©CopyrightJASSS

PiterDykstra,CorinnaElsenbroich,WanderJager,GerardRenardeldeLavaletteandRinekeVerbrugge(2013)

PutYourMoneyWhereYourMouthIs:DIAL,ADialogicalModelforOpinionDynamics

JournalofArtificialSocietiesandSocialSimulation 16(3)4<http://jasss.soc.surrey.ac.uk/16/3/4.html>

Received:19-Sep-2011Accepted:28-Dec-2012Published:30-Jun-2013

Abstract

WepresentDIAL,amodelofgroupdynamicsandopiniondynamics.Itfeaturesdialogues,inwhichagentsgambleaboutreputationpoints.Intra-groupradicalisationofopinionsappearstobeanemergentphenomenon.Wepositionthismodelwithinthetheoreticalliteratureonopiniondynamicsandsocialinfluence.Moreover,weinvestigatetheeffectofargumentationongroupstructurebysimulationexperiments.Wecomparerunsofthemodelwithvaryinginfluenceoftheoutcomeofdebatesonthereputationoftheagents.

Keywords:DialogicalLogic,OpinionDynamics,SocialNetworks

Introduction

1.1 Socialsystemsinvolvetheinteractionbetweenlargenumbersofpeople,andmanyoftheseinteractionsrelatetotheshapingandchangingofopinions.Peopleacquireandadapttheiropinionsonthebasisoftheinformationtheyreceiveincommunicationwithotherpeople,mainlywiththemembersoftheirownsocialnetwork;moreover,thiscommunicationalsoshapestheirnetwork.Weillustratethiswithsomeexamples.

1.2 Somepeoplehaveradicalopinionsonhowtodealwithsocietalproblems,forexample,theclimateandenergycrisisorconflictsaroundthethemeofimmigration."Radical"referstostrongorextremeconvictions,andadvocatingreformsbydirectanduncompromisingmethods.Duringacriticalevent,suchasanaccidentinanuclearreactor,adebateonthedeportationofayoungasylumseeker,ordiscussiononthesolvencyofanEUmemberstate,opposingradicalopinionsareoftenbroadcasted,whichinrecentyearshasbeenfacilitatedbysocialnetworksites,blogsandonlineposts.Opinionscanhaveastrongimpact,eitherbeingrejectedoracceptedbyothers,whentheyaretransmittedthroughthesocialsystem.

1.3 Iftherearemanyinteractionsinasocialsystem,unexpectedcascadesofinteractionmayemerge,facilitatingforexamplethesurprisingrevolutionsinNorthAfricawiththesupportofFacebook,

andcausingthenearbankruptcyofDexiaafterre-tweetedrumoursoninsolvency.1Thisisbecauseinsuchsocialsystems,theadoptionofaparticularopinionorproductbyasmallgroupofpeoplecantriggercertainotherpeopletoadopttheopinion,whichmaycreateacascadeeffect.However,alsorejectionsofcertainopinionsorproductsmaybeaired.Forexample,anegativeremarkof

JeremyClarkson(TopGear)onelectricalcarsmighthamperasuccessfuldiffusion.2.Thelatterexamplealsoillustratesthatsomepeoplehavemorepowertoconvinceandahigherreputationthanothers,whichcanbepartlyanemergentpropertyofthenumberoffollowerstheyhave.Thesesubsequentadoptionsandrejectionsgiverisetotheformationofsometimesrivallingnetworksofpeoplethatuniteinrejectingtheotherparty.

1.4 Ofparticularinterestaresituationswheregroupsofpeoplewithopposingopinionsandattitudesemerge.Duetothesenetworkeffects,personalopinions,preferencesandcognitionsmaydisplayatendencytobecomemoreradicalduetoselectiveinteractions,whichtranslatesinsocietalpolarisationandconflict.Theseprocessescanberelativelyharmless,liketheongoingtensionbetweengroupsofAppleandMicrosoftusers,butsuchpolarisationprocessesmaygetmoreserious,likethecurrentopinionsonwhethertoabandonortosupporttheEuroandthecontroversyaboutglobal

warming.Thesesocialprocessesmayevengettotallyoutofcontrol,causingviolentactsbylargegroups,suchasincivilwarsorbysmallgroups,suchastheso-calledDönerkillings83in

GermanyandtheHofstadNetwork4intheNetherlands,orbyindividuals,suchastherecentmassacreinUtøya,Norway.

1.5 Intheseandotherexamples,peopleshapetheirbeliefsbasedontheinformationtheyreceivefromother(groupsof)people,thatis,bydownwardcausation.Theyaremorelikelytolistentoandagreewithreputablepeoplewhohaveabasicpositionclosetotheirownposition,andtorejecttheopinionofpeoplehavingdeviantopinions.Theyaremotivatedtoutteranopinion,ortoparticipateinapublicdebate,asareactionontheirownchangingbeliefs,resultinginupwardcausation.Asaresult,inthiscomplexcommunicationprocess,groupsmayoftenwanderofftowardsmoreextremepositions,especiallywhenareputableleaderemergesinsuchagroup.

Tomodeltheprocessofargumentation,andstudyhowthiscontributestoourunderstandingofopinionandgroupdynamics,wedevelopedtheagent-basedmodelDIAL(ThenameisderivedfromDIALogue).Inthispaper,wepresentthemodelDIALforopiniondynamics,wereportaboutexperimentswithDIAL,andwedrawsomeconclusions.OurmainconclusionwillbethatDIALshowsthatradicalisationinclustersemergesthroughextremizationofindividualopinionsofagentsinnormativeconformitymodels,whileitispreventedininformationalconformitymodels.Here,normativeconformityreferstoagentsconformingtopositiveexpectanciesofothers,whileinformationalconformityreferstoagentsacceptinginformationfromothersasevidenceaboutreality(Deutsch&Gerard1955).

1.6 DIALisamulti-agentsimulationsystemwithintelligentandsocialcognitiveagentsthatcanreasonaboutotheragents'beliefs.ThemaininnovativefeaturesofDIALare:

Dialogue—agentcommunicationisbasedondialogues.Argumentation—opinionsareexpressedasarguments,thatis,linguisticentitiesdefinedoverasetofliterals(ratherthanpointsonalineasinSocialJudgementTheory(Sherif&Hovland1961).Gamestructure—agentsplayanargumentationgameinordertoconvinceotheragentsoftheiropinions.Theoutcomeofagameisdecidedbyvoteofthesurroundingagents.Reputationstatus—winningthedialoguegameresultsinwinningreputationstatuspoints.Socialembedding—whointeractswithwhomisrestrictedbythestrengthofthesocialtiesbetweentheindividualagents.Alignmentofopinions—agentsadoptopinionsfromotheragentsintheirsocialnetwork/socialcircle.

1.7 AnearlierversionofDIALhasbeenpresentedinDykstraetal.(2009).AnimplementationofDIALinNetLogoisavailable.5

1.8 DIALcapturesinteractionprocessesinasimpleyetrealisticmannerbyintroducingdebatesaboutopinionsinasocialcontext.Weprovideastraightforwardtranslationofdegreesofbeliefsanddegreesofimportanceofopinionstoclaimsandobligationsregardingthoseopinionsinadebate.Thedynamicsoftheseopinionselucidateotherrelevantphenomenasuchassocialpolarisation,extremismandmultiformity.WeshallshowthatDIALfeaturesradicalisationasanemergentpropertyundercertainconditions,involvingtheroleofwhetheropinionsareupdatedaccordingtonormativeredistributionorargumentativeredistribution,spatialdistribution,andreputationdistribution.

1.9 TheagentsinDIALreasonaboutotheragents'beliefs.Thisreasoningimpliesthatamuchmoreelaboratearchitecturefortheagent'scognitionisrequiredthanhasbeenusualinagent-basedmodels.Currentlythereisagrowinginterestinthistypeofintelligentagents(Wijermansetal.2008;Zoethout&Jager2009;Helmhout2006),andconsideringtheimportanceofdialoguesforopinionchangeweexpectthatamorecognitiveelaboratedagentarchitecturewillcontributetoadeeperunderstandingoftheprocessesguidingopinionandgroupdynamics.

