectthandonordegree(eitheroverallorcommu- icantly. For Democratic donations, the interaction of ex- nity degree). Donations in their neighbourhood increase posuretoDemocraticandRepublicancommunitydonors the likelihood of donation, especially when the previous is 0.15(t= 2.10,p=0.036),butthisisnotsignificant − − donorscomefromdifferentsocialgroups. Forolddonors, forRepublicandonations(p=0.13). Similarly,theinter- the effects are typically much weaker or even insignifi- action of Democratic and Republican common commu- cant. Their decision to donate is largely independent of nity donor degree has a slight negative effect on Demo- donations in their neighbourhood. The presidential elec- cratic donations (θ = 0.0031, t = 2.51 p = 0.012), − − tion campaign of 2008 discussed here shows the clear- which is again not significant for Republican donations. est effects, perhaps related to the unexpected success of This implies that when simultaneously exposed to both BarackObama. Resultsforotherelectioncyclesof2000, Republicans and Democrats, Democratic donations may 2004 and 2012 and for party donations—to the Demo- become less likely, in line with previous results [40], but cratic National Committee (DNC) or Republican Na- this is not the case for Republican donations. tional Committee (RNC)—are qualitatively similar (see Interestingly,effectsofcross-cuttingexposurevaryper Figs. S1–S8 and Tables S1–S8 in Appendix B). campaign. For example, while Republican donations 6 John McCain Barack Obama 10 3 − · 14 a b 12 10 o 8 N † 6 * usly bility 24 ** * ** † † *** o a 0 vi b e o 0 1 2 3 4 5 0 1 2 3 4 5 r r p p d n e o 10 2 Donat Donati 67 ·c − d ** 5 *** * 4 † es *** † † Y 3 2 1 0 0 1 2 3 4 5 0 1 2 3 4 5 Degree Communities χ2-testofconsecutivedifference: ∗p<0.05,∗∗p<0.01,∗∗∗p<0.001,†p<0.0001 Fig. 4. Conditional donation probability. Donation conditional on previous donation differs for (a,c) donor degree and (b,d) donor communities, with the effects for new donors being larger. were more likely after exposure to Democratic donors try to predict the total amount of money w raised in a i in the 2008 election, the reverse was true in 2004: ex- certain election cycle for any candidate (including sen- posure to Republican donors triggered Democratic do- atorial, congressional and presidential elections) based nations (Figs. S3 and S4). Another example, in the on the first quarter (Fig. 8) The total amount of money 2012election, anycommunityexposure(eithertoDemo- raised throughout the campaign largely depends on the craticorRepublicandonors)ledtoRepublicanpartydo- amount of money raised in the first quarter w (1), and i nations and neither had an impact on Democratic do- we find that wˆ = αw (1)β predicts w fairly well with i i i nations (Figs. S7 and S8). See Appendix B for further α=32.1 4.2andβ =0.90 0.0086. Takingintoaccount ± ± details on cross-cutting effects for other election cycles. thenumberofcommunitiesthathavedonatedinthefirst This may suggest that such cross-cutting exposure may quarter c (1) as wˆ =αw (1)βc (1)γ with α=21.6 3.7, i i i i ± betriggeredbyspecificdynamicsofsomecampaigns. We β =0.81 0.015, and γ =0.42 0.070 slightly improves ± ± briefly discuss this further in Section III. the fit, and is clearly favoured (∆AIC = 30.32). The number of donors itself has no significant effect and ac- tually degrades the fit, clearly favouring the model using the number of communities. Both β and γ < 1, so that B. Overall campaign additional donations and independent donors yield di- minishing returns. Every doubling of the amount raised We have seen that, at a micro level, when somebody inthefirstquartermultipliesthetotalamountbyroughly is exposed to multiple independent donors, (s)he is more 1.75. Doubling the initial number of communities multi- likelytodonate. Thismicroeffectcanpossiblyalsohave plies the total amount by about 1.34, while doubling the network wide repercussions at a macro level. We may initial number of donors has no significant effect. This expect that the total extent of the diffusion is greater if small exercise demonstrates that the effect of indepen- people from different communities have donated than if dent donors not only holds at the micro level, but can equally many people have donated from the same com- also be extrapolated to the macro level. munity. We here briefly investigate whether this extrap- olation of the micro effect to the macro level holds. Following the extrapolation, the number of communi- ties that donate at some point should be indicative of the amount of money raised afterwards. To test this, we 7 John McCain Barack Obama General Degree a 0.0016 −0.004 − Clustering 0.22 0.55− − Not donated previously Donor degree b 0.042 −0.032 − Donor communities 0.43 0.67 Donor source diversity 0.25 0.057 Donors common community 0.068 0.098 Donated previously c Donated previously 3.5 3.1 Donor degree 0.002 0.015 Donor communities 0.14 0.035 Donor source diversity 0.17 0.33 Donors common community 0.024 0.033 1 0 1 2 3 − Effect Fig. 5. Logistic regression results. Magnitude of (a) general effects, (b) network effects for new donors, and (c) network effects for old donors. Error bars show 95% confidence intervals for the coefficients. III. DISCUSSION We theorize that people infer population-wide be- haviour by