Endogenous group formation and responsibility diffusion : an experimental study

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Contents lists available atScienceDirect

Games

and

Economic

Behavior

www.elsevier.com/locate/geb

Endogenous

group

formation

and

responsibility

diffusion:

An experimental

study

✩

Katharina Brütt

a

,

∗

,

Arthur Schram

a

,

b

,

Joep Sonnemans

a

a_CREED,_University_of_Amsterdam,_P.O._Box_15867,₁₀₀₁_NJ_Amsterdam,_the_Netherlands

b_Department_of_Economics,_EUI,_San_Domenico_di_Fiesole,_Italy

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received20June2019

Availableonline13February2020

JELclassiﬁcation:

C92 D64 D71

Keywords:

Endogenousgroupformation

Diffusionofresponsibility

Groupdecisions

Self-selection Socialpreferences

Westudy theeffectsofvaryingindividualpivotalityandendogenousgroupentryonthe selfishnessofgroupdecisions.Selfishchoicesbygroupsareoftenlinkedtothepossibility of diffusing responsibility; the moral costs of these decisions appear smaller when individualpivotalityisreduced.Ourexperimentaldesignexploresunanimityvotingunder distinctdefaultstoidentifythiseffect.Inexogenouslyformedgroupswefindevidenceof responsibilitydiffusion,butthisdiminisheswithrepetition.Ourresultsalsodemonstrate the role of self-selection in generating differences in group behaviour depending on individual pivotality. Driven by a heterogeneous selection pattern, endogenous group formation amplifies the effectsof achange inpivotality. Some people activelyseek an environment to diffuse responsibility, while others join groups to promote pro-social behaviour.

1. Introduction

Thispaperrevisitstheroleofresponsibilitydiffusionasanexplanationofwhygroupsmakemoreselﬁshdecisionsthan individuals. Italsoexploreshowendogenousgroup formationaffectsthedegreeto whichgroupdecisionmaking induces selﬁshbehaviourandwhethergroupentryisexploitedasatooltodiffuseresponsibility.

Theliterature inbehaviouraleconomicshasestablishedthat decisionsbyexogenously formedgroupsoftendifferfrom those madeby individualsfacing the same environment. Foroverviews, see Charness andSutter (2012) or Kugleret al. (2012). Inmanycircumstances,group decisionsmorecloselyfollowstandard economictheory andaremoreselﬁsh com-pared to individual decisions. Examples includeSchopler et al.(1995) for prisoner-dilemma games, Bornstein and Yaniv (1998) forultimatumgamesandLuhanetal.(2009) indictatorgames.1 _In_search_of_an_explanation_for_this_phenomenon,

themorerecentliteratureexamines theroleofindividual responsibilityforimmoralgroup actions.Individualsinagroup collectivelysharetheresponsibility,whichistherebydiffused.ThisistheoreticallystudiedbyforinstanceRothenhäusleret al.(2018) andexperimentallyinBehnketal.(2017) andFalketal.(2020).Ifindividualsdonotexpecttobepivotaldecision

✩ _We_thank_Gary_Charness,_Martin_Kocher _and_Joël_van_der_Weele_for_their_valuable_suggestions_and_participants_at_the _CCC-meeting_(University_of

Amsterdam),theM-BEPS(MaastrichtUniversity)andtheEuropeanESAMeeting(BurgundySchoolofBusiness)fortheirhelpfulcomments.Wegratefully

acknowledge ﬁnancialsupport ofthe ResearchPriority AreaBehavioral Economicsof theUniversity ofAmsterdamand NWO Research TalentGrant

406.18.501.

*

Correspondingauthor.

E-mailaddresses:K.Brutt@uva.nl(K. Brütt),

A.J.H.C.Schram@uva.nl

(A. Schram),

J.H.Sonnemans@uva.nl

(J. Sonnemans).

1 _Cason_and_Mui₍₁₉₉₇_),_however,_observe_the_opposite_for_dictator_games,_with_groups_acting_less_selﬁshly_than_individuals. https://doi.org/10.1016/j.geb.2020.02.003

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makers, thisallowsevery actortobelievethat they arenotfullyresponsible forthe ﬁnaloutcome ofthegroup decision-making process.Thisreducesincentivestoact pro-sociallyortoact inaccordancewitha costlymoralnorm.Ina related phenomenon, increasing the numberofbystanderswitnessing anemergency makes anysingle bystander lessinclined to help,sinceindividualsfeellessresponsible(DarleyandLatané,1968;LatanéandDarley,1968).

While there isa large strandofliterature that compares the choicesofindividual decisionsto group decisionsin ex-ogenouslyformed groups,littleisknownabouthowthesechoiceswouldcomparetoan environmentwherethegroup is allowed toformendogenously.Theliterature therebyneglectstheobviousfactthatgroupsareevolvingentities,which,in naturally occurringsituations,oftenformvoluntarily. Fromboardsoverseeingﬁrms’activities andpoliticalcommittees de-terminingaparty’spolicytofamiliesthatjointlymakehouseholddecisions,groupdecisionmakingisubiquitous,butoften achoiceinitself.Somepeoplemightsimplyprefertomakecertaindecisionsinteams.

Ourexplorationstartswithstudyingwhetherconclusionsaboutselfishbehaviourin(exogenouslyformed)groupscarry over to an environment with endogenousgroup formation. Moreover, ifgroup decisionmaking facilitates selfish choices by reducingthedisutility subjectsexperienceduetotheresponsibility theybear,doindividualsanticipatethis?Doesthis make individualsprefergroup decisionmaking?Manystudiesemphasise theeffectsofso-called‘moral wiggleroom’, in-troducedinitiallybyDanaetal.(2007).Thisreferstothepossibilityofreducingindividualmoralbehaviourbyblurringthe relationshipbetweenactionsandconsequences.Becausegroupdecisionmakingmaybeseenasofferingsuchwiggleroom, we wanttoinvestigatewhetherindividualsactively seizesuchopportunitiesbyjoiningagroup.Ifthisisthecase,athird questionarises,aboutwho seizestheseopportunities.Consideracontextthatinvolvesatrade-offbetweenownandothers’ wellbeing.Canweexpectaselectioneffectwhenthereisvoluntarygroupmembership?Thatis,will‘selfish’individuals– those benefittingfroma reductionintheirresponsibility–disproportionatelyjoingroups?Thiswouldimplythat endoge-nouslyformedgroupsmake(even)moreselfishdecisionsthanthoseformedexogenously.Thestudyofexogenouslyformed groupswouldthen,infact,underestimatethetrueextentofselfishbehaviourbygroups.

To study how responsibility diffusion can serve asa determinantof group entry, a novel experimental design is in-troduced. Thisadoptsa simplebinary dictatorgame withapro-socialanda selﬁshoption.The gameisplayed by either individuals orgroups ofthree players. We distinguishbetween groupsthat are exogenously formed andgroupsthat are endogenously formed. Endogenously formed groups are composed of individuals statinga preference for group decision makingoverindividualdecisionmaking.

Ourdesignfocusesononecentraldimensionofresponsibilitydiffusion,whichisareductionofindividualpivotalityina groupdecision.Theideaisthatonedoesnotbearthefullresponsibilityofacollectiveactionifone’sindividualvoteisnot decisiveintheimplementationofthataction.Wewilltake thedistanceto beingpivotal(Engl,2018)asameasureofthe extentofthisdecisiveness.Inshort,thismeansthatan agentisdeemedlessresponsibleforagroupchoiceifmorevotes needtochangetomakehervotepivotalintheimplementationofaselfishoutcome.Thismeasurecaptureshowaspartof agroup,one’svotemaynotbeinfluentialintheimplementationofacertaindecision.Ifoneweretochangeone’svote,this wouldthennotaffecttheoutcomeofthegroupdecision-makingprocess.Anexampleofthisisvotinginpoliticalelections. Every individualonlybearsa smallfractionofresponsibility forthe outcomeofan electionandisusually farfrombeing pivotal.Theeffectofresponsibilitydiffusion,however,islikelytobeasymmetric,whichwearegoingtoassumethroughout thispaper.Agentsonlywanttodiffusetheirresponsibilityfortheimplementationofaselfishdecision,notforapro-social one.Giventhisasymmetriceffect,weonlyconsidertheeffectofbeingpivotalfortheimplementationofaselfishoutcome. We isolatethiseffectof beingpivotalforthe implementationofa selfishallocation byrequiringunanimous decisions and varying the default option in case of non-unanimity. With a pro-social default, the group decision-making process excludesthepossibilityofdiffusionofresponsibility.Theselfishoutcomeisonlyimplementedifthisisunanimouslyagreed upon, resultingin everyone’svotebeingpivotalandeveryone bearingthe fullresponsibility. In contrast,aselfish default facilitatesdiffusionofresponsibility,sinceonlyoneindividualisrequiredtovoteinsupportoftheselfishoutcomeforthis to be realised.Ifatleastoneadditional individualvotesinfavour oftheselfish outcome,theagent isnot pivotalforthe realisedoutcome.Thisdefaultthenreducestheindividualprobabilityofbeingpivotalforthisselfishoutcomeandtherefore individualresponsibilityforthisallocation.2