1.10 Groupformationisasocialphenomenonobservableeverywhere.Oneoftheearliestagent-basedsimulations,theSchellingmodelofsegregation,showshowgroupsemergefromsimplehomophilypreferencesofagents(Schelling1971).Butgroupsarenotonlyaggregationsofagentsaccordingtosomedifferentiatingproperty.Groupshavetheimportantfeatureofpossibleradicalisation,agroup-specificdynamicofopinions.

1.11 InDIAL,agentscompetewitheachotherinthecollectionofreputationpoints.Weimplementtwowaysofacquiringthosepoints.Thefirstwayisbyadaptingtotheenvironment;agentswhoaremoresimilartotheirenvironmentcollectmorepointsthanagentswhoarelesssimilar.Thesecondwayisbywinningdebatesaboutopinions.

Theremainderofthepaperisstructuredasfollows.InSection2wediscusstheoreticalworktopositionDIALwithinawiderresearchcontextofsocialinfluenceandsocialknowledgeconstruction.

http://jasss.soc.surrey.ac.uk/16/3/4.html 1 15/10/2015

InSection3wepresenttheframeworkofdialogicallogic.InSection4wediscussthemodelimplementationinNetLogo,whichisfollowedbySection5,inwhichwereportexperimentalresultsabouttheinfluenceofargumentationandthealignmentofopiniononthesocialstructureandtheemergenceofextremeopinions.Section6providesourinterpretationoftheseresults.InSection7,weconcludeandprovidepointersforfutureresearch.

TheoreticalBackground

2.1 OurtheoreticalinspirationliesintheTheoryofReasonedAction(Ajzen&Fishbein1980)andSocialJudgementTheory(Sherif&Hovland1961).TheTheoryofReasonedActiondefinesanattitudeasasumofweightedbeliefs.Thesourceofthesebeliefsisthesocialcircleoftheagentandtheweightingrepresentsthatotheragentsaremoreorlesssignificantforanagent.Weinterpretbeliefsasopinions,whichisintuitivegiventheevaluativenatureofbeliefs.Inourmodelanagent'sattitudeisthesumofopinionsofmembersofitssocialgroup,eachhavingadistinctimportance.

2.2 SocialJudgementTheorydescribestheconditionsunderwhichachangeofattitudestakesplace,withtheintentiontopredictthedirectionandextentofthatchange.Jager&Amblard(2004)demonstratethattheattitudestructureofagentsdeterminestheoccurrenceofassimilationandcontrasteffects,whichinturncauseagroupofagentstoreachconsensus,tobipolarise,ortodevelopanumberofsubgroups.Inthismodel,agentsengageinsocialprocesses.However,theframeworkofJager&Amblard(2004)doesnotincludealogicforreasoningaboutthedifferentagentsandopinions.

2.3 Carley'ssocialconstructionofknowledgeproposesthatknowledgeisdeterminedbycommunicationdependentonanagent'ssocialgroup,whilethesocialgroupisitselfdeterminedbytheagents'knowledge(Carley1986;Carleyetal.2003).WefollowCarley'sideaofconstructuralism:

''Constructuralismisthetheorythatthesocialworldandthepersonalcognitiveworldoftheindividualcontinuouslyevolveinareflexivefashion.Theindividual'scognitivestructure(hisknowledgebase),hispropensityto

interactwithotherindividuals,socialstructure,socialmeaning,socialknowledge,andconsensusareallbeingcontinuouslyconstructedinareflexive,recursivefashionastheindividualsinthesocietyinteractinthe

processofmovingthroughaseriesoftasks.[...]Centraltotheconstructuralisttheoryaretheassumptionsthatindividualsprocessandcommunicateinformationduringinteractions,andthattheaccrualofnewinformation

producescognitivedevelopment,changesintheindividuals'cognitivestructure.''(Carley1986,p.386)

2.4 Insummary,agents'beliefsareconstructedfromthebeliefsoftheagentstheyinteractwith.Ontheotherhand,agentschoosetheirsocialnetworkonthebasisofthesimilarityofbeliefs.ThiscapturesthemainprincipleofFestinger'sSocialComparisonTheory(Festinger1954),statingthatpeopletendtosociallycompareespeciallywithpeoplewhoaresimilartothem.Thisphenomenonof''similarityattracts"hasbeendemonstratedtoapplyinparticulartothecomparisonofopinionsandbeliefs(Sulsetal.2002).Lazarsfeld&Merton(1954)usethetermvaluehomophilytoaddressthisprocess,statingthatpeopletendtoassociatethemselveswithotherssharingthesameopinionsandvalues.Tocapturethis''similarityattracts''processinourmodel,weneedtomodelthesocialconstructionofknowledgebi-directionally.Hence,agentsinthemodelprefertointeractwithagentshavingsimilaropinions.

2.5 Thedevelopmentofextremizationofopinionshasalsobeentopicofinvestigationinsocialsimulation.Therearedifferentapproaches,seeforexample(Franksetal.2008;Deffuantetal.2002;Deffuant2006).Existingcognitivearchitecturesofferanagentmodelwiththecapabilityofrepresentingbeliefs,butprimarilyknowledgeisrepresentedintheformofevent-responsepairs,eachrepresentingaperceptionoftheexternalworldandabehaviouralreactiontoit.Weareinterestedinbeliefsintheformofopinionsratherthaninactionsandinsocialopinionformationratherthaneventknowledge.

2.6 Whatmattersforourpurposesarethesocio-cognitiveprocessesleadingtoasituationinwhichagroupofagentsseewhereopinionsradicaliseandout-groupsareexcluded.Tomodeltheemergenceofagroupideology,weneedagentsthatcommunicatewitheachotherandarecapableofreasoningabouttheirownopinionsandtheopinionstheybelieveotheragentstohave.Thebuoyantfieldofopiniondynamicsinvestigatestheseradicalisationdynamics.Asingroupformationwealsohavehomophilypreferences,usuallyexpressedinthe''boundedconfidence''(Huetetal.2008;Hegselmann&Krause2002)oftheagents.Boundedconfidencemeansthatinfluencebetweenagentsonlyoccursifeithertheiropinionsarenottoofarapart,oroneisvastlymoreconfidentofitsopinionthantheother.

2.7 Thedistinctionbetweeninformationalandnormativeconformitywasintroducedby(Deutsch&Gerard1955).Theydefineanormativesocialinfluenceasaninfluencetoconformwiththepositiveexpectationsofanother.Bypositiveexpectations,DeutschandGerardmeantorefertothoseexpectationswhosefulfillmentbyanotherleadstoorreinforcespositiveratherthannegativefeelings,andwhosenonfulfillmentleadstotheopposite,namelytoalienationratherthansolidarity.Conformitytonegativeexpectations,ontheotherhand,leadstoorreinforcesnegativeratherthanpositivefeelings.ThisinfluenceisimplementedinDIALbyincreasing(ordecreasing)eachcyclethereputationofallagentsproportionaltotheirsimilaritywiththeirenvironment(thepatchestheyareon).AninformationalsocialinfluenceisdefinedbyDeutschandGerardasaninfluencetoacceptinformationobtainedfromanotherasevidenceaboutreality.Thisisimplementedbytheadjustmentofthereputationaccordingtotheoutcomeofdebatesaboutpropositions.

2.8 Cialdini&Goldstein(2004)usethisdistinctionbetweeninformationalandnormativeconformityintheiroverviewarticleonsocialinfluence.Motivatedby(Kelman2006;Kelman1958),theyaddanotherprocessofsocialinfluence:compliance,referringtoanagent'sacquiescencetoanimplicitorexplicitrequest.CialdiniandGoldsteinrefertoasetofgoalsofcompliance:

1. Accuracy.Thegoalofbeingaccurateaboutvitalfacts.2. Affiliation.Thegoaltohavemeaningfulrelations.3. Maintainingapositiveself-concept.Onecannotadoptindefinitelyallkindsofopinions.Aconsistentsetofvalueshastoremainintactforapositiveselfimage.

