Socially Enforced Nepotism: How Norms and Reputation Can Amplify Kin Altruism

13 Pages·2016·1.83 MB·English

by  Doug Jones

RESEARCHARTICLE
Socially Enforced Nepotism: How Norms and
Reputation Can Amplify Kin Altruism
DougJones*
DepartmentofAnthropology,UniversityofUtah,SaltLakeCity,Utah,UnitedStatesofAmerica
*[email protected]
Abstract
Kinselection,whichcanleadorganismstobehavealtruisticallytotheirgeneticrelatives,
worksdifferentlywhen—asisoftenthecaseinhumansocieties—altruismcanbeboosted
bysocialpressure.HereIpresentamodelofsocialnormsenforcedbyindirectreciprocity.
a11111 Inthemodeltherearemanyalternativestableallocationsofrewards(“distributional
norms”);astablenormisstableinthesensethateachplayerisbestofffollowingthenormif
otherplayersdothesame.Stablenormsvarywidelyinhowequallytheyrewardplayers
withunequalabilities.Inapopulationofmixedgroups(somegroupmembersfollowone
norm,somefollowanother,andsomecompromise)withmodestwithin-groupcoefficientsof
relatedness,selectionwithingroupsfavorsthosewhocompromise,andselectionbetween
OPENACCESS groupsfavorsgenerousgeneralizedreciprocityratherthanbalancedreciprocity.Thus
Citation:JonesD(2016)SociallyEnforced evolvedsocialnormscanamplifykinaltruism,givingrisetoauniquelyhumanmodeofkin-
Nepotism:HowNormsandReputationCanAmplify basedsocialitydistinctfromspontaneousaltruismamongclosekin,orcooperationamong
KinAltruism.PLoSONE11(6):e0155596.
non-kin.
doi:10.1371/journal.pone.0155596
Editor:Cheng-YiXia,TianjinUniversityof
Technology,CHINA
Received:November10,2015
Introduction:BeatingHamilton’sRule
Accepted:May2,2016
Thisarticlepresentsasouped-upversionofthetheoryofkinselection.Inthestandardversion,
Published:June15,2016
anorganismhasachancetoprovidebenefitbtooneofherkinatcostctoherself.Natural
Copyright:©2016DougJones.Thisisanopen selectionfavorsthisaltruisticactaslongasHamilton’sRuleissatisfied,r(cid:1)b>c,whereristhe
accessarticledistributedunderthetermsofthe
coefficientofrelatednessofrecipienttodonor[1].Butinthetheorypresentedhere,altruism
CreativeCommonsAttributionLicense,whichpermits
towardkinisinfluencedbyawidersocialcontext,asmembersofagroupplayagameinwhich
unrestricteduse,distribution,andreproductioninany
medium,providedtheoriginalauthorandsourceare eachplayercanrewardothersforbehavinggenerouslytowardtheirmutualkin.Ishowthat
credited. thiscanfavortheevolutionofhighlevelsofaltruism,intheformofunbalancedgeneralized
reciprocityamongkin,evenwhenrissmall.
DataAvailabilityStatement:Code(Mathematica)is
availableattheOpenScienceFramework(osf.io) Thetheoryofsociallyenforcednepotismshouldbeofinteresttoscholarsinseveraldisci-
repositorywithidentifiersDOI10.17605/OSF.IO/ plines[2,3].Itbearsonargumentsamongevolutionarytheoristsabouthowusefulinclusivefit-
MXZ8H/ARKc7605/osf.io/mxz8h. nesstheoryisinaccountingforsocialbehavior,amongsocialscientistsabouttherelationship
Funding:Theauthorhasnosupportorfundingto betweenrationalchoiceandsocialnorms,andamongculturalanthropologistsabouthowfar
report. theirtheoriesofkinshipcanbereconciledwithevolutionarytheories.
Intherestofthisintroduction,Isummarizetheoreticalandempiricalreasonsforwanting
CompetingInterests:Theauthorhasdeclaredthat
nocompetinginterestsexist. toaddamodelofsocialnormsandtheirenforcementtothetheoryofkinselection.Onthe
PLOSONE|DOI:10.1371/journal.pone.0155596 June15,2016 1/13
SociallyEnforcedNepotism
theoreticalside:Kinselectiontheoryissometimesequatedwiththepropositionthatorganisms
areshapedbynaturalselectiontomaximizetheirinclusivefitness.Butthisresultrestsonthe
assumptionthatforeachactorinagroup,wecanseparateoutanindependentcontribution
thatshemakestothewell-beingofherkin[4].Thisamountstotreatingkinselectionasacol-
lectionofone-persongames.