observing their local networks. Such local observationsarenecessarilybiased,astheyareinfluenced Wefindthatpoliticalcampaigndonationsamongelite byhomophilyandotherselectioneffects. Onereasonable are socially contagious. Being exposed to other donors heuristic for trying to surmount such bias would be to increaseschancesofdonationsignificantly,alsoaftercon- onlyuseobservationsthatareasindependentaspossible. trolling for previous donations. Contagion is especially Whenever ego knows two observations are not indepen- likely after multiple exposures from different communi- dent, (s)he only counts them as one [38]; (s)he discards tiesorfromdifferenttypesofsources(e.g. family,friends, redundant observations. Alternatively, if two persons of business partners). This supports the idea of indepen- the same background show the same behaviour, people dent reinforcement of complex social contagions. attribute it to those particular characteristics or group Our results show that having a multiplex view of a membership[55], whereasiftwopeopleactthesamebut network may be important for understanding the diffu- haveverydifferentbackgrounds,peopleattributethebe- sion process. In particular, the perceived independence haviourtoitspopularity. Stateddifferently: peopleinfer ofpeoplemaybedifficulttoasseswithoutdistinguishing that the TV show The Big Bang Theory is widely popu- different types of links. Some of this information may lar when not only their geek friends watch it, but when also be contained in the “flat” network (where we disre- friends from all backgrounds watch it. It would be inter- gardthetypeofalink)dependingonhowthestructureis esting to further examine this hypothesis of attribution correlatedbetweendifferentmultiplexlayers. Ifthereisa bias[56]. Thisisconsistentwiththeideaofthe“majority positive correlation between two layers, a single commu- illusion”, generalizing local observations to population- nity in the flat network may consist of multiple types of wide estimates leading to a locality bias [57]. links, while if this correlation is negative, different types It is well known that viability of candidates plays a of links are likely to be contained within different com- majorroleincampaigndonations[58–60]. Campaigndo- munities. The latter seems to be the case for the Little- nationsplayanespeciallyimportantroleduringprimary Sis data, where only about 3000 links out of more than nominations [61, 62], as do (party) elites more gener- 1.6 million links are of more than one type, explaining ally[63]. Whenacandidate’ssuccessseemsoutofreach, the congruency between community degree and different people are reluctant to donate. After all, supporting a types of sources. (guaranteed) losing candidate simply squanders money, 8 John McCain Barack Obama 10 3 25 · − a 20 ** *** 15 ** * * 10 *** † *** *** † 5 0 5 4 3 2 1 0 1 2 3 4 5 Democrat Republican ∆ Degree 10 2 10 · − b 8 6 4 † † 2 ** † † † † 0 5 4 3 2 1 0 1 2 3 4 5 Democrat Republican ∆ Communities χ2-testofconsecutivedifference: ∗p<0.05,∗∗p<0.01,∗∗∗p<0.001,†p<0.0001 Fig.6. Cross-cutting donation probability. Cross-cuttingdonationprobabilityby(a)degreeand(b)communitiesshows that exposure to one side can increase donations to the other side. whichcouldbeallocatedtoamoreviablecandidate. Us- be costly, thereby making cohesive reinforcement more ingindependentobservationstoinfertheviabilityofcan- likely. Whilecascadesofcooperationhavebeenobserved didates seems a good heuristic, especially early on in the totakeplaceinexperimentalstudiesofpublicgoods[66– campaignwhencandidatesarenotyetwidelyknown. We 69],itisanopenquestionwhethersucheffectsaredriven theorizethatindependentreinforcementisespeciallyrel- by cohesive or independent reinforcement contagion. evant for campaign donations to assess viability. Alternatively, if a network externality depends not on Moregenerallyspeaking,wehypothesizethatcomplex the number of people, but on the connections between contagion with independent reinforcement is especially them, we may expect cohesive reinforcement. Take the likely with population-wide network externalities—if the mundane example of hanging out at a bar with friends. value of the behaviour depends on the number of people Thejoyofsuchanactivitydependsnotonthenumberof showing such behaviour [64]. A previous study of conta- friendsitself,butonwhetherthosefriendsalsoknoweach gion in signing up to Facebook reported similar results otherandenjoyspendingtimewitheachother. Similarly, to our own [28]; a clear case of behaviour with network teamperformancemaynotdependsomuchonthenum- externalities—using a social network site is only useful if ber of people, but on how they are connected [70, 71], enough other people use it. Cases where network exter- favouring cohesive reinforcement. nalities are present are abundant, ranging from commu- Inferring population-wide estimates from local obser- nication devices and services to file formats and techni- vations may not only have positive contagious effects. cal standards [65]. In such situations we expect complex Knowing that sufficient people are already contributing contagions to be driven by independent reinforcement. to a public good may make it less likely for people to However, not all network externalities necessarily lead contribute themselves [68, 