ThesegoalsalsohavetheiroriginintheworkofKelmanwheretheyarecalled:interests,relationshipsandidentities(Kelman2006).

2.9 Foramorecomplexsocialreasoningarchitecture,seeforexample(Sun2008;Breigeretal.2003).Theprogram''Construct''isasocialsimulationarchitecturebasedonCarley'swork,see(Lawler&Carley1996).Thereisalsoresearchconcerningsocialknowledgedirectly.Helmhoutetal.(2005)andHelmhout(2006),forexample,callthiskindofknowledgeSocialConstructs.Neithertheiragents,northeagentsin(Sun2008;Breigeretal.2003),haverealreasoningcapabilities,inparticulartheylackhigher-ordersocialknowledge(Verbrugge2009;Verbrugge&Mol2008).

2.10 Representingbeliefsintheformofalogicofknowledgeandbeliefseemswellsuitedforthekindofhigher-orderreasoningweneedtorepresent,seeforexample(Fagin&Halpern1987).Themostprevalentlogicapproachesformulti-agentreasoningareeithergame-theoretic,forexample,(vanBenthem2001),orbasedondialogicallogic,forexample,(Walton&Krabbe1995;Broersenetal.2005).Neitheroftheselogicapproachesiswellsuitedforagent-basedsimulationduetotheassumptionofperfectrationality,whichbringswithitthenecessityforunlimitedcomputationalpower.

2.11 This''perfectrationalityandlogicalomniscience"problemwassolvedbytheintroductionoftheconceptofboundedrationalityandtheBelief-Desire-Intention(BDI)agent(Bratman1987;Rao&Georgeff1995;Rao&Georgeff1991).TheBDIagenthasbeenusedsuccessfullyinthecomputersciencesandartificialintelligence,inparticularfortasksinvolvingplanning.See(Dunin-Keplicz,B.&Verbrugge2010,Chapter2)foradiscussionofsuchboundedawareness.Learninginagame-theoreticalcontexthasbeenstudiedby(Macy&Flache2002).ThereareextensionstothebasicBDIagent,suchasBOID(Broersenetal.2001a;Broersenetal.2001b),integratingknowledgeofobligations.ThereisalsoworkonasociallyembeddedBDIagent,forexample(Subagdjaetal.2009),andonagentsthatusedialoguetopersuadeandinformoneanother(Dignumetal.2001).

2.12 Inagent-basedsimulation,theagentmodelcanbeseenasaverysimpleversionofaBDIagent(Helmhoutetal.2005;Helmhout2006).Agentsinthosesimulationsmakebehaviouraldecisionsonthebasisoftheirpreferences(desires)andinreactiontotheirenvironment(beliefs).Theirreasoningcapacityissolelyaweighingofoptions;thereisnofurtherreasoning.Thisispartlyduetosocialsimulationsengagingwithlarge-scalepopulationsforwhichanimplementationofafullBDIagentistoocomplexaswellaspossiblyunhelpful.TheseBDIagentsarepotentiallyover-designedwithtoomuchdirectawareness,forexamplewithobligationsandconstraintsbuiltintothesimulationtostartwithratherthanmakingthememergentphenomena.Themainproblemwithcognitivelypooragentsisthat,althoughemergenceofsocialphenomenafromindividualbehaviourispossible,wecannotmodelthefeedbackeffectthesesocialphenomenahaveonindividualbehaviourwithoutagentsbeingabletoreasonaboutthesesocialphenomena.Thiskindoffeedbackisexactlywhatgroupradicalisationinvolvesincontrasttomeregroupformation.

2.13 Inrecentyearsinthesocialsciences,therehasbeenalotofinterestinagents'reputationasameanstoinfluenceotheragents'opinions,forexampleinthecontextofgames(Brandtetal.2003).McElreath(2003)notesthatinsuchgames,anagent'sreputationservestoprotecthimfromattacksinfutureconflicts.Inthecontextofagent-basedmodelling,Sabater-Miretal.(2006)havealsoinvestigatedtheimportanceofagents'reputations,notingthat''reputationincentivescooperationandnormabidinganddiscouragesdefectionandfree-riding,handingouttoniceguysaweaponforpunishingtransgressorsbycooperatingatameta-level,i.e.atthelevelofinformationexchange",seealso(Conte&Paolucci2003).Thisdescriptioncouplesnormswithinformationexchange,inwhich,forexample,agentsmaypunishotherswhodonotsharetheiropinion.WewillincorporatetheconceptofreputationasanimportantcomponentofourmodelDIAL.

ThemodelDIAL

3.1 Inthissection,wepresentthemodelDIAL.Firstwementionthemainingredients:agents,statements,reputationpoints,andthetopicspace.ThenweelaborateonthedynamicsofDIAL,treatingtherepertoireofactionsoftheagentsandtheenvironment,andtheresultingdialoguegames.

IngredientsofDIAL

3.2 DIALisinhabitedwithsocialagents.Thegoalofanagentistomaximizeitsreputationpoints.Anagentcanincreaseitsnumberofreputationpointsbyutteringstatementsandwinningdebates.Theywillattackutterancesofotheragentsiftheythinktheycanwinthedebate,andtheywillmakestatementsthattheythinktheycandefendsuccesfully.

3.3 Agentsarelocatedinatopicspacewheretheymaytravel.Topicspaceismorethana(typicallylinear)orderingofopinionsbetween(typically)twoextremeopinions.Ontheonehand,itisaphysicalplaygroundfortheagents;ontheotherhand,itspointscarryopinions.Thepointsintopicspace'learn'fromtheutterancesoftheagentsintheirneighbourhoodinasimilarwayasagents

http://jasss.soc.surrey.ac.uk/16/3/4.html 2 15/10/2015

learnfromeachother.InDIAL,topicspaceismodeledastwo-dimensionalEuclideanspace.Itservesthreefunctions:

1. Agentsmovetowardsthemostsimilarotheragent(s)initsneighbourhood.Thedistancebetweentwoagentscanbeconsideredasameasurefortheirsocialrelation:thisresultsinamodelforsocialdynamics.Movingaroundintopicspaceresultsinchangingsocialrelations.

2. Thetopicspaceisalsoamediumthroughwhichtheutterancesoftheagentstravel.Thelouderanutterance,thewideritsspatialrange.Thelocalloudnessofautteranceisdeterminedbytheproductofthespeaker'sreputation,thesquarerootofthedistancetothespeaker'spositionandaglobalparameter.

3. Moreover,thepointsinthetopicspacecarrythepublicopinions:theylearnfromtheutterancesoftheagentsintheirneighbourhoodinasimilarwayasagentslearnfromeachother,usingtheacceptancefunctionAdefinedinAppendixB.Whileagentsdecidetoacceptanutterancefromanotheragentbasedontheirrelationwiththespeakeranditsreputation,acceptorignoreit,orrememberitforafuturepersonalattackonthespeaker,theacceptancebythetopicspaceisunconditionally,anonymousandwithoutcriticism.Opinionsaregraduallyforgottenduringeachcycle.Evidenceandimportanceofeachpropositiongraduallyconvergetotheirneutralvalue(0.5,meaningnoevidentopinion).

Asaconsequenceoftheirmovingtosimilarothers,agentstendtoclustertogether.Bythelearningmechanismofthepointsinthetopicspace,thelocationofaclusteracquiresthesameopinionsasitsinhabitants.Thisleadstoa'home'locationfortheagentsintheclusterwheretheyfeelcomfortable.Theclustershavenoexclusivemembership:anagentmaybeatthecentreofacluster,atitsborderorevenintheoverlapoftwoclusters.

3.4 Topicspacediffersfromphysicalspaceinthefollowingrespects.

1. Anagentcanonlybeatonephysicalplaceatthesametime,butitcanholdcompletelydifferentpositionsintwoindepenenttopicspaces.Soforindependenttopicswecanmeaningfullyhaveseparatespaces,whichenablescompleteindependenceofmovementofopinion.