Howeverkinselectiongetsmorecomplicatedwhenthereismoreinthewayofstrategic
interactionamongactors.Considerasimplemodelwhichcombinesgametheoryandpopula-
tiongenetics,theBrothersKaramazovGame[5].Thegameisplayedamongthreebrothers,
withacoefficientofrelatednessr=1/2foreachpair.Onebrotherisapotentialrecipientof
altruism,andtheothertwoarepotentialdonors,sowearelookingatatwo-persongame
betweenthetwodonorsregardinghowtheytreatthethird.Toestablishabenchmarkfor
comparison,webeginwitheachofthetwopotentialhelpersdecidingindependentlyofthe
otheronewhethertohelptheirneedysibling.Inthiscase,theevolutionofaltruismisgov-
ernedbyHamilton’sRule.Eachbrothershouldhelpaslongashiscostcandtheneedybroth-
er’sbenefitbsatisfy1/2(cid:1)b>c.Butnowconsiderthecasewherethetwopotentialhelpers
adoptastrategyofconditionalnepotism:eachwillprovideextrahelpaslongastheotherdoes
thesame.Itistemptingtoanalyzethispackagedealusinginclusivefitnesstheory,withcosts
andbenefitstoone’ssiblingscountingforhalfasmuchascoststooneself.Bythisaccounting,
withtwobrotherstakingturns,eachonhisturnpayingcostcandprovidingbenefitbtothe
third,theruleforaltruismis2/3(cid:1)b>c.Butamorecarefulanalysisusinggeneandgenotype
frequenciesgivesadifferentanswer:theconditionfortheevolutionofaltruismisrC(cid:1)b>c,
whererC=(1+6p)/(2+8p),withpbeingthefrequencyofthealleleforconditionalaltruism.
TheconditionalcoefficientofrelatednessrCincreasesfrom1/2to7/10aspincreasesfrom0
to1.Aconditionalnepotismgenecannotinvadeapopulationwhenveryrare,butcanspread
onceitgainsafoothold.
TheBrothersKaramazovGamedemonstratesseveralthings.First,itshowsthelimitations
ofinclusivefitnessaccounting.Thecalculationbasedonthegenealogicalcoefficientofrelated-
nessof1/2betweensiblingsdoesn’twork,becausetheprobabilitythatthetwohelpersareiden-
tical-by-descentfortheconditionalnepotismalleleisrelatedinacomplicatedwaytothe
strategieseachchooses.Whileinclusivefitnesstheorycanofferqualitativeinsights,ittakesan
explicitpopulationgeneticcalculationtogetthecorrectanswer.Second,themodelprovidesa
proof-of-conceptthatasociallyenforcedrulecanamplifykinaltruism.Theconditionalstrat-
egycanleadeachdonorbrothertobehaveasifhewerecloserkinthanabrother.Onewayto
understandthisistonotethataltruismtowardkinisapublicgood.Whenonebrotherprovides
help,heisalsogivingafreeboosttotheinclusivefitnessoftheotherpotentialhelper,andvice
versa.Aswithotherpublicgoods,moreisprovidedwhenplayersreducefree-ridingbyenforc-
ingagreed-uponrules.Inthiscase,ifwegaugekinaltruismbyc/b,thenconditionalnepotism
beatsindividualnepotismfollowingHamilton’sRulebyupto40percent.
TheBrothersKaramazovGameisperhapsthesimplestpossiblemodelofsociallyenforced
nepotism.Thebulkofthisarticleexploresamoregeneralmodelofann-persongamethat
differsfromtheBrothersKaramazovGameinseveralrespects.First,themodelhereisnot
builtaroundasimpletwo-folddivisionofplayersintothosewhohelpandthosewhoare
helped.Insteaditincludesplayerswitharangeofhelpingabilities.Second,playersinthe
modeldonotrelyonasimpleconditionalstrategytoboostaltruismtokin.Suchastrategy
(“I’llhelpifyoudotoo”)worksfortwohelpers.Butthen-personconditionalstrategy(“I’ll
helpifeveryoneelsedoestoo”)breaksdownfornmuchgreaterthantwo,becauseitimposes
animpossiblystringentunanimityrequirement[6].Instead,playersrelyonindirectreciproc-
ityandhonestadvertisingofabilitytoenforcenormsofsharing.Themodelletsusexplore
thecontrast,andtheevolutionarycontest,betweennormsofbalancedreciprocity(where
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playerjhelpsplayeriasmuchasihelpsj)andgeneralizedreciprocity(wherej,concerned
withherreputationamongotherplayers,helpsievenificannotreciprocate).Manyanthro-
pologistsregardgeneralizedreciprocity,orcommunalsharing[7],asahallmarkofrelations
amongkin.