In thisway,thisdesign allows ustoisolate theeffects ofchanging pivotalityforselfish outcomeson groupdecisions andto study howthiseffect isinfluencedby selection duetoendogenousgroup entry.3 Diffusion ofresponsibility likely hasmultipledimensions.Notethatwe areinterestedinadimensionofresponsibilitydiffusionthatgoesbeyondafeeling ofshared guilt.Accordingto ourunderstandingofsharedguilt, anindividual’sdisutility fromcausinga harmfuloutcome diminishes purely becausethisisdonetogether withothers.Inthiscase,the decisionmakers sharetheburdenofacting selfishly so the guilt is shared. Sharedguilt is then unrelated to an individual’sown impact on the group decision. Our design holdsguiltsharingconstant. Incontrast,the dimensionofresponsibilitydiffusionwe examineisdirectlylinkedto a person’s individual impact on the decision. In thecases we study, thepresence of other decisionmakers reduces this individual impactwhenthereisaselfishdefault, butnotwhenthereisapro-socialdefault.Guiltissharedirrespectiveof thedefault.

2 _We_abstract_from_social-image_concerns_here._In_the_discussion_of_Result

₂

_,_we_will_address_why_these_concerns_do_not_seem_to_be_an_important_force here.

3 _Below,_we_discuss_an_additional_selection_effect._A_pro-social_default_allows_group_members_to_force_a_pro-social_outcome,_irrespective_of_their_group members’votes.Thisisnotpossiblewithaselﬁshdefault.Thus,apro-socialdefaultmayattractindividualsthatwishtopromotepro-sociality.

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Toprovide a benchmark forbehaviour observed in the experiment, we employ a simple categorisationof individuals basedontheir degreeofresponsibilityaversion.Thispredictsdifferencesinselectionandvotingbehaviour.Fromthis, we derivehypothesesabouttheinﬂuenceofresponsibilityaversiononselectionbehaviouranddecisionsinendogenouslyand exogenouslyformedgroups. Asweobservebehaviourinrepeatedchoices, ourexperimentcanalsospeaktotheeffectsof responsibilitydiffusiononcesubjectsdevelopexperiencewiththeirdecisionenvironment.

Our experimental data provide strong evidence forthe importance of the group formation process. For exogenously formed groups, we find evidence that the diffusion of responsibility generates selfish choices in initial periods. This ef-fectdiminisheswithrepetition,whichcontrastswithargumentsputforwardintheprevious literature.Withendogenously formed groups, ontheother hand,there are strikingdifferencesthroughoutthe courseofthe experimentbetween envi-ronmentswhereresponsibilitycanbediffusedandthosewhereitcannot.Iftheselfishchoicerepresentsthedefault,more subjectsvoteselfishlythanifthepro-socialoptionservesasadefault.Ourdesignallowsustoattributethiseffectdirectlyto thefactthatgroupparticipationisvoluntary.Tounderstandgroupdecisionmaking,boththepossibilitytoreduceindividual responsibilityforselfishactionsandagroup’sformationprocessshouldthereforebetakenintoaccount.

We continue andexamine the role ofself-selection ofindividuals into groups withspecific defaults. First, we detect differencesacrosstypesin theimpactof aselfish defaulton selectiondecisions.More specifically,we confirm thattypes whovoteselfishlyifresponsibilitydiffusionfacilitatesthis,oftenseekresponsibilitydiffusioningroups.Inother words,a selfishgroupdefaulthasapositiveinfluenceonthepropensityofselfishindividualstojoinagroup.

Second,theexperimentalsoprovidesevidencethatindividualswho–regardlessofthetypeofdecisionmaking–choose thepro-socialalternative,entergroupsiftheycan guaranteethatthepro-socialoutcomeisimplemented.Thissuggestsa secondmotivedrivinggroupentry(asidefromseekingresponsibilitydiffusion).Wefindthiseffecttobestrongerandmore robustthantheselectioneffectofselfishtypes.Thisfindingisconsistentwiththesocialidentityliterature(e.g.Tajfel,1974). Ifapro-socialdefaultattractsgroupentryofpro-socials,thisallowsthemtoselectintoanenvironmentwithlike-minded individuals.Thisidentityeffectseemstobemorepronouncedforpro-socialsthanforselfishindividuals.

Finally,ourstudyallowsustodirectlycomparethedecisionsofindividualstogroupdecisionsinanenvironmentwhere groupsformvoluntarily.Asaresultofthedescribed self-selection,weﬁndthatdifferencesbetweengroupandindividual decisionsparticularlyemergeinenvironmentswithapro-socialgroupdefault.

Theremainder ofthispaperisorganisedasfollows:First, werelate thisstudy totheliterature insection 2.Next,we explain theexperimental designinsection3 andoutline thehypothesesto betestedinsection 4.Section5presentsthe results.Last,wewillconcludeandbrieﬂydiscusstheﬁndingsinsection6.

2. Relatedliterature

Thisstudyisattheintersectionofthree strandsofliteratureinbehaviouraleconomics;theliterature onresponsibility diffusionandguiltsharingingroups,theliteratureonendogenousgroupformation,andtheliteratureonsorting.

2.1. Responsibilitydiffusionandguiltsharing

Severalauthorshavestudiedhow responsibilitycanbe assignedtosingle actorsthat are partofacollective decision-making process andhow responsibility may be diffusedin groups. Recent theoretical contributions define andformalise theconceptofresponsibility. BartlingandFischbacher(2012) defineameasureofresponsibilitythatassigns toeachagent a degree of responsibilityfor the implementationof an allocation that dependson the impactof the individual’saction on its realisationprobability. Theydoso in thecontext ofdecision delegation.More closelyrelatedto ourframework is Engl(2018).Heinvestigateshowresponsibilitycanbeattributedifmultipleagentsareinvolvedinajointdecision-making process. He proposesto take the distanceto beingpivotalas ameasure of an individual agent’s(ex-post) responsibility. This isdefined asthe number ofchanges in individuals’ votes neededto generate a situationwhere thisagent’s choice can bedecisive inchangingthe outcome.We willapply thismeasure below.Finally,Rothenhäusler etal.(2018) develop amodeltoidentifythecausaleffectsofguiltsharingonmoraltransgressionwithheterogeneousmoralcosts.Despitethe similarities,sharedguiltdiffersintheirset-uptoournotionofresponsibilitydiffusionasitdependsontheabsolutenumber ofsupportersofimmoralbehaviour,independentofhowdecisiveanindividual’svoteis.

Asidefromthesetheoretical contributions,thereisexperimental workon responsibilityingroup decisions.Bartlinget al.(2015) issomewhatrelatedtoourresearch.Theystudytheimpactofpivotalityonresponsibilityattribution.Theauthors showinasequentialvotinggamethatvoterswhoarepivotalfortheimplementationofanunfairdistributionofresources arepunishedmoreharshlythannon-pivotalvoters.Ourexperimentdoesnotstudypunishment.Instead,ourdesignallows ustodirectly linkthedegree ofresponsibility tothe selﬁshnessofa decision. Furtherexperimental evidenceis obtained inalabourmarketsettingby Charness(2000,2004).Hisresultshighlightthat effortprovision inagift-exchangegameis adverselyaffectediftheresponsibilityfortheoutcomecanbeassignedtoothersortoanexternalprocess.Onceagain,this providesevidencefortheimportanceofresponsibilityattribution.