2. Formorecomplextopicswecanhavemorethantwodimensions,ifwewantouragentstohavemorementalfreedom.

DynamicsofDIAL

3.5 ArunofDIALisasequenceofcycles.Duringacycle,eachagentchoosesandperformsoneofseveralactions.Aftertheactionsoftheagents,thecycleendswithactionsoftheenvironment.Thechoiceisdeterminedbytheagent'sopinionsandits(recollectionofthe)perceptionofitsenvironment.

3.6 Tomodeltheirsocialbeliefsadequately,theagentsneedtobeableto

1. reasonabouttheirownandotheragents'beliefs;2. communicatethesebeliefstootheragents;3. revisetheirbeliefbase;and4. establishandbreaksocialties.

Thepossibleactionsthatanagentcanperformare:

movetoanotherplace;announceastatement;attackastatementofanotheragentmadeinanearliercycle;defendastatementagainstanattackmadeinanearliercylcle;changeitsopinionbasedonlearning;changeitsopinioninarandomway.

3.7 Theactionsofannouncing,attackinganddefendingastatementarecalledutterances.SeeFigure1.

Figure1:Flowchartofthemainagentactions.Theopinionchangeactionsareleftoutofthisflowchartforsimplicityreasons.

http://jasss.soc.surrey.ac.uk/16/3/4.html 3 15/10/2015

3.8 Attheendofacycle,allagentsforgetallannouncementswhichareolderthan10cycles6.Moreover,thelocalpublicopinioninthetopicspaceisupdatedattheendofacycleinsuchawaythatthetopicspaceforgetsitsownopinionastimepassesbyandnoopinionsareuttered,bydecreasingthedistancebetweentheopinionandtheneutralvaluebyaconstantfactor.

Dialogues

3.9 Webeginwithanexample.

Example1Anyaispartofagroupwheretheyhavejustdiscussedthatschoolsareterriblyunderfundedandthatlanguageteachingfornewlyarrivedrefugeesisparticularlyhardtoorganise.Thisleadstothefollowingdialogue.

1. Anya:Ifwedonothaveenoughfundingandrefugeescreateadditionalcosts,thentheyshouldleavethiscountry.[Ifnobodyopposes,thestatementbecomesthenewpublicopinion,butifBobattacks,...]

2. Bob:Whydoyousaythat?3. Anya:Well,provemewrong!Ifyoucan,Ipayyou1ReputationPointbutifIamrightyouowemearewardof0.50ReputationPoints.[TheseoddsmeanthatAnyaisprettysureaboutthe

truthofthefirststatement.]Everyoneheresaysthatschoolsareunderfundedandthatlanguageteachingposesaburden!4. Bob:Ok,deal.Ireallydisagreewithyourconclusion....5. Anya:Doyouagreethenthatwedonothaveenoughfundingandthatrefugeescreateadditionalcosts?6. Bob:Yesofcourse,thatcanhardlybedenied.7. Anya:Right...–People,doyoubelieverefugeesshouldleavethiscountry?

Clearly,thevotecangoeitherway.TheymightagreeorAnyamighthavemiscalculatedthebeliefsofthegroup.Dependingontheoutcomeofthevote,thepaymentwillbemade.Anyamay,ifsheloses,wanttoleavethegroupsettingorreevaluateheropinion.

3.10 Thesteps1and2formaninformalintroductiontotheannouncementofAnyainstep3,whichexpressesheropinioninaclearcommitment.EveryagentwhohearsthisannouncementhastheopportunitytoattackAnya'sutterance.ApparentlyBobbelievesthattheoddsofwinningadialogueaboutAnya'sutteranceisgreaterthanoneoutofthree,orsimplyhebelievesthatheshouldmakehisownpositioncleartothesurroundingagents.SoBobuttersanattackonAnya'sannouncementinstep4.SinceAnyautteredaconditionalstatement,consistingofapremise(antecedent)andaconsequent,thedialoguegameprescribesthataspecificruleapplies:eitherbothparticipantsagreeonthepremiseandthewinnerofa(sub-)dialogueabouttheconsequentisthewinnerofthedebate,ortheproponentdefendsthenegationofthepremise.InthiscaseAnya'sfirstmoveofdefenceis:demandingagreementofBobonthepremiseofherstatement(step5).Bobhastoagreeonthepremise,otherwisehewilllosethedialogue(step6).Nowallparticipantsagreeonthepremiseandtheconsequentisalogicallysimplestatement,forwhichcasethegamerulesprescribeamajorityvotebythesurroundingagents,Anyaproposestotakeavote.(step7).

3.11 Theannouncementofastatementcanbefollowedbyanattack,whichinitsturncanbefollowedbyadefense.Thissequenceofactionsformsadialogue.Thewinnerofthedialogueisdeterminedbyevaluationoftheopinionsoftheagentsintheneighbourhood.Dependingontheoutcome,theproponent(theagentwhostartedthedialogue)andtheopponent(theattackingagent)exchangereputationpoints.Differentrulesarepossiblehere:

1. Theproponentpaysacertainamount,say1RP(reputationpoint)totheopponent,incaseitlosesthedialogueandgetsnothingincaseitwins.OnlywhenanagentisabsolutelysureaboutSwillitbepreparedtoenterintosuchanargument.

2. Theproponentoffers1RPtotheopponentifitlosesthedialogue,butitreceives1RPincaseitwinsthedialogue.Thisopenstheopportunitytogamble.IftheagentbelievesthattheprobabilityofSbeingtrueisgreaterthan50%,itmayconsideradialogueaboutSasagamewithaprofitableoutcomeinthelongrun.

3. Theproponentmayspecifyanyamountpitispreparedtopayincaseoflosing,andanyamountritwantstoreceiveincaseofwinningthedialogue.

ThefirstrulewasproposedbyGiles(1978)forLorenzentypeofdialoguetodefineasemanticsforexpressionsthatcontainstatisticalpropositions.Theothertwoareourvariantstogetthe

communicationstarted.InDialthethirdoptionisadopted,becauseitnotonlyenablesaproponenttoexpressthedegreeofbelief(ahighp/r-ratio)7inaproposition,likethesecondoption,butitalsoexpressesthegreedtostartadialogueaboutthatproposition(ahighstakeexpressedbyp+r).Thep/r-ratioreflectsanagent'sbeliefintheprobabilityofwinningthedialogue.IfanagentAbelievestowinthedialogueaboutapropositionin2/3ofthecases,itmightconsiderofferingpA=2RPtoarewardrA=1RPastheleastratiothatisstillreasonable.ForanagentBwhodisagreeswithapropositionSwithvaluespBandrB,attackingthatpropositionisarationalthingtodo.If,forexample,forapropostionS,pB/rB<pA/rAholds,thismeansthatopponentBexpectstowinadialoguemoreoftenthantheproponentAbelievesitdoes.

3.12 TheformalconceptofdialogueshasbeenintroducedbyKamlah&Lorenzen(1973),inordertodefineanotionoflogicalvaliditythatcanbeseenasanalternativetoTarski'sstandarddefinitionoflogicalvalidity.ApropositionSislogicallytrueifaproponentofShasawinningstrategy(i.e.theproponentisalwaysabletopreventanopponentfromwinning)foraformaldialogueaboutS.Aformaldialogueisoneinwhichnoassumptionaboutthetruthofanypropositionsismade.Inourdialogues,however,suchassumptionsaboutthetruthofpropositionsaremade:wedonotmodelaformalbutamaterialdialogue.Inourdialoguegame,thewinnerofadialogueisdecidedbyavoteonthepositionoftheproponent.Iftheevidencevalueontheproponent'spositionismore

similartotheproponent,itwins;otherwisetheopponentwins8.

3.13 WenowdescribethedialoguesinDIALinsomewhatmoredetail.

AnannouncementconsistsofastatementSandtwonumbersp,rbetween0and1.Whenanagentannounces(S,p,r),itsays:'IbelieveinSandIwanttoargueaboutit:ifIlosethedebateIpaypreputationpoints,ifIwinIreceiverreputationpoints'.