Thisbringsustotheempiricalmotivationforthepresentwork.Longbeforeevolutionary
biologistsdevisedthetheoryofkinselection,culturalanthropologistsdevelopedtheirown
theoryofkinship—perhapsthediscipline’ssinglegreatestcontributiontothehumansci-
ences.Thestudyofkinshipisimportantbecause,asonescholarwrites,“Inmanysocieties,
bothprimitiveandsophisticated,relationshipstoancestorsandkinhavebeenthekeyrela-
tionshipsinthesocialstructure;theyhavebeenthepivotsonwhichmostinteraction,most
claimsandobligations,mostloyaltiesandsentiments,turned”[8].Thestudyofkinshiphas
resultedinanumberofimportantfindings;ofspecialinteresthereisageneralizationregard-
ingtheconnectionbetweenkinshipandaltruism:“Kindredandkindnessgotogether—two
wordswhosecommonderivationexpresses...oneofthemainprinciplesofsociallife”[9].
Inotherwords,
thecentralvaluepremiseassociatedwith[thenotionofkinship]isuniform.Kinshippredi-
catestheaxiomofamity,theprescriptivealtruismexhibitedintheethicofgenerosity....
[T]heruleposits...that“kinsfolk”haveirresistibleclaimsononeanother’ssupportand
consideration...simplybyreasonofthefactthattheyarekin.Kinsfolkmustideallyshare
...andtheymust,ideally,dosowithoutputtingapriceonwhattheygive.[10]
Theobservationthatpeopleactaltruisticallytowardtheirkinevenwhentheycanexpect
nothinginreturnsoundslikewhatthetheoryofkinselectionpredicts.Butthereisacrucial
complication:humankinshiphasanormativeside,asimpliedbythewords“prescriptive,”
“ethic,”“rule,”and“ideally”above.Howonepersontreatsothers,includingherkin,ispartly
guidedbyherpersonalfeelingstowardthembutalsopartlydictatedbysocialconventions.
Thismeans,accordingtomanyanthropologists,thathumankinaltruismcomesintwovarie-
ties.(Muchoftheevidenceregardingthetwovarietiesofnepotismcomesfromalargebodyof
qualitativeethnographicstudies,butthedistinctionhasalsobeenupheldbyrecentquantitative
research[11,12].)Onevariety(callitindividualnepotism)ismotivatedbybenefactors’feelings
ofattachmenttotheirbeneficiaries.Itislargelydirectedtoclosekin(consistentwithinclusive
fitnesstheory,sincecoefficientsofrelatednessfalloffrapidlywithgenealogicaldistance).The
secondvariety(callitsociallyenforcednepotism)isgovernedbyconventionsabouthowkin
oughttobetreated,andismotivatedbysocialpressureandconcernforone’sstandingina
moralcommunity.Itcanextendeventodistantkin.“[T]hemostconvincingevidence...of
kinshipamity[isfoundin]situationswherekinshipissotenuousastobeonlynominal,as
whenpersonsseekoutremoteclansfolk...andwithoutfurtheradoclaimandreceivehospital-
ityandprotection.”[10]Itissociallyimposednepotismthathelpsmakekinshipimportantnot
justforfamilylife,butforsocialorganizationonalargerscale.
Individualnepotismlooksalotlikekinaltruisminotherspecies[13].Sociallyenforcednep-
otismisdifferent.Itdependsonthemoralregulationofbehavioraccordingtosociallytrans-
mittednorms—somethingregardedbymanysocialscientists,includingsomeevolution-
mindedones,asadistinguishingfeatureofourspecies[14–16].Hencethemodelbelow,com-
bininggametheoryandpopulationgenetics,inwhichthestartingpointisnotanindividual
decidingonherownhowmuchtohelpherkin,butagroupofunequalindividualssettlingon
andenforcinganormdeterminingwhogetshowmuch.