Closesttoourworkistheexperimental literaturethatstudies thediffusionofresponsibilityingroup decisionmaking. One such study is Dana etal. (2007), who compare decisions of individuals andtwo-person groups (pairs) in a binary dictator game. A pair only implements the selﬁsh outcome if both group members vote in favour of this option. As a consequence,bothindividualsinapairarepivotalforan unfairoutcome.Notethathereisnovariationinthedimension

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ofresponsibilitydiffusionweareinterestedin,whichislinkedtopivotality.WhileDanaetal.(2007) keepthepivotalityin caseofaselfishoutcomeconstant,thisisexactlywhatwewanttovaryandtheeffectwewanttoisolate.Yet,theauthors observethatpairsaresignificantlymoreselfishthanindividuals.

Similarly, Behnk et al. (2017) observe more selfish decisions by pairs than by individuals in sender-receiver games. However, pairscanonlysendadeceptivemessageifbothmembersagreetodoso.Thisimpliesthat everygroupmember ispivotalforsendingadeceptivemessage.AsinDanaetal.(2007),theresultssuggestthatthehigherselfishness inpairs istheresultofsharingguiltratherthanreducingpivotality.SelfishdecisionsbygroupsarealsoobservedbyIrlenbuschand Saxler(2019).Theyinvestigatethediffusionofresponsibilitybycomparingdecisionsbyindividualsandgroupstotradein amarketenvironmentwheretradecausesanegativeexternalitytoathirdparty.Otherthingsequal,groupsaremorelikely toengageinsuchtrade.Giventhevetopowerofanindividualgroupmember,anindividualvoteisagainpivotalingroups. All in all, group decisions tend to be less pro-social than individuals’ in these studies. Nevertheless, this cannot be attributedtoresponsibilitydiffusioninthesenseofreducingpivotality,butrathertosharedguiltduetothemerepresence ofanotherselfishdecider.Inall ofthesestudies,anindividual’svotecontributesjustasmuchtotheimplementationofa selfish actioninagroup asitdoesinindividualdecisionmaking.Thiswill holdforanyenvironment whereunanimityis required forthegroup tochoose selfishly.See Kocheretal.(2017) foran overviewofalternative explanations forselfish groupbehaviour.

Falk etal.(2020) study thediffusion ofresponsibilityin groupsinan original manner.Participants ingroups ofeight face the choice betweenreceiving money atthe cost ofvoting to kill eight mice orforegoing the monetary payoff and not votingto killthe mice. Agroup implementsthefirst optionassoonasone group membervotesto killthe mice. In contrasttothestudiesmentionedbefore,thismeansthatgroupmembersareunlikelytobepivotalforthedecisiontokill the mice(suchpivotality onlyoccurs ifallothers forgothemoney). Theresults show thatthe diffusionofresponsibility in groupchoicesresultsinsignificantlymoremicebeingkilled.Aninteresting observationinFalketal.(2020) isthatan individual’swillingnesstochoosetheselfishoptiondecreaseswiththeperceived likelihoodofbeingpivotal.Thissupports thehypothesisthatresponsibilitydiffusiondrivesdifferencesbetweenindividualandgroupdecisionshere.

Allinall,thisliteratureshowsthatgroupsmakemoreselfishdecisionsthanindividualsandthatareductionof respon-sibilitymaybeoneofthefactorsthatplays arole.Weadd tothisliterature intwoimportantways.First,weintroducea newmechanismthat allowsustodirectlymanipulatethe possibilitytoreduce pivotalityandisolateitfromsharedguilt. Second, endogenisinggroup entryallowsustostudywhetheragentsexploitgroup decisionmakingtomakemoreselfish choicesandwhetherthisresultsinendogenouslyformedgroupsbeingevenmoreselfishthansuggestedbytheliterature. 2.2. Endogenousgroupformation

To date,endogenousgroup formationhas primarily beenstudied inpublic goodexperiments. Forinstance,Ahn etal. (2008) reportasigniﬁcantimpactofthegroupformationprocessonpublicgoodprovision.Both EhrhartandKeser(1999) andBrekkeetal.(2011) demonstrate thatendogenously formedgroupscan sustainhigherlevelsofpublicgoodprovision becausemorepro-socialindividualsselectintogroups.

Aside fromtheliteraturethat studiesthe endogenousformation ofinstitutionsinexogenouslyformed groups,such as Sutter etal. (2010), there is an emerging literature that looks atthe endogenousformation of groupswith punishment institutions.Kosfeldetal.(2009) showthatthisendogenousformationincreasespublicgoodprovision.Gürerketal.(2006,

2014) and Fehr andWilliams (2018) show that self-selection into groupsand endogenousmigration across groupswith distinct punishmentinstitutionsfosterscooperation.Nicklischetal.(2016) addthattheobservabilityofcontributionlevels inapublicgoodgameencouragesindividualstojoingroupswithpunishmentopportunities.Robbett(2014) furtherstresses thatnexttotheabilitytoentergroupswithdifferentinstitutions,theabilitytothenshapetheseinstitutionsiscrucial.

Similarly,inweakestlinkgamesRiedletal.(2015) andChen(2017) findindividualschoosingthesetofplayersandthe grouptointeractwithiseffectiveinpromotingefficientcoordination.Incontests,Herbstetal.(2015) findthatself-selection intogroupshasasignificant impactoneffort,both throughintensifiedfree-ridingandincreasedin-groupfavouritism.The field study by Hamiltonet al.(2003) considers self-selectioninto group production,finding(somewhat surprisingly)that thereisnoadverseselectionofteammembers.

Importantly,groupsarenotdecisionmakersinanyofthesestudies.Instead,individualsmakedecisionsthataffectothers in their group.Nevertheless,such findings suggestthat the neglectofthe endogeneityofgroup membershipis aserious gapintheexistingliterature.Theonlystudyweareawareofthatconsidersendogenousgroupformationinthecontextof group decisionmaking isKocheretal.(2006), whodoso forbeautycontests. Theyfindthatwhile endogenouslyformed groupsperform betterthanindividual decisionmakers,highabilitysubjectsaremorelikelytoopt forindividualdecision making.The contextweproposehereinvolvesanentirelydifferentstrategicenvironment.Furthermore,tothebestofour knowledge, ours is the first study that directly compares distributive decisionsby endogenously and exogenously formed groups,asopposedtobehaviourwithin thosegroups.

2.3. Sorting

Few studiesconsidertheeffectofsortingorself-selection onthedecisionenvironment.OnenotableexceptionisDana et al.(2006). They demonstratethat a substantial fraction ofsubjects opt out of playinga dictator game when this

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en-Table 1

Treatmentoverview.

Exogenous group formation Endogenous group formation

•Individual decision making (ExoInd) •A default (Endo A)

•Group decision making A default (ExoGroup A) •B default (EndoB)

•Group decision making B default (ExoGroup B)

suresthat thereceiverstaysuninformed aboutthe optionofplayingthisgame.AlsoLazearetal.(2012) showthat some typesofindividualssortintoenvironments thatdonotprovidetheopportunitytosharetheirearnings.Thisself-selection signiﬁcantlyaltersthedegreeofpro-socialbehaviourinadictatorgame.

Grossman and Van der Weele (2017) investigate sorting of dictators into differentinformation states concerning the payoffsofreceivers.Theyﬁndsubstantiallymorepro-socialbehaviourofdictatorswhoself-selectedintoenvironmentswith knowledgeofthereceiver’spayoff.

Similar toourexperiment, thesestudies underline thatsorting providesa mechanismthat candecrease theextentof pro-socialbehaviour.Weaddtothisbyconsideringsortingintovarioustypesofgroupsassuchamechanism.

3. Experimentaldesign

Ourexperimental designaims toshedlight onthe effectsofresponsibility diffusionandendogenousgroupformation ondifferencesin groupandindividual choices. Inparticular,it willallow usto study selectioneffects inresponse tothe possibilitytoreducepivotalityforselﬁshdecisions.

Thedesignemploysabinarydictatorgamewiththefollowingtwooptions:

A

: (

10

,

0

)

B

: (

6

,

6

)

wheretheﬁrstnumberdepictsthedictator’sandthesecondnumberthereceiver’spayoffinexperimentaltokens. A repre-sentstheselﬁshoptionandB thepro-socialoption.Thisdictatorchoiceinvolvesnostrategicinteraction.Asaconsequence, choices are independent ofbeliefs about other players’ behaviour. Throughout theexperiment, the dictator andreceiver rolesareneutrallylabelledasPlayer1andPlayer2,respectively.