Theutterancesofagentsareheardbyallagentswithinacertainrange.Thetopicspaceservesasamediumthroughwhichtheutterancestravel.Anagentcanuseanamountofenergycalledloudnessforanutterance.Itdeterminesthemaximumdistanceofotheragentstotheutteringagentthatarecapableofhearingtheutterance.

Anagentmayrespondtoastatementutteredbyanotheragentbyattackingthatstatement.Thespeakerofanattackedstatementhastheobligationtodefenditselfagainsttheattack.Thisresultsinadialogueaboutthatstatement,givingtheopponenttheopportunitytowinpreputationpointsfromthepropopentsreputation,ortheproponenttowinrreputationpointsfromitsopponent.Thechoiceismadebyanaudience,consistingoftheneighbouringagentsofthedebaters,bymeansofamajorityvote.

3.14 FortheacceptanceofaparticularstatementS,weuseaacceptancefunctionA:[0,1]2×[0,1]2 [0,1]2.Howeverthisfunctionisnotdefinedintermsofpay-rewardparameters,butinsteadintermsofevidence-importanceparameters,whichsystemwillbeexplainedinthenextsubsection.SoAhastwo(e,i)pairsasinput(onefromtheannouncerandonefromthereceiver)andcombinesthemintoaresulting(e,i)pair.Theevidenceoftheresultonlydependsontheevidenceoftheinputs,whiletheimportanceoftheresultdependsonthefullinputs.ThedefinitionofAanditspropertiesarediscussedinAppendixB.Wewillshowthattheevidence-importanceparameterspaceisequivalenttothepay-rewardspace,butevidence-importanceparameterspaceprovidesamorenaturalspecificationofanagent'sopinionthanthepay-rewardspace,whichisespeciallyadequatefordealingwiththeconsequencesofwinningandlosingdialoguesintermsofreputation.

3.15 TheacceptancefunctionisusedinDIALinaweightedform:themoreanagenthasheardaboutasubject,thelessinfluentialannouncementsaboutthatsubjectbecomeonthecognitivestateoftheagent.

Thebeliefofanagent:tworepresesentations

3.16 Intheprevioussubsection,wehaveintroducedanannouncementofanagentasatriple(S,p,r)whereSisastatementand(p,r)isapositioninthepay-rewardspace:pandrarethegamblingoddstheagentiswillingtoputonthestatementwinninginaspecificenvironment.Thepay-rewardspaceisatwo-dimensionalcollectionofvaluesthatcanbeassociatedwithastatement.Itcanbeseenasavariantofthefour-valuedlogicdevelopedbyBelnapandAndersontocombinetruthandinformation:seeBelnap(1977)andAppendixA.Inthissubsection,wegiveanexampleoftheuseofpay-rewardvalues,andweintroduceanalternativetwo-dimensionalstructurebasedonevidenceandimportance.

Example2ThreeagentsA1,A2,A3havedifferentopinionswithrespecttosomestatementS:theyaregiveninFigure2.WeassumethatagentA1hasannouncedhisposition(S,0.8,0.2),soitwantstodefendstatementSagainstanyopponentwhoispreparedtopayr1=0.2reputationpointsincaseA1winsthedebate;A1declaresitselfpreparedtopayp1=0.8pointsincaseitlosesthedebate.A2agreeswithA1(theyarebothintheN-Wquadrant),butthetwoagentshavedifferentvaluations.A2believesthattherewardshouldbebigger,r2=0.6,onwinningthedebate,meaningA2islessconvincedofSthanA1.A3disagreescompletelywithbothA1andA2.A3believesthattherewardshouldbetwiceashighasthepay(p3=0.1againstr3=0.2).ThismeansthatA3believesitisadvantageoustoattackA1,becauseitexpectstowin0.8pointsintwooutofthreetimes,withtheriskofhavingtopay0.2pointsinoneoutofthreetimes.SotheexpectedutilityofA3'sattackonA1is0.8*2/3-0.2/3=0.4667.

http://jasss.soc.surrey.ac.uk/16/3/4.html 4 15/10/2015

Figure2:Beliefvaluescanbeexpressedeitherasanevidence–importancepairorasapay–rewardpair.Thediagonal(left)representsevidence=0.5,meaningdoubt.Thearealeft-abovethe

diagonalrepresentspositivebeliefswithevidence>0.5;thearearight-underthethediagonalrepresentsnegativebeliefs(evidence<0.5).SeeExample1formoredetailsaboutthebeliefsof

agentsA1,A2andA3.

Agent Pay Reward Evidence Importance

A1 0.8 0.2 0.8 0.5

A2 0.8 0.6 0.571 0.7

A3 0.1 0.2 0.333 0.15

3.17 Payandrewardarerelatedtotwomoreintrinsicepistemicconcepts:theevidence(e)anagenthasinfavourofastatementandtheimportance(i)itattachestothatstatement.Wewillusetheseparametersasdimensionsoftheevidence-importancespace(tobedistinguishedfromthepay-rewardspace).Theevidenceeistheratiobetweenanagent'spositiveandnegativeevidenceforastatementS.Anevidencevalueof1meansanagentisabsolutelyconvincedofS.Anevidencevalueof0meansanagentisabsolutelyconvincedoftheoppositeofS.Noclueatallisrepresentedby0.5.Animportancevalueof0meansastatementisunimportantand1meansveryimportant.Importanceisexpressedbythesumofbothodds.Thismeansthemoreimportantanissuethehighertheodds.Informula:

e= i=

(Intheunlikelycasethatp=r=0,wedefinee=0.5.)Conversely,wecancomputethe(p,r)-valuesfroman(e,i)-pair

p=2.e. ir=2. i. (1-e)

Thisisillustratedwiththecomputationofthe(e,i)-valuesofthe(p,r)-pointsA1,A2,A3inthetableinFigure2.

3.18 Sincethereasoningcapabilitiesofouragentsarebounded,weneedsomeformofgeneralisation.Verheij(2000)suggeststhatinacourtroomcontext,argumentationcanbemodelledbydefeasiblelogicandempiricalgeneralisationmaybetreatedusingdefaultlogic.Prakkenetal.(2003)provideareviewofargumentationschemeswithgeneralisation.Wemadecommunicationefficientbyprovidingagentswiththecapabilitytogeneralisebyassumingaspecificopiniontoberepresentativeoftheagentsintheneighbourhood.Whenanagentmeetsanotherpreviouslyunknownagent,itassumesthattheotheragenthasbeliefssimilartowhatisbelievedinitsenvironment.Thisruleisjustifiedbythehomophilyprinciple(Sulsetal.2002;Festinger1954;Lazarsfeld&Merton1954),whichmakesitmorelikelythatgroupmembershaveasimilaropinion.

3.19 Muchworkhasbeendoneonthesubjectoftruststartingwith(Lehrer&Wagner1981),whichhasbeenembeddedinaBayesianmodelin(Hartmann&Sprenger2010).Parsonsetal.(2011)presentamodelinanargumentationalcontext.Ourmessage-protocolfreesusfromtheneedtoassumeatrust-relationbetweenthereceiverandthesenderofamessage,becausethesenderguaranteesitstrustworthinesswiththepay-value(p).Wewanttheannouncementofdefensibleopinionstobeaprofitableaction.Soanagentshouldberewarded(r)whenitsuccessfullydefendsitsannouncementsagainstattacks.

TheImplementationofDIAL

4.1 AswementionedintheIntroduction,wehaveimplementedDIALinNetLogo.Inthissection,weelaborateonsomeimplementationissues.

4.2 ThemainloopoftheNetLogoprogramperformsarun,i.e.asequenceofcycles.Agentsareinitialisedwithrandomopinionsonastatement.Anopinionisanevidence/importancepair(e,i) [0,

1]×[0,1].Theprobabilitiesoftheactionsofagents(announceastatement,attackanddefendannouncements,moveinthetopicspace)areindependent(alsocalled:input,control,instrumentalorexogeneous)parametersandcanbechangedbytheuser,evenwhileasimulationisrunning(cf.Figure3).Globalparametersfortheloudnessofspeechandthevisualhorizoncanbechangedlikewise.Attheendofacycle,thereputationpointsarenormalizedsothattheiroverallsumremainsunchanged.