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Results
Distributionalnorms,reputation,andincentives
Imaginesociallifeasadrama[17].Eachindividualplaystherole(s)appropriatetoherstatus,
treatingotherplayersasdirectedbyherroleandtheirs,withallplayersactingfromashared
script.Aspartofthedrama,realcostsarepaidandbenefitsreceived,soaplayerhasanextrin-
sicmotivetosticktothescript:ifshebreakscharacter,otherplayersreactsoastoleaveher
withlowernetbenefits.HereItranslatethisdramaturgicalmetaphorintoagame-theoretical
modelinwhichplayersuseindirectreciprocityandreputationtogetoneanothertoplaytheir
parts.Inthemodel,playersdifferintheirabilitytohelpothers(=status);theyhelpandare
helpedbasedontheiradvertisedabilities(=assumedroles);andeachhasanincentivetohon-
estlyadvertiseherabilitybyfollowingadistributionalnorm(=sharedscript).
Consideragameamongagroupofnplayers.Ineachroundofplay,eachplayerhasthe
opportunitytohelpsomerandomlyselectedtargetplayers.Costsandbenefitsofhelpingare
relatedbytheproductionfunction
b ¼a1(cid:3)tct ð1Þ
ij j ji
wherebijisthebenefitthatireceivesfromj,cjiisthecostthatjincursinhelpingi(bothaver-
agedoveralongspanofplay),αjisameasureofj’sproductiveability,andτgeneratesdimin-
ishingmarginalreturnstohelping,withbij,cji,andαj(cid:4)0,and0<τ<1.
Weareinterestedinindirectreciprocity,whereplayerjproducesbenefitsforplayeribased
onthebenefitsihasproducedforotherplayersinearlierroundsofplay[18–25].Whopro-
duceshowmuchforwhom—thevalueofbij—dependsondistributionalnormsandreputa-
tions.Let’sassumeinitiallythatmembersofagroupagreeonasingledistributionalnorm,call
itA,definedbyafunctionbA[x,y]overx(cid:4)0,y(cid:4)0.Thisfunctiondictateshowmuchbenefita
playerwithabilityxoughttogetfromaplayerwithabilityy.Ifiandjhaveabilitiesαiandαj,
andjfollowsthenorm,thenbij=bA[αi,αj].Supposehoweverthatjcannotassessi’sability
directly,butmustactaccordingtoanascribedability,orreputation,fori.Toachievethis,the
functionbAmustmadetooperateintwodirections,determiningboththebenefitsjproduces
forotherplayersandthereputationothersassignher.First,ifjknowsherownability,αj,and
ascribesabilitysitoplayeri,shecanrewardiaccordingtobij=bA[si,αj].Second,ifsomeplayer
kknowswhatbenefitsjhasproducedforotherplayers,andhasascribedabilitiesforthem,she
canworkbackwardtoassignanewreputation,sj,toj,wheresjisimplicitlygivenbybA(as
spelledoutbelow).Thismeansthatreputationisdefinedrecursively:thereputationofeach
playerdependsonthebenefitsshebestowsonothersandontheirreputations.Theresult,at
equilibrium,isthatreputationequalsability(sj=αj)andplayersreceivebenefitsaccordingto
bij=bA[αi,αj]andpaycostsaccordingtocji ¼a(cid:3)j 1(cid:3)ttbA½ai;aj(cid:5)1=t,foralliandj.
Inprinciple,anynormwithnon-negativebA[x,y]isallowed,includinganormofpure
altruism,“fromeachaccordingtohisability,toeachaccordingtohisneed”(Fig1A).Buthere
weareespeciallyinterestedintheclassofincentive-compatiblestablenorms,whichmotivate
eachself-interestedplayertohonestlyadvertiseherabilitybyfollowingthenorm,provided
othersdolikewise.Astablenormandassociatedreputationfunctionmustsatisfyseveral
conditions.
(i)Positivenetbenefits.Foreachactiveplayerj,summedbenefitsminussummedcostsaver-
agedovermanyroundsofplaymustbegreaterthanzero.
X X
bA½a;a (cid:5)(cid:3)a(cid:3)1(cid:3)tt bA½a;a(cid:5)1=t >0 ð2Þ
j k j i j
k i
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Fig1.Threedistributionalnorms.Howbenefitsshouldbedistributedasafunctionofrecipient(x)anddonor(y)ability,according
tonormsof(A)PureAltruism,(B)AlmostBalancedReciprocity,and(C)GeneralizedReciprocity.Onleft,benefits,b[x,y];onright,
recipientnetbenefits,b[x,y]−c[x,y].Colorsscalewithbenefitsornetbenefits,1.0isred,0.0islightblue.Blacklinesshowwhere
netbenefitsequalzero.
doi:10.1371/journal.pone.0155596.g001
(ii)Penaltyforimpersonation.Foreachactiveplayerj,hersummednetbenefitsmustbe
greaterifshehonestlyadvertisesherability,αj,thanifshe“impersonates”aplayeroflesseror
greaterability,y:
X X
bA½a;a (cid:5)(cid:3)a(cid:3)1(cid:3)tt bA½a;a(cid:5)1=t
j k j i j
Xk Xi ð3Þ
> bA½y;a (cid:5)(cid:3)a(cid:3)1(cid:3)tt bA½a;y(cid:5)1=t
k j i
k i
fory6¼αj.Sosummednetbenefitsmustincrease,neithertooslowlynortooquickly,with
donorability.