3.1. Treatments

The experiment uses a within-subjectdesign. There are ﬁve distinct treatments, varying along two dimensions. First, treatmentsdifferwithrespecttohowdecisionsaremadeandsecond,theydifferinthewaygroupsareformed,seeTable1. Groupsalwaysconsistofthreeindividuals.

Allsubjects makedecisions inthe dictatorrole (how payoffsare determinedis explainedbelow). Decisions aremade individuallyorinagroup.Tostart,weexplainthetreatmentsinwhichgroupsareformedexogenously(asistheallocation totheindividualdecision-makingtreatment).Eachparticipantismatchedwithoneotherindividual,thereceiver.

Ifdecisionsaremadeindividually,asinExoInd,subjectsdecideabouttheirpayoffandthepayoffoftheotherparticipant theyare matchedwith.Ifdecisionsare madeinagroup,asin ExoGroup A and ExoGroup B,agroup jointlydecides about their payoff andthe payoff of another group, consistingof the three individuals the group members are matched with. Within matching groups of nine individuals, subjects are rematched into different groups in each period that involves group decisionmaking. Subjectsknow that they are rematched inevery group decision-making period,butare unaware of the matching groups. Each group member in the dictator and the receiver group obtains the payoffs corresponding to the implemented option. This ensures that group decisions do not differ from individual decisions in terms of per-capitaincentives,whichcouldaltertheperceptionoftheselﬁshnessofchoosingeitheroption.Therole ofoutcome-based explanationsfordifferentchoicesisthereforelimited.

Group decisions are made by each group member simultaneously casting a vote. Every period, every individual has only one chance to casta vote. Adecision isimplemented ifgroup members unanimously voteinfavour of it.There is no communicationbetweengroup members. Thisis inline withother studies like Dana etal.(2007), Falk etal. (2020) andBehnketal.(2017).Ifgroupmembersdonot unanimouslyvoteforeitheroption,adefaultoptionisimplemented.In ExoGroup A thisdefaultoptionis A,in ExoGroup B itisB.

This speciﬁcation of the voting process serves as a mechanism to isolate the effects of the pivotality dimension of responsibilitydiffusionongroup choices.Ifthepro-socialoutcome B isthe default,thenthereisno possibilitytodiffuse responsibility, asin having a reducedprobability ofbeingpivotal fora selﬁsh decision (comparedto when thedecision ismadeindividually).Asall group membersneedtoagree on A for thistobeimplemented, everyvoteispivotalif A is implementedandevery groupmemberbearstheresponsibility forA beingtheaggregate decision.Incontrast,if A isthe default,thisallowsfordiffusionofresponsibility.Avoteinfavourof A ishereonlypivotalforimplementing A ifthetwo othergroup membersvoteinfavourof B.Assoonasatleastoneothergroupmembervotesinfavourof A,an individual

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voteinfavourof A isnolongerpivotal.Inexpectation,ifweassumeapositiveprobabilityofanyindividualvotinginfavour of A,morevotesneedtochangeifthedefaultis A thanifthedefaultisB tochangetheoutcomefromselfishtopro-social. Withdefault A,anagentvotinginfavourof A canexpecttobefurtherawayfrombeingpivotalfortheselfishgroupchoice A.Thisreducestheexpectedresponsibilityforimplementingtheselfishoutcome.Ifoneindividualwouldchangehervote, theselfishoptionA couldstillbeimplemented.

IncontrasttoBehnketal.(2017) andFalketal.(2020),analysingtheeffectofdiffusionofresponsibilityhereinvolves thecomparisonofgroupdecisionsindistinctenvironments.BothBehnketal.(2017) andFalketal.(2020) comparegroup to individual decisions, while we leave all aspects of group decisionmaking constant exceptthe defaultoption.4 _This _is

especiallyimportantastheevidenceinfavourofashifttomoreselfishbehaviourindictatorgamesisinconclusive.Luhan etal.(2009) findmoreselfishbehaviourbygroupsbutCasonandMui(1997) findtheopposite.Weapplythedictatorgame becauseitslackofstrategicinteractionprovidesacleanmeasureofpro-sociality.Weprefertocomparegroupstogroups(as opposedtogroupstoindividuals)becausethisallowsustodirectlycapturevariationsinthediffusionofpivotalitywithout confoundsfromotherdriversofdifferencesbetweengroupandindividualdecisions.

Thetwotreatmentsinwhichgroupsareformedendogenously,Endo A and EndoB,involvedecisionsintwostages.First, individuals choose between group and individual decision making. When choosing, they know the defaultoption for a group theywouldjoin.Thisis A in Endo A and B inEndoB.Inthesecondstage,individualsface,dependingontheir ﬁrst stagedecision,oneortwochoices.Ifindividualdecisionmakingischosen,participantsfacethesamechoiceasinExoInd.If, instead,groupdecisionmakingispreferred,subjectshavetoindicate,both,howtheywouldvoteiftheyindeedjoinagroup andhowtheywoulddecideiftheycannotjoinagroupfordecisionmaking.Weusethestrategymethodherebecausethis allows usto study groups that areformed purely voluntarily. In casethenumber ofsubjectsthat indicates a preference forgroupdecisionmakingisnotamultipleofthree,randomlyselectedparticipantswhoprefergroupdecisionmakingare assignedtomake theindividualdecision.5 Thisiscommonknowledge. Outofninesubjectsinamatchinggroup,atmost twosubjectsmayhavetodecideindividuallyinsteadofinagroup,despitepreferringgroupdecisionmaking.6

3.2. Beliefelicitation

Ifsubjectsjoingroupsbecausethisallowsthemtodiffuseresponsibility,thenthelikelihoodthataselfishindividualwill join agroupishigher,themoreotherselfishchoicessheexpects.Tomeasurethis, weelicitparticipants’beliefsaboutthe numberofselfishchoicesbyothers.7_We_do_so_for_four_distinct_cases,_{distinguished}_by_the_default_and_whether_the_decision

isindividualorinagroup.

Eachparticipantisaskedtoindicate howmanyout oftenrandomlysampledother subjectsare expectedto choose A. Foreachelicitation,subjectsareendowedwithoneeuro.Theelicitation isincentivisedbysubtractingtencentsmultiplied by theabsolutedifferencebetweentheestimatedandobservedfrequenciesfromthisendowment.8 Askingforfrequencies inthiswayinsteadofsubjectiveprobabilitiesyieldsamoreaccurateelicitationofbeliefs(Schlagetal.,2015).

3.3. Timing

Thisexperimentconsistsof25periodsplusthebeliefelicitationstage.These25periodsincludemultipleperiodsofeach treatment.AsillustratedinFig.1,theexperimentissplitintoaninitialnine periodswithoutendogenousgroupformation and an additional 16 periods that alternate in a ﬁxed order between exogenous individual and group decision-making periodsandendogenousgroupformation.Thebeliefelicitationtakesplaceinbetweenthesetwosetsofperiods.9

Theﬁrstpartservestoallowsubjectstogainexperiencebothwithindividualandwithgroupdecisionmakingin envi-ronments where A and B are the defaults.Thispart consistsofthree roundsof ExoInd,three roundsof ExoGroup A and three roundsof ExoGroup B.Comparingexogenous groupdecisionsintheﬁrstparttothosedecisionsinthe laterpartof theexperimentallowsustoinvestigatewhethertheeffectofresponsibilitydiffusionisstableacrosstime.

The second partofthe experimentcomprisesfourperiodsof Endo A and EndoB each, twoperiodsof ExoGroup A and ExoGroup B eachandfourperiodsof ExoInd.Toreduceasmuchaspossibleanyeffectsfromtheorderofdecisionstaken, periods are organisedin blocksof fourinthe second part.Each block ismadeup of one Endo A period, one EndoB pe-riod, one ExoInd periodandone exogenousgroup decision-makingperiod.The latteralternatesbetweenExoGroup A and

4 _As_explained_above,_only_{ExoGroup A allows}_for_a_diffusion_of_{responsibility;}_{ExoGroup B provides}_agents_with_veto_power_against_the_{implementation}

ofselﬁshchoices.Ifanagentfavoursapro-socialallocationofresources,avoteinfavourofB guaranteesthisallocationinExoGroup B.