4.3 ThenumberofreputationpointsRPofanagentaffectsitsloudnessofspeech.Thereisagreatvarietyinhowtoredistributethereputationvaluesduringarunofthesystem.Wedistinguishtwodimensionsinthisredistributionvariety.

NormativeRedistributionrewardsbeinginharmonywiththeenvironment.Ineachcycle,thereputationvalueofanagentisincremented/decrementedbyavalueproportionaltothegain/lossinsimilaritywithitsenvironment.ArgumentativeRedistributionrewardswinningdialogues.Winninganattackordefenceofastatementyieldsanincreaseofthepermutationvalueoftheagentinquestion,andlosinganattackordefenceleadstoadecrease.

IntheimplementationofDIAL,theparameterforce-of-NormsregulatesthedegreeofNormativeRedistribution,andtheparameterforce-of-ArgumentsregulatesthedegreeofArgumentativeRedistribution.Thesedimensionsarethemostrelevantfortheemergenceofdifferentbehaviour,andtheywillbethemainfocusinourexperimentswiththeimplementationofDIAL.

4.4 Toillustratedifferencesinbehaviour,wepresenttheresultsoftworunsofDIAL:onewithonlyNormativeRedistribution,anotherwithonlyArgumentativeRedistribution.WeadopttheparametersettingthatisgiveninFigure3.AcompletedescriptionofallparameterscanbefoundinAppendixC.

Figure3:IndependentparametersfortheprogramrunsofFigure4.Thebehaviourrelatedparameters(thoseparametersthatstartwithchance)arenormalizedbetween0and100.Theratioofthevalueoftwobehavioural

parametersisequaltotheratiooftheprobabilitiesoftheperformanceofthecorrespondingactionsbytheagents.

4.5 TheoutcomeofaprogramruncanbevisualizedintheinterfaceofNetLogo.Herewepresentthevaluesoftheimportanceandtheevidenceparameters.Whenanagentuttersastatementthatisnotattacked,ortheagentwinsthedebateaboutastatement,theaccordancebetweentheagentanditsenvironmentincreases.Ifthatstatementwasdifferentfromtherulingopinioninthatarea,it

http://jasss.soc.surrey.ac.uk/16/3/4.html 5 15/10/2015

willbevisualizedasabrightoradarkcloudaroundtheagentintheevidencepaneoftheuserinterfaceofNetLogo.Intheimportancepane,adarkcloudwillappeararoundanagentwhenitutteredastatementthatisinagreementwiththeenvironment,indicatingthatthisstatementlosesimportancebecausetheagentsagreeonit.If,however,theutteredstatementisinconflictwiththerulingopinion,thecolourofthesurroundingcloudwillbecomebrighter,indicatingaconflictarea.Thoseconflictsappearatthebordersbetweendarkandbrightclusters.Astatementmadewillbeslowly'forgotten'andthecloudwillfadeawayastimepasses,unlessastatementisrepeated.

4.6 Mostoftherunsreachastableconfiguration,wheretheparametersvaryonlyslightlyaroundameanvalue.Itappearsthatmostparametersmainlyinfluencethenumberofcyclesneededtoreachastableconfiguration,andonlyinalesserdegreethetypeoftheconfiguration.Figure4andFigure5illustratetwotypesofstablestates:Asegregatedconfigurationandanauthoritarianconfiguration.Agentsarerepresentedbycircles.

SegregatedConfiguration.InFigure4,therearetwoclustersofagents:theblacksandthewhites.Botharedividedintosmallercliquesofmoresimilaragents.Thereisalsoasmallclusterof5-6yellowagentsinthecenterwithamorelooseconnectionthantheformerclusters.Whenthemutualdistanceisgreater,theopinionsdiffermore.DifferencesinRParenotverylarge.Thenumberofdifferentopinionsisreduced;theextremeonesbecomedominant,buttheimportance,reflectingtheneedtoargueaboutthoseopinions,dropswithintheblackandwhiteclusters.However,intheyellowclustertheaverageimportanceishigh.AuthoritarianConfiguration.InFigure5onlyfouragentshavealmostalltheRPpointsandtheotheragentsdonothaveenoughstatustomakeortoattackastatement.Asaconsequence,therearehardlyanyclusters,sothereisnoonetogoto,exceptforthedictatororopinionleaderinwhoseenvironmentopinionsareofminorimportance.However,thedistributionofopinionsinthemindsoftheagentsandtheirimportancehashardlychangedsincethebeginningoftheruns.InthiscasetheRPvaluesbecomeextreme.

Figure4:ApplicationofNormativeRedistribution,leadingafter481cyclestoastablesegregatedstate.Agentsarerepresentedbycirclesandthediameteroftheagentsshowstheirreputationstatus.Intheleftvideo(evidence),theagents'colourindicatestheirevidence,rangingfromblack(e=1)viayellow(e=0.5)towhite(e=0).Forclarityreasonsthecolourofthebackgroundiscomplementarytothe

colouroftheagents:whitefore=1,bluefore=0.5andblackfore=0.Intherightvideo(importance)theimportanceofapropositionisdepicted:whitemeansi=1,blackmeansi=0,andredmeansi=0.5fortheagents;theenvironmenthasthecolourswhite(i=1),green(i=0.5),andblack(i=0).Thelinksbetweentheagentsofaclusterinthevideosdon'thaveanysignificanceinthefollowingexperiments.

(evidence) (importance)

Figure5:ApplicationofArgumentativeRedistribution,leadingafter1233cyclestoastableauthoritarianstate.DimensioningandcolouringasinFigure4.Thelinksbetweentheagentsofaclusterinthevideosdon'thaveanysignificanceinthefollowingexperiments.

(evidence) (importance)

4.7 Itturnsoutthatthechoiceofreputationredistributionisthemostimportantfactorintheoutcomeofthesimulationruns.IfNormativeRedistributionisapplied,thenasegregatedconfigurationwillbetheresult.IfArgumentativeRedistributionisapplied,theresulttendstobeanauthoritarianconfiguration.Wemayparaphrasethisasfollows.Whenargumentationisconsideredimportantintheagentsociety,anauthoritariansocietywillemergewithstrongleaders,alowgroupsegregationandavarietyinopinions.Whennormativityisthemostrewardingcomponentinreputationstatus,asegregatedsocietyemergeswithequalityinreputation,segregation,andextremizationofopinions.

4.8 Inthenextsectionwediscussmoreexperimentsandtheirresults,aimedatinvestigatingtheeffectsofthechoicebetweennormativeandargumentativeredistributionandofotherparametersontheemergenceofsegregated-andauthoritarian-typesocieties.

Simulationexperiments

5.1 Inthissectionweinvestigatetheresultsofseveralsimulationexperiments,focusingonpossiblecausalrelationsbetweentheparameters.Firstweexplainhowthedependent(output,responseorendogeneous)parametersarecomputed.Thenwetakealookathowindividualagentschangetheiropinion,andweinvestigatewhatdeterminesthebeliefcomponentsandtheirdistributionbylookingatthecorrelationbetweenthesimulationparameters.Thisinformationcombinedwithaprincipalcomponentanalysisjustifiestheconstructionofaflowchartrepresentingthecausalrelations.

5.2 Inourexperimentsarunconsistsof200-5000consecutivecycles.Iftheindependentparametersarenotchangedbytheuser,thesituationbecomesstableafter200-500cycles.Weexperimentedwith25-2000agentsinarun.Itturnsoutthatthenumberofagentsisnotrelevantfortheoutcomeoftheexperiments.Weuse80agentsintherunsweperformedforthepicturesfor

http://jasss.soc.surrey.ac.uk/16/3/4.html 6 15/10/2015

reasonsofestheticsandclarity.

5.3 Weshallfocusonsixdependentparametersrelatedtoreputation,evidenceandimportance.Wearenotonlyinterestedinaveragevalues,butalsointheirdistribution.WemeasurethedegreeofdistributionbycomputingtheGinicoefficientwiththeformuladevelopedbyDeaton:

Gini(X)= -

HereX=X1,...,Xnisasequenceofnvalues,sortedinreversedorder,withmeanvalue ;see(Deaton1997).TheGinicoefficientrangesbetween0and1:thelowerthecoefficient,themore

evenlythevaluesaredistributed.