(iii)Penaltyforinconsistency.Playerjmightbelessgeneroustosomeplayersandmoregen-
eroustoothersthanisconsistentwithhonestlyadvertisingherabilityajorimpersonatinga
playerwithabilityy:theremightnotbeanyoneysuchthatbij=bA[si,y]foralli.Inthiscase,j
isassignedanintermediateweightedaveragereputation,sj,chosensothatbij<bA[si,sj]for
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someiandbij>bA[si,sj]forotheri.Theaimisnottomakesjanaccurateestimateofαj,butto
penalizejforbehavinginconsistently.Forexample,let
X(cid:2) (cid:3)
0¼ b1=t(cid:3)bA½s;s(cid:5)1=t oðb1ij=t(cid:3)bA½si;sj(cid:5)1=tÞ ð4Þ
ij i j
i
Thisgivessjasanimplicitfunctionofthebenefitsjproduces,bij,andthereputationsofher
P
beneficiaries,si.Supposeω=1.Thentheωtermdropsout,andj’sactualcost,a(cid:3)j 1(cid:3)tt ibi1j=t,is
P
equaltothecost,a(cid:3)1(cid:3)tt bA½s;s(cid:5)1=t,shewouldpayifsheconsistentlyimpersonatedaplayer
j i i j
withabilitysj.Soinconsistentplaygetsherthesamereputation,forthesamecost,asconsistent
play.Butsupposeinsteadthat0<ω<1.Thenjpaysthesamecostasbefore,butherreputa-
tionisnowlower,becausesubparbij’saremoreheavilyweighted,andreducesjmorethan
excessivebij’sincreaseit.Sowemake0<ω<1:eitherjisconsistent,andgetstheappropriate
sjforhonestadvertisingorconsistentimpersonation,orjisinconsistent,andpaysareputa-
tionalpenalty.
Withadistributionalnormandareputationfunctionthatsatisfytheseconditions,consis-
tenthonestadvertisingisthebeststrategyforeachplayer,aslongasothersfollowthenorm.So
thehonestadvertisingconstraintssetlimitsonwhatdistributionalnormsarestableamong
self-interestedplayers—forexample,thenormmatchingthepayoffsunderpurealtruismisnot
stable.Butwithintheselimits,thereisawiderangeofstablenorms,includingthetwobelow,
whichdifferinhowwelltheytreatweakplayers,andaremeanttocapturetheanthropologist’s
distinctionbetweenbalancedandgeneralizedreciprocity.
AlmostBalancedReciprocity
Onefamilyofdistributionalnormsassignsequalpayoffsinbothdirections,bA[x,y]=bA[y,x]
forallxandy.Playersgetonlyasmuchtheygive,and“thereain’tnosuchthingasafree
lunch.”Wecanpickonememberofthisfamilybyallowingtheweakerplayertoset
bA[x,y]=bA[y,x]toherpreferredvalue,t(cid:3)1(cid:3)ttxforx(cid:6)y.Thisnormisstableunderdirectrec-
iprocity,andalsounderindirectreciprocitywhereplayersestimatereputationsaccordingto
Condition4.
There’sahitch,however.Exactbalancedreciprocity,directorindirect,isnotdynamically
stable.Ifplayersstartsomewhereotherthanatequilibrium,andestimateoneanother’sabilities
basedonpastplay,thenreputationsandbenefitsproduceddon’tconvergeontheequilibrium.
Evensmallperturbationsaredestabilizing.TheunderlyingproblemisfamiliarfromtheIter-
atedPrisoner’sDilemmagame:twotit-for-tatplayersdon’tgettothecooperativeequilibrium
iftheyaren’talreadythere.Intheprisoner’sdilemmacase,thiscanbefixedwithaforgiving
amendmenttothetit-for-tatstrategy[26].Inthepresentcase,theanalogousfixistoset
bA[x,y]slightlyhigherthanbA[y,x]forx<y,withthedifferenceadjustedtosatisfyCondition
3.WecalltheresultingstabledistributionalnormAlmostBalancedReciprocity,orB,with
definingfunctionbB(Figs1Band2).