5 _The_design_is_not_symmetric_here._Subjects_opting_for_individual_decision_making_only_face_one_question,_because_individual_decision_making_is

guar-anteedifthisispreferred.Sotheirvoteincaseofjoiningagroupwouldnothavebeenincentivised.Sincesubjectsmayespeciallydislikeinconsistencies betweentheirindividualandgroupdecisioninasimultaneouschoice,ourresultsprovidealowerboundoftheselectioneffect.

6 _Note_that_there_is_no_need_to_exclude_these_data._Since_we_use_the_strategy_method,_subjects_decide_between_{A and}_{B for}_both_the_case_they_end_up

asanindividualdecisionmakerandthecasetheyendupaspartofagroup.Theydosobeforetheyknowwhethertheyareanindividualdecisionmaker

orpartofagroup.Bothofthesechoicesareproperlyincentivised,asitispossibletoendupineithercase.

7 _Eliciting_such_beliefs_also_enables_us_to_estimate_whether_participants_believe_that_others_use_groups_to_diffuse_{responsibility.} 8 _This_linear_scoring_rule_is_used_to_facilitate_{understanding}_of_the_mechanism.

9 _Since_the_payoff_of_the_belief_elicitation_only_depends_on_{other subjects’}_behaviour,_this_belief_elicitation_is_not_expected_to_affect_behaviour_in_the secondpartoftheexperiment.

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Fig. 1. Timing.

ExoGroup B.Ourmainanalysiswillfocusonthissecondpartoftheexperiment,sincethelevelofexperienceisheresimilar inthebetween-treatmentcomparison.

Atthe endofthe experiment,participants arerandomlysplit intodictatorsandreceivers.Onlythe decisionsbythose allocatedto the dictatorrole are implemented. Asa consequence,every subject’s choicespotentially determinesomeone else’spayoffineachofthe25rounds.

3.4. Procedures

TheexperimentiscomputerisedusingPHP(theprogrammeisavailableuponrequest).ItwasrunattheCREEDlaboratory oftheUniversityofAmsterdam.Weran12sessionsinJuneandOctober2018withatotalof216students.10Subjectswith avarietyofbackgroundswererecruited.Aquestionnaireadministeredattheendoftheexperimentshowsthat63%havea backgroundineithereconomicsorbusinessand50%arefemale.Eachsessionconsistedof18participants,constitutingtwo matchinggroups. Subjectsdidnot knowthe identityofthe participantswhowere intheir matchinggroup.Upon arrival, subjects were randomly allocatedto computer stations and further communicationwas prohibited. The instructionsand imagesofthedecisionsscreensareavailableinappendixAandappendixB(Figs.B.1,B.2,B.3),respectively.Understanding oftheinstructionwastestedusingpracticequestions(cf.appendixA).Subjectswereonlyallowedtomoveonandstartthe ﬁrstperiodoftheexperimentiftheyansweredallquestionscorrectly.

Finalpayoffsconsistedofa show-upfee ofseven euros plusthe earnings ofthe25periods andthebelief elicitation. Eachexperimentalpointcorrespondstoapayoffof0.08euros.Averageearningswere21.71euros;sessionslastedonaverage approximately45minutes.

4. Behaviouralhypotheses

Toderivetestablehypotheses,weassumethat,nexttotheirmonetarypayoff,individualscareabouttheextenttowhich theyareresponsiblefortheimplementationofaselﬁshoutcome.Theassociatedmoralcostsdependontwofactors.

Wecallthefirst‘responsibilityaversion’.Thisreflectsanindividual-specificparameterthatcapturesthedegreetowhich anindividualisaffectedbybeingresponsiblefordecreasingsomeoneelse’searningsincomparisontothealternativechoice. Intheexperiment,individualswithdistinctresponsibilityaversionwouldeachattachadifferentweighttodiminishingthe receiver’searnings fromsixtozerobychoosing A insteadof B.Thehighertheresponsibilityaversion,thehigherarethe moralcostsfordiminishingsomeoneelse’spayoff.

Thesecond factorreflectsthe‘degree ofresponsibility’forimplementing aselfishoutcome. Moreprecisely,itcaptures the extent to whichthe individual concerned ispivotal inthe decision to choose A. Holdingthe responsibility aversion constant, thedisutility from decreasingsomeone else’spayoff increasesin the degreeof responsibility. As introduced by Engl (2018),we take thedistance tobeingpivotalasa measureofresponsibility, witha higherdistancereflecting lower responsibility.11_An_agent’s_distance_to_being_pivotal_is_defined_as_the_number_of_votes,_including_that_agent’s_vote,_that_need

to changesuch that her votewouldbe pivotalforchangingthe outcome.The expecteddistance tobeingpivotalis then theexpectednumberofvotesthat needtochange.It givesthesimplebinary conceptofpivotalityasthedeterminantof individualresponsibilityincollectiveactionmorenuance.

Asarguedabove,thisdistancetobeingpivotalforchoosing A isexpectedtobehigheringroupdecisionswithdefault A thanwithdefaultB andthaninindividualdecisions.If,forexample, A isthedefaultandeveryonevotesinfavourofA, thedistanceto beingpivotalisthree. Everyoneneedsto changetheir voteforthe outcometochange.If B is thedefault andeveryone votesinfavourof A,thedistancetobeingpivotalisone.Soevenifeveryone votesselﬁshly, thedistanceto beingpivotalremainslowwithB asthedefault.IfB isthedefault,theexpecteddistancetobeingpivotalforimplementing A isthereforeindependentofagents’beliefsaboutothers’behaviour.

10 _There_was_a_pilot_session_before_these_12._After_the_pilot,_we_introduced_a_small_change_in_waiting_times_in_endogenous_periods._This_guaranteed_that individualshavenoincentivetodecideindividuallyinordertoavoidwaitingforotherparticipants.

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Table 2

Classiﬁcationofdifferenttypesofindividuals.

Group decision Selection

Responsibility A B Type A B

Aversion default default default default

low A A selﬁsh group individual

intermediate A B switcher group or individual indifferent

high B B pro-social individual indifferent

Thelevelofresponsibilityaversion(column1)determinesdecisionsingroupswithdefault

A (column2)anddefaultB (column3)whichresultsinthetypeclassiﬁcation(column4).

Classiﬁcationdeterminesselectionofenvironment(columns5and6).

Toderivetestablehypotheses,weclassifyindividualsbasedontheirdegreeofresponsibilityaversionintothreetypes.A givenlevelofresponsibilityaversionleadstospecificchoicepatternsingroupswithvaryingdefaults.Realisethatdecisions ofindividualdecisionmakersshouldbethesameastheirvotesingroupswithB asthedefault,sinceinbothcasestheyare fullypivotalincaseofaselfishdecisionandresponsibilitythuscannotbediffused.12InAppendixCwepresentandanalyse adecision-theoreticmodelthatformalisestheclassificationpresentedhere.Thismodelalsoprovidesaformalunderpinning forthehypothesespresentedbelow.

Individualswithalowlevelofresponsibilityaversionchoose A irrespectiveofthegroup’sdefault;evenifresponsibility cannot be diffused,they prefertovotefortheselfishoutcome. Notethattheseindividualsarenot necessarilycompletely indifferenttotheconsequencesoftheiractionsforothers’payoffs.However,theirresponsibilityaversionisnothighenough to make themforego themonetary gainsassociated withtheselfish optionundereither default.Because oftheir choice pattern, wecalltheseindividuals‘selfish’.Inperiodswithendogenousgroupentryand A asthedefault,theseindividuals will choosetodecideinthe groupbecausethey canassurea selfishgroup choicebutstillmightgetsome benefitout of thediffusionofresponsibility.Theexpecteddistancetobeingpivotalforimplementing A isincreased,ifthereisapositive probabilityofoneotherindividualvotingA,whileA canstillbeguaranteed.IfB isthedefault,theycannotguaranteetheir preferredoutcome A andbylackofresponsibilitydiffusion,thereisnoadvantagetojoiningagroup.Theythereforeprefer todecideindividuallyandthenchoose A.