69]. When estimates of con- to independent reinforcement. For example, in the pres- tribution to a public good are derived from local esti- ence of a public goods dilemma or a collective action mates, we may see a negative contagion effect. In our problem, we may expect cohesive reinforcement rather case,thiscouldexplainthecounter-intuitivefindingthat than independent reinforcement. If two alters are un- exposure to one side can trigger donations to the other related (such that ego is the broker between these two side. Here, people could deem it necessary to rally sup- alters), this may make coordination between the three port for their candidate of choice because they observe more difficult; when the alters do know each other, it too much support for the opponent. In the 2004 cam- may facilitate communication and thereby agreement paign, when George W. Bush was seeking re-election, on a common course of action. Especially when the potential Democratic donors may have been reacting to stakes are high, failing to coordinate an action can exposure to donations to Bush to oppose his candidacy. 9 John McCain Donatedpreviously Barack Obama No Yes Degree a b Republican Democrat Interaction CommonCommunity c d Republican Democrat Interaction Communities e f Republican Democrat Interaction SourceDiversity g h Republican Democrat Interaction 0.5 0 0.5 0.5 0 0.5 − − Effect Effect Fig. 7. Logistic regression results for cross-cutting effects. Effect sizes for cross-cutting exposure distinguished by old/new donors for (a)–(b) donor degree, (c)–(d) common community donor degree, (e)–(f) donor communities, and (g)–(h) source diversity. Error bars show 95% confidence intervals for the coefficients. Similarly in the 2008 campaign, potential Republican dantanddonotreinforcecontagion. Incontrasttocohe- donors may have wanted to oppose Obama’s election. sive reinforcement, independent reinforcement may per- More generally speaking, people may react to their local meate group boundaries. Depending on the type of con- estimate of population-wide behaviour rather than the tagion and the type of network, we may expect different actual population-wide behaviour. dynamics, which should be explored further. Ourfindingsmayalsohaveimplicationsforrecommen- Finally, as we stated at the outset, money is vital to dation systems in online social networks [72]. It may be anypoliticalcampaignintheUS.Raisingmoneyisacru- morerelevantwhatstoryorproductislikedorboughtby cial short-term goal in order to further the end goal of manyindependentfriendsthanbyfriendsfromthesame getting elected. Our findings suggest that appealing to socialgroup. Thisisalsowhattheresultsofthestudyon constituencies of diverse backgrounds may actually aid joining Facebook suggests [28]: the adoption of the ser- in diffusing support through networks. Moreover, the vice depends on the number of independent friends that numberofcommunitiesthathavedonatedissignificantly have joined Facebook. However, this may depend on the predictive of total fund-raising capabilities, whereas the type of product which is recommended. number of donors is not. The number of communities The two different modes of complex contagion also af- was also found to be predictive of the virality of online fect the speed of the spreading process on networks [23, memes [74]. While this is congruent with the idea that 73]. Independentreinforcementhasarelativelyslowand independent reinforcement takes place on the network, steady rate of diffusion in clustered networks, as addi- it could also indicate the candidate’s more widespread tional contagions in the local neighbourhood are redun- appeal—bothinterpretationssupportthestrategyoftar- 10 Data Model amount Model communities 108 a b 107 nt 106 u o m A 105 al t To 104 103 102 102 103 104 105 106 107 100 101 102 Amount Q1 No. communities Q1 Fig. 8. Predicting total campaign contributions. We predict the total amount donated throughout the campaign based on donations in the first quarter only. Line shows average and the shade shows the 5% and 95% percentiles. geting people in communities that have not yet donated. fect overall because donations are more likely to spread, Doublingtheamountofmoneyraisedbutonlytargeting even though fewer may immediately assent to the re- the same communities only multiplies the total amount quest. We consider this a hopeful sign, suggesting that by about 1.75, while doubling the number of communi- rather than addressing narrow interests and petty con- ties at the same time more than doubles the amount of cerns,politiciansshouldappealtothegeneralpopulation money, resulting in a super-linear scaling. Contagious and the greater good. effects may multiply the efforts of fund-raising, and they should be taken into account. This suggests a (perhaps counter-intuitive) change to fund-raising strategy, sug- ACKNOWLEDGMENTS gested earlier in a study on soliciting donations [8]: it may be more effective to target people who are rela- tively difficult to recruit, rather than the easy picks. Al- This work is supported by the Royal Netherlands though targeting likely donors may seem to have greater AcademyofArtsandSciences(KNAW)throughitseHu- directeffectswithrelativelymorepeopleassentingtothe manities project. 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