5.4 Thedependentparametersoftherunsthatweshallconsiderintheexperimentsare:

ReputationDistributiontheGini-coefficientofthereputationoftheagents;SpatialDistributiontheGini-coefficientoftheevidenceofthelocationsinthetopicspace;AverageBeliefthemeanvalueoftheevidenceoftheagents;BeliefDistributiontheGini-coefficientoftheevidenceoftheagents;AverageImportancethemeanvalueoftheimportanceoftheagents;ImportanceDistributiontheGini-coefficientoftheimportanceoftheagents.

5.5 Theparameters3-4reflectthebeliefstateoftheagentsandareforthatreasonreferredtoasbeliefparameters.ThevaluesoftheindependentparameterswhichremainunchangedduringtheexperimentarelistedinTable1.SeeAppendixCforanexplanationoftheirmeaning.

Sometypicalruns

5.6 WebeginwithsometypicalrunstoillustratethebehaviourofthedependentparametersinthefourextremesituationswithrespecttoNormativeRedistributionandArgumentativeRedistribution.

5.7 InFigure6,7,8and9,weshowthedevelopmentofthedependentparametersfortheextremeparametervaluesfornormativeandargumentativeredistribution.InFigure6neitherNormativeRedistributionnorArgumentativeRedistributionisactive.TheattentivereadermightexpectablackhorizontallineforReputationDistribution,becausenoneoftheintroducedfactorsthatinfluencereputationaresupposedtobeactive.Howeverthereisanonzeroparameter,lack-of-principle-penalty,whichprescribesareputationpenaltyforagentwhochangetheiropinion.ThesechangesinreputationcauseanincreaseinReputationDistribution.InFigure7andFigure8onlyNormativeRedistributionrespectivelyArgumentativeRedistributionisactive,andinFigure9bothNormativeRedistributionandArgumentativeRedistributionareactive.

Figure6:NeitherNormativeRedistributionnorArgumentativeRedistribution.

Figure7:OnlyNormativeRedistribution.

Figure8:OnlyArgumentativeRedistribution.

http://jasss.soc.surrey.ac.uk/16/3/4.html 7 15/10/2015

Figure9:BothNormativeRedistributionandArgumentativeRedistribution.

Table1:Rangeandchosenvaluesoftheparameters.

Parameter Range Value

chance-announce 0-100 38

loudness 0-20 2.5

chance-walk 0-100 27

stepsize 0-2 0.8

visual-horizon 0-20 5

forgetspeed 0-0.005 0.00106

undirectedness 0-45 26

chance-question 0-100 0

chance-attack 0-100 12

chance-learn-by-neighbour 0-10 0

chance-learn-by-environment 0-10 1

chance-mutation 0-2 0

neutral-importance 0-1 0.5

lack-of-principle-penalty 0-1 0.07

5.8 Weseethatinalltheseextremesituations,SpatialDistributionandAverageBelieftendtorise,whileBeliefDistributionandAverageImportancetendtodecrease.Moreover,ReputationDistributionrisesinthebeginningfromastartvalueofabout0.2toavaluecloseto0.5.Thismaybeattributedtoaninitialprocessofstrengtheningofinequality:agentswithhighreputationgain,thosewithlowreputationlose.

5.9 However,weseeacleardistinctionbetweenthesituationswithhighandwithlowNormativeRedistribution.IfNormativeRedistributionishigh,thenReputationDistributiondecreasesaftertheinitialrise,whileImportanceDistributionfluctuatesaroundanintermediatevalueandSpatialDistributionandAverageBeliefrisetovaluesnear1.TherelativeinstabilityofImportanceDistributionmayberelatedtothelowlevelofAverageImportance.Thesesocietiesqualifyas'segregated',asexplainedinSection4.

5.10 IfNormativeRedistributionislow,ReputationDistributionrisessteadily,andImportanceDistributiondecreasesslowly,whileSpatialDistribution,AverageBelief,BeliefDistributionandAverageImportancetendtolessextremevaluesthaninthehighNormativeRedistributioncase.Theseareauthoritarian-typesocieties.

IndividualChangesofOpinion

5.11 Sofar,wehaveonlyseenplotsofglobalparameters,butwhathappenstoindividualagentsduringarun?Dotheyfrequentlychangetheiropinionornot?Wepresentplotsofthechangeinevidenceduringtworuns,onewithNormativeRedistributionresultinginasegregatedsociety,andonewithArgumentativeRedistributionresultinginanauthoritariansociety.Thereare60agents.Eachagentisrepresentedbyacurveintheplots,whichiscolouredaccordingtoitsinitialopinion.Therainbow-coloursrangefromred(evidence=0)viaorange,yellow,green,andbluetopurple(evidence=1).

http://jasss.soc.surrey.ac.uk/16/3/4.html 8 15/10/2015

Figure10:HistoryoftheindividualdevelopmentoftheevidenceunderNormativeRedistribution(Segregatedconfiguration).

Figure11:HistoryoftheindividualdevelopmentoftheevidenceunderArgumentativeRedistribution(Authoritarianconfiguration).

5.12 Inasegregatedconfiguration(Figure10),theevidenceoftheagentstendstodrifttowardsthevalues0and1.Thepopulationbecomesdividedintotwoclusterswithoccasionallyanagentmigratingfromoneclustertotheother,i.e.changingitsopinioninanumberofsteps.

5.13 Inanauthoritarianconfiguration(Figure11),thedrivingforcestowardstheextremesoftheevidencescaleseemtobedissolved.Occasionally,agentschangetheiropinioninrigidsteps.Butthereisaforcethatpullstheevidencetowardsthecentrewithaconstantspeed.Thisistheresultofaprocessofforgetting,whichismoreorlessinbalancewiththeprocessofextremization.Theagentsareuniformlydistributedoverthecompletespectrumofopinionvalues.

5.14 Thesepicturescorrespondtotheconsensus/polarization-diagramsinHegselmann&Krause(2002).Theydescribesegregationascausedbyattractionandrepulsionforcesbetweenagentswithsimilar,respectivelymoredistinctopinions.Inoursimulationmodelthesegregationissimilar;however,incontrasttoHegselmann&Krause(2002),theforcesarenotsimplyassumed,butinsteadtheyemergeinourmodelfromthedynamicsoftheagents'communication.

Causalrelations

5.15 Wehaveseenthatchangingtheindependentparametersinfluencesthedependentparameters,andwesuggestedsomeexplanationsfortheobservedfacts.Butareoursuggestionscorrect?IsitthecasethattheindependentparameterscontrolReputationDistributionand/orSpatialDistribution,whichontheirturninfluencethebeliefparameters?Orcoulditbetheotherwayaround:areReputationDistributionandSpatialDistributioninfluencedthroughthebeliefparametersAverageBeliefthroughImportanceDistribution?

5.16 OurclaimisthatthecausalrelationsareasshowninFigure12.Welistsomespecificconjectures:

1. ArgumentativeRedistributioninfluencesReputationDistributionpositivelyandSpatialDistributionnegatively.2. ReputationDistributioninfluencesAverageBeliefnegativelyandAverageImportancepositively.3. SpatialDistributioninfluencesAverageBeliefpositivelyandAverageImportancenegatively.

Figure12:Theconjecturedcausalitymodel.Therelevantindependentparametersareonthelefthandside,theotherparametersarethedependentparameters.Arrowsthatdesignateapositive

influencehaveanwhitehead.Ablackheadreferstoanegativeforce.