GeneralizedReciprocity
WithAlmostBalancedReciprocity,astrongplayercouldprovideaweakplayerwithgreater
benefitsatlittleaddedcosttoherself,butdoesn’tdosobecauseitwouldbetoocostlyforthe
weakplayerto(almost)matchtheextrabenefits.Discardingtheprinciplethatexchangesmust
balanceallowsforamoreevendistributionofbenefitsandgreatertotalnetbenefits.Consider
thenormthatmaximizesgroupnetbenefits,subjecttothehonestadvertisingconstraints.
Withthisnorm,astrongplayergivessubstantialhelptoweakplayers,evenentirelyhelpless
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Fig2.ReachingequilibriumwithAlmostBalancedReciprocity.Inagroupof40players,eachplayerj
producesbenefitsforarandom5playersiineachround,followingbBandbeginninginround1usingrandom
privateestimatesofsi.Foreachj,everyotherplayerkcalculatesarevisedsjofherown,afterobservinga
random3ofj’s5randomactsofkindness,bypluggingthe3bij’sandher3unrevisedsi’sintotheimplicit
functiongivenbyCondition4.Foreachj,playerkthenaveragesherrevisedandunrevisedsj’stogeneratenew
sj’sthatwilldeterminehowmuchshehelpsarandom5playersinthenextround.Chartshowsatypicalresult
forarandomplayer’sprivateestimatesofsj’sfor10otherrandomplayersj:hersj’sconvergeonαj’s.
(GeneralizedReciprocitygivessimilarresults.)
doi:10.1371/journal.pone.0155596.g002
playerswithα=0,inordertoupholdherreputationandberewardedbyotherstrongplayers.
Thisissociallyenforcedaltruism.Itislessgenerousthanpurealtruism,becausestrongplayers
needtodobetterthanweakplayerstoencouragehonestadvertising,butmoregenerousthan
AlmostBalancedReciprocity.
Anevenmoregenerousdistributionispossibleifwemaximizetotalnetbenefits,butallowj
someknowledge,notjustofthebenefitsiproduces,butofthecostsipays.Inthiscase,aweaki
helpingothersatsomecosttoherselfcanreceivemorecreditthanastrongerplayerproviding
thesamebenefitsatlesscost[27],makingitpossibletoenforcemoregenerositytowardweak
playerswithoutmotivatingshirkingamongstrongplayers.Hereweuseaversionofadistribu-
tionalnormwithsomeknowledgeofcosts,callingitGeneralizedReciprocity,orG,withdefin-
ingfunctionbG(Fig1C).
Mixedgroups,compromise,andkinselection
Eithernorm,AlmostBalancedReciprocity(B)orGeneralizedReciprocity(G),isstableif
everyoneagreestoit.Butwhathappensifplayersdon’tagree?Evolutionaryconsiderationscan
helpanswerthisquestion.
Consideramixedgroup,inwhichsomeplayersfollownormBandsomefollowG.Insuch
agroup,eachplayerjcanbeassignedtworeputations,sBandsG,dependingonthebenefitsshe
j j
producesandthereputations,sBandsG,ofherbeneficiaries.Wecannumericallycalculatean
i i
equilibrium,atwhichtypeBplayersrewardotherplayersaccordingtotheirsBreputationsand
typeGplayersrewardaccordingtosG(Table1).Wecanfurthercalculatethemeannetbenefits
accruingtoeachtype.SimulationsshowthatingroupswithagivenfrequencyoftypesBand
G,themorecommontypeusuallygetsgreatermeannetbenefits;butinacollectionofgroups
withdifferentfrequenciesofBandG,bothtypesusuallygetgreatermeannetbenefitsinthose
groupswhereBislessfrequentandGmorefrequent(Fig3,lowerportion).
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Table1.Reputationinamixedgroup.Equilibriumreputations,sBandsG,calculatedforamixedgroupof
40playersofvaryingability(α).Arandom20playersfollownormBand20followG;resultsaregivenfor
threerepresentativeplayersofeachtype.Playersaccuratelyassessabilitiesofthoseoftheirowntype,but
under-oroverestimateabilitiesofthoseofunliketype.)