At the other extreme are those who have a high level of responsibility aversion. This leads them to choose B even withdefault A,sotheychoose B irrespectiveofthedefault.With A asthedefault,theexpecteddistancetobeingpivotal for allocation A ishigher, butthisdoesnot sufficeto compensate forthe moral costs that resultfrombeing (even only partly) responsibleforaselfishoutcome.Because ofthisvotingpattern, wecallthem‘pro-social’.Theseindividualsprefer todecideindividuallywhenA isthedefaultbecausetheconsequencesofbeingpartlyresponsibleforaselfishgroupchoice ( A) weighstooheavilyonthem.Therefore,they prefertodecideindividually andimplementthepro-social B.When B is thedefault,theyareindifferentaboutjoiningagroup,becausetheycanalwaysensureoutcome B eitherway.

Finally, thereare individualswithan intermediate level ofresponsibility aversion.Given their degreeof responsibility aversion, they choose A when A is thedefaultandB when B isthedefault. Theirresponsibilityaversion ishighenough to kick in andmakethem choose B when B is the defaultandthe distanceto beingpivotalforimplementing A is not increased; the moral costs of voting selfishly are too high if responsibility is not diffused. Yet responsibility aversion is low enoughto make them choose A if theexpected distanceto beingpivotalfor theselfish choice is higherwith A as the default. Responsibilityisthen diffusedsufficiently suchthat the higherpayoff offsetsthe moralcosts of beingpartly responsibleforsomeoneelse’slowpayoff.Wecallthistypeofindividualsa‘switcher’.Suchanindividualwillbeindifferent aboutjoininga groupwhen B isthe defaultbecauseher choiceswill ensurethe outcome B in anycase.When A is the default, she may choose to decide individually or to join a group, depending on the precise value of her responsibility aversion. Ifresponsibility aversionis relativelylow,diffusionof responsibilitystill makes itsufficiently attractiveto enter groupsandexploitthisfeature.HigherlevelsofresponsibilityaversionensurethatvotingindividuallyforB dominatesbeing selfishinagroup,asthecostsofbearingtheresponsibilityforselfishoutcomesaretoohighdespiteresponsibilitydiffusion.

Table2summarisesthisdiscussion. 4.1. Experimentalhypotheses

Ourclassiﬁcationyieldsthefollowingtestablehypotheses.

Hypothesis1.Inexogenouslyformedgroups,option A willbechosenmoreoftenifA isthedefaultthanifB isthedefault. This assumesa positive mass inthe type distribution on theswitching type. Inthat case, this hypothesis follows di-rectly fromTable2byobservingthat switcherschoose A (B)when A (B)isthedefault,whileother typesdonotchange

12 _We_have_no_way_to_know_whether_subjects_realise_that_they_are_as_pivotal_for_implementing_{A if}_this_is_done_in_a_group_with_{B as}_the_default_as_they

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their behaviourbasedonthedefault. Because A isthedefaultwhichallowsfordiffusionofresponsibility,thishypothesis predictsthatthediffusionofresponsibilitygeneratesmoreselfishdecisions.Thisisbecauseitdecreasesthemoralcostsof makinga selfishchoice. Inourexperiment,we expect theshareof A choicestobe higherintreatment ExoGroup A than in ExoGroup B.Thisfirsthypothesis servesasarobustnesscheckofpreviousfindingsofBehnketal.(2017) andFalketal. (2020) usingadifferentidentificationmechanismfortheeffectsofdiffusionofresponsibility.

Hypothesis2.ThedifferenceintheshareofvotesinfavourofA betweengroupswithA asthedefaultandgroupswithB asthedefaultislargerinendogenouslythaninexogenouslyformedgroups.

GiventhetheoreticalselectionpatternsdepictedinTable2,individualswithlowerresponsibilityaversion–thatis,those morelikely tochoosethe selfishoption –selectintogroupswhen thisentailsthe possibilitytoreduce responsibility for selfishactions.Inaddition,thosewithhighresponsibilityaversion(whoarelikelytochoosethepro-socialoption B)select out of groupswhen responsibility can be diffused.Together, thismeans that endogenously formed groups with default A have ahigherfractionofselfish individualsthanthe randomlyformedexogenous groupswiththisdefault.Similarly, a groupwithdefaultB willnotbejoinedbyselfishindividuals,sothefractionofselfishtypesinthesegroupswillbelower thanin exogenousgroups. Thisselection ofselfishtypes intoendogenously formedgroupswitha selfishdefaultandout ofendogenously formedgroupswitha pro-socialdefaultyieldsthe conclusionthat endogeneityamplifiesthedifferences betweenthedefaults.Hence,comparingthedifferenceinselfishdecisionsintreatmentsEndo A and EndoB tothisdifference inExoGroup A and ExoGroup B,weexpecttheformertobehigher.Thisassumesapositivemassonatleasttwotypeswith differentselectionchoicesunderdefault A.

Hypothesis3.IndividualsclassiﬁedasselﬁshjoingroupsmoreoftenifA isthedefault.

Thisfollowsdirectly fromTable2andthe discussionfollowing Hypothesis 2.The fractionofselﬁshgroup entrantsin Endo A isthuspredictedtoexceedthefractionofselﬁshgroupentrantsinEndoB.

Hypothesis4.Individualsclassiﬁedaspro-socialjoingroupsmoreoftenifB isthedefault.

We predict that the opposite ofHypothesis 3 holds truefor typesthat do not take advantage of thediffusion of re-sponsibility,thepro-socialtypes.Thisis,however,moreofaconjecturethanaformalresult.Thoughpro-socialtypesprefer individualdecisionmakingifA isthedefault(cf.Table2),theyareindifferentwhenB isthedefault.Thehypothesisfollows ifweassumethatindifferenceyields apositiveprobabilityofjoiningagroup.Inthatcase,we predictthatthefractionof pro-socialtypesthatjoingroupsishigherinEndoB thanin Endo A.

NotethatthebehaviourpredictedinTable2isdeterministicinthesensethatsomeoneeitherjoinsagroupordoesnot. Addingnoisetodecisionswouldmeanthatthechoicesbecomeprobabilistic.Thatis,asthelevelofresponsibilityaversion increases,thelikelihoodtojoinagroupwithdefault A (B)decreases(increases).Then, theideas underlyingHypotheses3

and 4can also be tested using the elicitedbeliefs. In the reasoning underlyingTable 2, a selfish subject’s or switcher’s propensity to join groups in Endo A will increase in her beliefs about the share of selfish votes in groups because this increasesthelikelihoodthatshewillbeabletodiffuseresponsibility. Thesameholdsforswitchers.Thereverseholdsfor pro-socialtypes,whosepropensity tojoingroupsshoulddecreaseintheirbeliefsabouttheshareofselfishvotesbecause moreofsuchvoteswillincreasethelikelihoodofaselfishoutcome.

5. Experimentalresults

Asmentionedabove,wehavedatafrom12sessions(foratotalof216participants)inawithin-subjectdesign.Westart byoutliningthemethodologyunderlyingthedataanalysis.

5.1. Methodology

We useboth parametric and non-parametric techniques.Because of thedependence ofobservations within matching groups,observationsareaveragedatthematchinggrouplevelwheneverusingnon-parametrictests.Thisresultsin24 ob-servationspertreatment.WeapplyFisher-Pitmanpermutationtestsforpairedreplicates(FPP)whenmakingwithin-subject comparisons. When comparing choices across differenttypes of individuals, we useFisher-Pitman tests forindependent samples (FPI) (Kaiser,2007). These permutation tests are non-parametric anddo not require distributional assumptions (Siegel,1956). Atthesametime,permutationtestsaremorepowerfulthantraditionalnon-parametrictechniquessuchas theWilcoxonsigned-rankandMann-WhitneyUtests.Moir(1998) demonstratesinaMonteCarloanalysisthatpermutation testsallowformorerobustinferencewithsmallsamples,asdiscussedinSchrametal.(2019).

In the parametric analysis, standard errors are clustered at the matching-group level to ensure consistent estimates despitedependentobservations. p-valuesreportedinthemaintext stemfromtheseclusteredstandarderrors.Toaccount forapossibledownwardbiasintheestimatedresiduals dueto thesmallnumberofclusters(CameronandMiller,2015),

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Fig. 2. Share of selﬁsh choices per period.

weincludearobustnesscheckusingscorewildclusterbootstraptocalculate p-valuesbasedonKlineandSantos(2012) in alltables.