Type α sB sG
B 1.925 1.925 1.156
B 1.025 1.025 .934
B .325 .325 .229
G 1.725 1.958 1.725
G .925 .968 .925
G .125 .178 .125
doi:10.1371/journal.pone.0155596.t001
Nowconsideralargepopulationofgroups,eachofsizenandaveragewithin-grouprelated-
nessr,wheretheoverallfrequencyoftypeBinthepopulationispB.Onaverage,aBplayer
findsherselfinagroupwheretypeBnumbers1+(n−1)(r+pB−r(cid:1)pB),andaGplayerfinds
herselfinagroupwheretypeBnumbers(n−1)(pB−r(cid:1)pB)(lowerarrowsinFig3).Ifnisnot
verysmall,andrisnotverylarge,eithernumberiscloseton(cid:1)pB.Ifnetbenefitsarepropor-
tionaltoincrementsinfitness,thenthecommontype(awayfromtheequalpayoffcrossover
point)isexpectedtohavehigherfitnessinmostgroups.Selectionwithingroups,favoringthe
commontype,isstrongerthanselectionbetweengroups,favoringG.Whicheverdistributional
normstartsoutathighfrequencygoestofixation.
Yetthesurvivalofthecommonestisnottheendoftheevolutionarystory.Theequilibrium
wheresomegroupmembersplayBandothersGisnotaNashequilibrium.Individualsof
Fig3.Mixedgroups.Averagenetbenefitsinmixedgroupsof40players,withnBplayingAlmostBalanced
ReciprocityandnGplayingGeneralizedReciprocity—orwiththetwotypescompromisingonanintermediate
norm—basedonrandomsamplingofplayerswithdifferingabilities.Linesshowquadraticbestfitstopoints.
Arrowsshowthatwithamodestcoefficientofrelatedness(r=.06,suggestedby[5,28])andnocompromise,
araretypeGdoesworsethanacommontypeB,butwithcompromise,araretypeGdoesbetter.
doi:10.1371/journal.pone.0155596.g003
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eithertypecandobetteriftheydon’tsticktotheirpreferredstrategy,butadapttothepresence
oftheothertype.Suchaccommodationwithinamixedgroupcantakevariousforms.
First,allplayerscancompromiseonanintermediatestrategy.Acompromisedistributional
norm(callitW)canbedefinedbyaparameterw ,with0<w <1,suchthatthesummednet
0 0
benefitreceivedbyaplayerwithabilityyisaweightedmeanofthesummednetbenefits
receivedbyayplayerundernormsBandG,withweightsw and1−w .Foragivenw ,abene-
0 0 0
fitfunctionbWcanbedefinedsuchthatthecorrespondingnormWisstable,givingeachplayer
anincentivetohonestlyadvertiseherabilitiesaslongasothersfollowthenorm.Hereweallow
eachgrouptosettleonthew forwhichbW1/τgivesaleast-squaresbestfittob1=tfortypeBand
0 ij
typeGplayers.
Whenplayerscompromiselikethis,simulationsgivedifferentresultsthanwhentheydon’t
(Fig3).BothtypesdobetterwhentheysettleonanintermediatenormW.Furthermore,
amongcompromisinggroupswithagivenfrequencyoftypesBandG,Busuallydoesslightly
betterthanG.Thisisbecausestrongplayershavemoreinfluenceonthevalueofw thanweak
0
players.IngroupswheremoreofthestrongplayersaretypeB,theB’s“vote”greaternetbene-
fitsforthestrongestplayers,themselves;wheremoreofthestrongplayersaretypeG,theG’s
“vote”greaternetbenefitsfortheaverageplayer.ButGcanstillprevail:withpositivewithin-
grouprelatedness,typeGplayersaremorelikelytofindthemselvesingroupswithextratype
Gplayers(upperarrowsinFig3).StrongGplayers’supportforhighermeannetbenefitsin
thesegroupscangiveGagreateraveragefitness.
Inanalternativeformofcompromise,typeBandGplayerspersistinplayingtheirrespec-
tivestrategies,whileathirdtypeofplayer,typeW,adoptsthecompromisestrategycorre-
spondingtothegroup’sleast-squaresw .Experimentationwitharangeofparametervalues
0
showsthatingroupswhereBandGplayersrefusetocompromise,typeW—amoralchame-
leonwhotakesontheaveragecolorofhersurroundings—generallydoesbetter(Fig4).Once
typeWreacheshighfrequency,selectionchanges,andtheraresttypeisnolongeratsuchadis-
advantage.InapopulationwithaverycommontypeW,raretypeG,lessraretypeB,andmod-
eratewithin-grouprelatedness,atypeGplayermayoftenfindherselfinagroupcontaining
manytypeW’s,severaltypeGkin,andfewertypeB’s.Suchagroupwillleantowardenforcing
agenerous,G-weightednorm,totheadvantageoftypeG.