WecategorisesubjectsintotypesalongthelinesofTable2.Todoso,weusechoicesinperiodswithexogenousgroup decisionsinthesecondpartoftheexperiment(constitutingtwochoiceseachwithdefaults A andB).IfsubjectsvoteforA, irrespective ofthedefault,theyarecategorisedasselfish,andiftheyalwaysvotefor B,theyarethepro-socialtype.Ifout ofthefourresponsesconsidered,subjectsmoreoftenvoteforA ifA isthedefaultthanifB isthedefault,theyareassigned to beaswitcher.Thisclassificationcaptures78%ofthesubjects,with17%ofallsubjectsbeingcategorisedasselfish,24% asswitcherand37%aspro-social.

To investigate whetherour analysisrequires a trend correction, Fig. 2shows the shareof individuals deciding foror votingfor A overthe25periods.Thisfractioniscloseto50% inall periods,whichallows testingtheoutlinedhypotheses without fearing boundary effects. The mild downward trend inthe fraction of selﬁsh choicesor votes (Spearman’s

ρ

=

−

0

.

047; p

<

0

.

001)suggeststhatexperienceslightlymatters.Unlessstatedotherwise,wethereforeconsideronlydecisions inthesecondpartoftheexperiment,wherethereisnodetectabledownwardtrend(Spearman’s

ρ

= −

0

.

017; p

=

0

.

324).13 Thisisespeciallyimportantinthecomparisonofendogenousandexogenousperiodstoensurethatsubjectsinexogenous andendogenousroundshaveacomparablelevelofexperience.Here,treatmentsarespreadoutevenly.

5.2. Results

Table3presentssummarystatisticsforthemainvariablesofinterest(thefractionof A choicesandthechoicetoenter agroup).

Intheupperpanels,wecomparethefractionofA choicesandthechoicetoenteragroupacrossdefaults.Inthelower panels,thetabledisplays theresultsofadifference-in-differenceanalysis. Theinequalitiesindicatedaredifferencesinthe fractionof A choicesordifferencesinthechoicetoenteragroupacrossdefaults.Inthelower-leftpanel,thecross-default difference inthefractionof A choicesiscomparedbetweenendogenously andexogenously formedgroups. Inthe lower-rightpanel,differencesinthechoicetoenteragrouparecomparedbetweenindividualsclassiﬁedornotclassiﬁed(“others”) asacertaintype.14

Result1.Inexogenouslyformedgroups,optionA isnotchosensigniﬁcantlymoreoftenwhenA isthedefaultthanwhenB isthe default.

Hypothesis 1canthus notbe confirmedwhenfocusingondecisions inthesecondpartoftheexperiment(see below, however,forresultsonthefirstpart).UsingthenumbersfromTable3,Fig.3illustratesthefractionofvotesinfavourof A acrossthegrouptreatments. Althoughthefractionofvotesinfavourof A isslightlyhigherinexogenouslyformedgroups when A isthedefault(0.38)thanwhenB isthedefault(0.36),thisdifferenceisnotstatisticallysignificant(FPP;p

=

0

.

373).

13 _For_the_two_correlation_tests_observations_are_not_averaged_at_the_matching_group_level.

14 _For_example,_the_selfish_join_the_group₁₅_percentage_points_more_often_when_{A is}_the_default_than_when_{B is}_the_default._Together,_those_not_classified asselfishjoinagroup8percentagepointslessoftenwhenA isthedefaultthanwhenB isthedefault.Thediff-in-diffbetween+15percentagepointsand -8percentagepointsisstatisticallysignificantwithp<0.01.

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Table 3

Summarystatisticsandtestsonselﬁshvotesandgroupentry.

A votes Group entry

Exo Endo Total Selﬁsh Switching Pro-social

Overall 0.37 >∗ 0.31 0.40 0.28 0.39 0.47 A default 0.38 > 0.38 0.38 0.35 0.40 0.39 ∨ ∧∗∗∗ _∨∗∗∗ _∧∗ _∨∗∗ _∨ _∧∗∗∗ B default 0.36 >∗∗ 0.25 0.42 0.20 0.38 0.56 Others Difference between defaults -0.08 <∗∗∗ 0.15 0.02 <∗∗∗ 0.13 -0.06 <∗∗ 0.02 0.03 >∗∗∗ -0.17 Observations 863 692 1727 288 416 640

CellsreporttheaveragefractionofA votesingroupsandtheaveragefractionofindividualschoosing

toenteragroup.Differencesofmeansanddifferencesindifferences aretestedwithFisher-Pitman

permutationtestsusingmatchinggroupaverages.Thenumbersinthelowerpanelsareexplainedinthe

maintext.∗p<0.10,∗∗p<0.05,∗∗∗p<0.01.

Fig. 3. Comparisonofthefractionofselﬁshchoicesacrosstreatments.FractionofvotesinfavourofA acrosstreatmentsinpart2.Errorbarsindicate95% conﬁdenceintervalbasedonindividualobservations.

Thisresultisincontrasttotheﬁndings ofBehnketal.(2017) andFalketal.(2020).Recallthat thesestudiesmeasure responsibilitydiffusionbycomparingindividual’sdecisionswhenalonetotheirdecisionswheninagroup.Dimensionsof responsibility diffusionother thana changeinpivotality might,however,causedistinctbehaviour inthe twosettings. Of course,we cannotexclude thepossibilitythatforsomereasonresponsibilitydiffusionplays arole inthesettingsstudied byBehnketal.(2017) andFalketal.(2020),whileitdoesnotinourexperimental setting.Nevertheless,wecanconclude thatchangesinanindividual’spivotalitydonotalwaystriggermoreselﬁshbehaviouringroups.

Given that our design comprises 25periods, we can investigatewhether andhow responsibility diffusion mattersat differentstagesoftheexperiment.Toinvestigatewhetherourtreatmentvariationissuccessfulinvaryingthesubjects’ per-ceptionofresponsibility,weexplorebehaviourofsubjectsinexogenouslyformedgroupsinthefirstpartoftheexperiment. Thisallows ustoseewhetherthe increaseinthe probability ofbeingpivotalinitiallyleads tomoreselfish behaviour by thosesubjectssusceptibletoavariationinresponsibility.Incontrasttotheresultsinthesecondpartoftheexperiment,we observethatinthefirstpartsubjectsvotesignificantlymoreselfishlyingroupswithaselfishdefault.Overthewholecourse oftheexperiment, 41%ofthevotesareselfish inexogenouslyformedgroupswithaselfishdefault, whichissignificantly morethanthe37%insuchgroupswithapro-socialdefault(FPP;p

=

0

.

043).Thiseffectisevenstrongerifweonlyconsider periodsintheﬁrstpartoftheexperiment(44%vs.38%;FPP;p

=

0

.

015).Table4summarisesthis.

The effectof a reduction in theprobability ofbeingpivotal thus seems to diminishwithrepetition. Thismeans that our resultsare consistent with theprevious literature, such asFalk etal. (2020) andDana et al.(2007). These previous studiesapplyone-shotinteractionsoronlyafewrepetitions.Falketal.(2020) ﬁndintheir‘charityparadigm’thatsubjects aremoreselﬁshina secondperiod,wheresubjectsare abletoformmoreaccuratebeliefsaboutpivotality. Similarly,itis

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Table 4

Comparisonofvotesincludingﬁrstpartoftheexperiment.

A votes

Only 1st part 1st and 2nd part

Exo Group Exo Ind Exo Group Exo Ind

A default 0.44 < 0.41 <

∨∗∗ ₀_.₄₈ _∨∗∗ _0.44

B default 0.38 <∗∗∗ 0.37 <∗∗∗

Observations 648 648 1080 1513

CellsshowperdefaulttheaveragefractionofA votesinexogenouslyformedgroups

andexogenouslyimposedindividualdecisionmaking.Differencesinmeansaretested

with Fisher-Pitmanpermutation tests using matching groupaverages. ∗p<0.10,

0

.

017,seeTable3).Interestingly,thissuggests that theamplification of differencesin endogenously formed groupsis not primarily driven by thepossibility to diffuse responsibility forselfishchoices, butbythe possibilitytoensurenon-selfish allocations. Thisisinlinewiththeexpected selection of pro-socialtypesdepicted inTable 2,that predicts that pro-socialtypes doto not joingroups with A as the default,yieldingrelativelyfewerselfishchoicesifB isthedefault.