Socombiningasmallmeasureofprincipledrule-followingwithalargemeasureofself-
interestedcompromiseopensupnewspaceforkinselection.WhentypesBandGcompromise
onnormW,variancewithingroupsdecreases.WhenBandGdon’tcompromiseandthe
compromisingtypeWbecomesmorefrequent,variancebetweengroupsincreases.Eitherway,
compromisestrengthensselectionbetweengroupsrelativetoselectionwithinthem.With
sociallyenforcedaltruism,alittlerelatednesscangoalongway.
Discussion
Abigmotivefordevelopingthetheoryofkinselectionwastheproblemofaltruism:Whydoes
oneorganismsometimeshelpanotherwhenthathelpwillnotbereciprocated?Theanalogous
motivefordevelopingatheoryofsociallyenforcednepotismistheproblemofdistribution:
Howarethegainsfromcooperationdistributed?[29]Whydoessocialexchangesometimes
shadeintouni-directionalgenerosity—balancedreciprocityintogeneralizedreciprocity?
Previoustheory[19]andevidence[30,31]showthatindirectreciprocitycanmotivatecoop-
erationintheformofcontributionstopublicgoods.Themodeldevelopedheregoesfurther.It
issimultaneouslyaboutmotivatingcooperationandaboutdistributingthegainsfromcoopera-
tionamongplayersofunequalabilities.Kinshipispartofthestorybecauseevenmodestcoeffi-
cientsofrelatedness—toolowtomotivatemuchindividualnepotism—canturntheproblemof
PLOSONE|DOI:10.1371/journal.pone.0155596 June15,2016 9/13
SociallyEnforcedNepotism
Fig4.Threetypes.StreamplotofselectionvectorsforpopulationswithfractionspB,pG,andpWplaying
AlmostBalancedReciprocity,GeneralizedReciprocity,andaWeightedCompromise.Fitnessesare
proportionaltonetbenefits,averagedoverrandomsamplesofmixedgroupsof40playerswithcoefficientof
relatednessr=.06.BluelineshowsaneutrallystablemixofBandWplayers,greenlineaneutrallystable
mixofGandWplayers.Atswitchpoint,themixtureofBandWisunstable:populationleavesB/Wequilibrium
forG/W,nevertoreturn.Group1:TypicalgroupcompositionexperiencedbyarareGplayerandherrelatives
whentypeWisabsent.TypeG(greencircles;sizestandsforability)isoutnumberedbytypeB(bluecircles).
Group2:TypicalgroupcompositionexperiencedbyarareGplayerandherrelativeswhentypeWis
common.GplayerandherGrelativesoutnumbertypeB;typeWplayers(whitecircles)skewtheirplay
towardGeneralizedReciprocity,amplifyingsmallr.
doi:10.1371/journal.pone.0155596.g004
distributionfromaconstantsumgameintoapublicgoodsgame:allarebetteroffevolution-
arilyifstrongplayersgiveuppotentialnetbenefitstohelpweakplayers.(Aruleofthumb:if
r(cid:7)1/n,thenaplayercanexpectthatothergroupmemberscarrymorecopiesofhergenes
thanshedoes,andsheshould“vote”forthenormthatisbestfortheaverageplayer,evenifit’s
notbestforher.[5])
Theworkhereextendsearlierfindingsthatindirectreciprocitydependsonreputationand
reputationmustbedefinedrecursively,sothateachplayer’sreputationdependsbothonthe
benefitssheprovidesandonthereputationsofthebeneficiaries.Inthemodelhere,reputation
isanindexofability,and,likeability,canvarycontinuously.Sothemodelfacestheproblemof
assigninganumericalreputationtoeachplayerbasedonthereputationsofotherplayers.This
ismorecomplicatedthansimplychoosingtocooperateornotbasedonwhethertheother
playerisingoodorbadstanding.Itisclosetotheproblemofdesigningapage-rankingalgo-
rithmthatranksacollectionofwebpagesbyassigningascoretoeachpagebasedonthescores
ofthepagesthatlinktoit[32].Someofthesameissuesariseinbothcases:forexample,
whetheragivendistributionalnormorpage-rankingalgorithmisdynamicallystableandcon-
vergesonaconsistentresult.
Themodelmustsatisfyafurthersetofconditions.Werequirethatadistributionalnormbe
enforceable(orincentivecompatible):aplayerofwhateverabilityshoulddobetterstickingto
thenorm,ratherthanimpersonatingastrongerorweakerplayerorplayinginconsistently,as
PLOSONE|DOI:10.1371/journal.pone.0155596 June15,2016 10/13