Thisresultalsodemonstratesthelimitedroleofself-imageconcernsinthissetting.Individualgroupentrydecisionsare notprimarilymotivatedbytheopportunitytocasteapro-socialvoteatnoactualcostingroupswithA asthedefault.This would haveimpliedmore pro-socialvotesinendogenously formed groupswithdefault A, whichiscontraryto whatwe ﬁnd.

We will now investigate the type-speciﬁc selection behaviour inmore detail. Overall, individualsjoin groups 40% of the time, documenting a willingness to forego autonomyfor the sake of group decision making. At the aggregate level,

15 _To_check_whether_the_lack_of_differences_in_the_exogenous_treatments_may_be_due_to_subjects’_strive_for_consistency,_we_examine_the_{intra-individual}

correlationsinexogenousperiodsinthesecondpartoftheexperiment.Theseareonlymoderate(Pearson’sρ=0.4 betweengroupdecisionperiodswith

A andB asthedefault;Pearson’sρ=0.42 betweengroupdecisionperiodswithA asthedefaultandindividualdecisions;Pearson’sρ=0.49 between

002).As predicted,thistype ofindividualdoesnotseemtowanttofree rideonothers’selﬁshvotingbehaviourtobeneﬁtfroma highpayoffwithoutbearingtheresponsibilityforit.Infact,theyjoingroupsif,giventhedefault,anequalsplitofresources islikely. Thissuggeststhatpro-socialtypesjoin groupswhenthey canguaranteean equitable splitforawhole groupof participants(theycanensurethatthegroupdecisionisequitableifB isthedefault).NotefromthebottomrowofTable3

that there are more pro-social types than selﬁsh orswitchers. With default B, the pro-socials also havea much higher probability ofjoiningthe group.Asa consequence,amajorityofthegroup memberswithdefaultB is pro-social(56%of thosewe canclassify). Itispossiblethat thesesubjectsalsojoin groupstobeamonglike-minded individuals.Individuals

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Fig. 5. Comparison of selection distribution across defaults. Cumulative distribution of individual frequencies of joining groups by type and default.

mayderiveahigherutilityfromactingpro-socially(choosing B)ifthisisdone inagroupthey canidentifywith.16_While

selﬁshindividualsmightalsoprefertobeinagroupwithsimilarotherindividuals,thisurgeislikelystrongerforpro-socials. Aside from a comparison of means, we also see that the distributions of selection frequencies differ across types. Fig. 5 showsthe distribution ofindividual frequencies of selecting intogroups.17 _The _ﬁgure _illustrates _that _the

=

0

.

006).Incontrast, pro-socialindividualsjoingroupssigniﬁcantlylessfrequently,theaveragemarginaleffectofapro-socialdefaultB is17.2% (p

<

0

.

001).

16 _As_noted_by_an_anonymous_reviewer,_joining_a_group_and_subsequently_acting_pro-socially_could_also_be_explained_by_{outcome-based}_social_preferences.

Choosing B,subjectscanguaranteethatsixsubjectsreceiveapayoffofsixeach,whileA wouldonlygivethreesubjectsapayoffof10each.Suﬃciently strongFehrandSchmidt(1999) orCharnessandRabin(2002) typeofpreferenceswouldallowforthis.However,asweobservepre-dominantlypro-social votinginthesegroups,thepro-socialdefaultB isimplementedin98%ofthecases.Anindividual’svoteispivotalinonly10%ofthesecases.Joininga group,then,typicallydoesnotyieldafairoutcomeformoreindividuals.Thisiswhywesuggestapreferenceforjoiningagroupofsimilarindividualsas anexplanation(ontopofthedesiretoforceapro-socialoutcome).ThiswouldbeinlinewithHettetal.(2019),whoshowthatindividualsarewillingto foregosubstantialmonetarygainstobepartofagrouptheyidentifywith.

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Table 5

TheeffectofA beingthedefaultongroupentry.

(1) (2) (3) (4)

Sample Total Selﬁsh Switching Pro-social

Entry Entry Entry Entry

A default -0.176∗ 0.777∗∗ 0.121 -0.696∗∗∗ (0.102) (0.305) (0.192) (0.154) [0.0901] [0.0170] [0.5335] [0.0010] -0.042∗ 0.153∗∗∗ 0.029 -0.172∗∗∗ Constant -0.315∗∗∗ -1.378∗∗∗ -0.511∗∗∗ 0.239 (0.120) (0.302) (0.191) (0.203) Observations 1727 288 416 640 Clusters 24 17 23 21

LogitregressionestimatingtheeffectofA beingthedefaultongroupentryfor differ-enttypes.Standarderrorsclusteredatthematchinggrouplevelareinparentheses. Insquarebrackets,scorewildclusterbootstrapp-valuesadjustedforsmallsamples arereported.Averagemarginaleffectsarereportedinitalics.∗p<0.10,∗∗p<0.05,

∗∗∗_p_<₀_._01.

Table 6

Compositionofendogenouslyformedgroups.

Fraction of type in group

Selﬁsh Switching Pro-social

A default 0.16 0.26 0.38

∨∗∗ _∨ _∧∗∗∗

B default 0.08 0.21 0.49

Groups 24 24 24

Cellsreportthefractionofgroupmembersthathaveacertaintypeingroupswith

A andB asthedefault.Theunitofobservationistheaveragepermatchinggroup.

DifferencesaretestedwithFisher-Pitmanpermutationtestsusingmatchinggroup

averages.∗p<0.10,∗∗p<0.05,∗∗∗p<0.01.

Tostudy the impact oftheseselection patterns,we compare thefractionof selfish,switching andpro-socialtypes in groupswith A as thedefaultto groupswith B as thedefault, see Table6. Thishighlights how theobserved differences inselectionbehaviourtranslateintodifferencesinthegroupcomposition.Ifweallowsubjectstoreducetheprobability of beingpivotalforaselfishoutcome,thegroupcompositionisaffectedintwoways:First,therearemoreselfishindividuals ingroupswithA asthedefault(16%vs.8%;FPP;p

=

0

.

016).Second,therearefewerpro-socialindividualsingroupswith A asthedefault(38%vs.49%;FPP; p

<

0

.

001).

Theseresultsare allrobust tousing traditionalnon-parametrictests, theMann-Whitney Utestforcomparisonsof in-dependentsamplesandtheWilcoxonsigned-ranktestforwithin-subjectcomparisons,asreportedinAppendixD.Wealso investigatetype-specificbehaviourunderalternativeclassificationmechanisms,withsimilarresults,whicharediscussedin AppendixE.Inparticular,theselectionbehaviourofpro-socialtypesprovesveryrobusttohowindividualsareclassified. 5.3. Differencesinindividualandgroupbehaviour

So far,we have exploitedthe speciﬁc characteristicsof ourdesign by considering individual behaviour ingroupsand their entrydecision, both under distinct defaults. We can also directly compare individual decisions in isolation andin groups,asiscommoninmuchofthepreviousliterature.Weadd tothisby includingendogenously formedgroupsinthe comparison.OurresultsaresummarisedinTable7.

The results show that the fraction of selﬁsh choices is lowest (25%) when the default is B and groups are formed endogenously andhighest(48%)forindividualswho hadtheoptiontojoin such groupsandchosenot to.The difference ishighly signiﬁcant(FPI; p

=

0

.

001). Bothcanbe explainedasfollows.Recallthat wepreviously observedfrequentgroup entryby pro-socialsin thisenvironment,wherethey could impose their preferenceonthe group.As a consequence,the groups haverelatively manypro-socials and thereare relativelymany selﬁsh amongst the remaining individual decision makers.

Incontrast,votinginself-selectedgroupsandby individualdecision-makersisvery similarifthedefaultistheselﬁsh choice A (38%and39%,respectively;seeTable7).Thedifferenceisstatisticallyinsigniﬁcant(FPI; p

=

0

.

921).Thisconfirms ourearlierconclusion thatgroup entrybasedon adesire to diffuseresponsibility ismuch weakerthan entrytobe with other pro-socials.To seewhethertheseaggregate resultshide anydifferencesacross rounds,Fig. 6showsthefraction of selfishchoicesforthefourroundsinwhichaspecificenvironmentwasimplemented.Thisshowsthatthemeanfractionof selfishchoicesisrelativelyconstantacrossthefourcasesineachofthefoursituationsanindividualcanendupin.