5.17 Wewilltesttheseconjecturesonthedatafromalargerexperiment.Initially,weperformedrunsof200cycleswith21differentvalues(viz.0,0.05,0.1,...,0.95,1)foreachoftheindependentparametersforce-of-Normsandforce-of-Arguments,computingthesixdependentparameters.Theoutcomessuggestedthatmostinterestingphenomenaoccurintheinterval[0,0.1]offorce-of-Norms.Wethereforedecreasedthestepsizeinthatintervalto0.005,sotheforce-of-Normsvaluesetis(0,0.005,0.01,...,0,095,0.10,0.15,...,0.95,1).Theevidenceandimportancevaluesoftheagentsarerandomlychosenatthestartofarun,andsoarethepositionsoftheagentsinthetopicspace.AllotherparametersarefixedforallrunsandareasinTable1.

5.18 Sincewehavetwoindependentparameters,eachruncanbeassociatedwithapointinsidethesquaredescribedbythepoints(0,0),(0,1),(1,1),(1,0).Thisallowsustoplotthevaluesofthedependentparametersin3d-plots.Foreachdependentparameteraplotisgiven,withthex-y-plane(groundplane)representingtheindependentparameters,andtheverticalz-axisrepresenting

http://jasss.soc.surrey.ac.uk/16/3/4.html 9 15/10/2015

thevalueoftheparameterinquestion.Thecolouringrangesfromgreen(low)viayellow(medium)towhite(high);theothercoloursareshades.

Figure13:ReputationDistribution.

http://jasss.soc.surrey.ac.uk/16/3/4.html 10 15/10/2015

Figure14:SpatialDistribution.

Figure15:AverageBelief.

http://jasss.soc.surrey.ac.uk/16/3/4.html 11 15/10/2015

Figure16:BeliefDistribution.

Figure17:AverageImportance.

http://jasss.soc.surrey.ac.uk/16/3/4.html 12 15/10/2015

Figure18:ImportanceDistribution.

5.19 InallFigures13to18,asignificantdifferencecanbenoticedbetweentheareawithlowNormativeRedistribution(i.e.force-of-Normsvaluesintherange[0,0.1])andtherest.Theseregionscorrespondwithanauthoritariantypeandasegregatedtype,respectively.Surprisingly,thelevelofArgumentativeRedistributiondoesnotseemtobeofgreatinfluence.

5.20 ReputationDistributionishigh(i.e.unevendistribution)whenNormativeRedistributionislow,andlowwhenNormativeRedistributionishigh(Figure13).ThesameholdsforBeliefDistribution(Figure16)andAverageImportance(Figure17),buttoalesserextent.ThereverseholdsforSpatialDistribution,AverageBeliefandImportanceDistribution(Figures14,15and18).

5.21 ThebumpyareainFigure18reflectsthesamephenomenonasshownbytheunstableImportanceDistributionparameterintheFigures7and9andisaresultofthelowAverageImportance.

5.22 Tocomparesegregatedtypeandauthoritariantyperuns,wedistinguishtwodisjointsubsets:thesubsetwithlowNormativeRedistribution(force-of-Normsin[0,0.085],containingtheauthoritariantyperuns)andthesubsetwithhighNormativeRedistribution(force-of-Normsin[0.15,1],containingthesegregatedtyperuns).Eachsubsetcontains18×21=378runs.TheboxplotofthesesubsetsisgiveninFigure19.Itshowsthatbothsubsetsdifferinthevaluerangeofthedependentparameters.Foralldependentparametersweseethatthecentralquartiles(i.e.theboxes)donothaveanyoverlap.AWelchTwoSamplet-testontheImportanceDistributionvaluesofbothsubsetsgivesap-valueof0.000007,whichissmallerthan0.05.Thismeansthattheprobabilitythatbothvaluesubsetshavethesamemeanandthatdeviatonbetweentheaveragevalueofbothsubsetsisbasedoncoincidenceissmallerthan0.05.Therefore,bothsubsetsshouldbeconsidereddifferent.Fortheotherparametersthep-valuesareevensmaller.

5.23 Thisconfirmswhatwehavealreadyseenintheprevioussampleruns(Figures7to8):SpatialDistributionishigherandReputationDistributionlowerinthesegregatedtyperuns.Moreover,AverageBelief,BeliefDistributionandAverageImportancearemoreextremethaninthelowNormativeRedistributionruns,whichiscoherentwiththedifferencebetweensegregatedandauthoritariantyperuns.

Figure19:BoxplotcomparinglowNormativeRedistribution(authoritariantype,lefthandside)andhighNormativeRedistribution(segregatedtype,righthandside).WiththeexceptionofAverageImportance,allparametershave

moreextremevaluesinthehighNormativeRedistributionpart.

Correlationsbetweentheparameters

http://jasss.soc.surrey.ac.uk/16/3/4.html 13 15/10/2015

5.24 Togiveabetterideaaboutthecorrelationbetweentheindependentanddependentparameters,wepresentpairwiseplotsofalltheparameters.Eachtile(exceptthoseonthemaindiagonal)inthesquareof64tilesintheFigures20to23representsthecorrelationplotoftwoparameters.Onedotforeachoftherunsoftheconsideredsubset.Anideaaboutthevalueoftheindependentparametersofeachdotisgivenbyitscolour.Thecoloursrangefromred,forlowvalues,toblue,forhighvalues.

5.25 Figures20and21representthedataofthelowforce-of-Norms(authoritariantype)subset,andFigures22and23representthedataofthehighforce-of-Norms(segregatedtype)subset.Eachtileinthesquareof64tilesintheFigures20to23representsthecombinationoftwoparameters,andcontainsonedotforeachofthe378runsoftheconsideredsubset.Thecolourofadotcorrespondswiththevalueofeitherforce-of-Normsorforce-of-Arguments,andrangesfromred(lowvalue)viaorange,yellow,green,bluetopurple(highvalue).

Figure20:LowNormativeRedistribution(force-of-Normsin[0,0.085]),colouringcorrespondstoNormativeRedistribution.

http://jasss.soc.surrey.ac.uk/16/3/4.html 14 15/10/2015

Figure21:LowNormativeRedistribution(force-of-Normsin[0,0.085]),colouringcorrespondstoArgumentativeRedistribution.

http://jasss.soc.surrey.ac.uk/16/3/4.html 15 15/10/2015

Figure22:HighNormativeRedistribution(force-of-Normsin[0.15,1]),colouringcorrespondstoNormativeRedistribution.

Figure23:HighNormativeRedistribution(force-of-Normsin[0.15,1]),colouringcorrespondstoArgumentativeRedistribution.

5.26 Whenthedotsinasquareformalineshapeinthesouth-westtonorth-eastdirection,theplottedparametershaveapositivecorrelation.Thecorrelationisnegativewhenthelineshaperunsfromnorth-westtosouth-east.Thenarrowerthelineis,thehigherthecorrelation.Theabsenceofcorrelationisreflectedinanamorphicdistributionofdotsoverthesquare.

5.27 WeseethatthenegativecorrelationbetweenAverageBeliefandBeliefDistributionisveryhighinbothdatasets,suggestingthatbothparametersexpressthesameproperty.Theconsequenceisthatthefifthandsixthcolumn(andthefifthandsixthrow)mirroreachother.

5.28 Figure20andFigure21showthatNormativeRedistribution(i.e.force-of-Norms)correlateswithalldependentparameters.ForArgumentativeRedistribution(force-of-Arguments)therearenosuchcorrelations.ThisconfirmsourimpressionfromFigures13to18,thatArgumentativeRedistributionhasverylittleinfluenceonthestatedescribedbythesixdependentparameters.

5.29 AdifferencebetweenlowandhighNormativeRedistributionisthatthecorrelationbetweenthedependentparametersisweakerwhenNormativeRedistributionishigh(withafewexceptions).ItisalsoremarkablethatwhilecombinationsofhighReputationDistributionandhighAverageBeliefarepossibleforlowNormativeRedistribution,itisnotpossibletohavetheopposite:lowReputationDistributionandlowAverageBelief.ThisasymmetrysuggeststhatReputationDistributionitselfhasapositiveinfluenceonAverageBelief–whichseemsnatural–forlowNormativeRedistribution.

5.30 ThematricesinFigure24andFigure25showthecorrelationbetweenallparameters.Theyconfirmtheconjecturesthatweformulatedabove,viz.

http://jasss.soc.surrey.ac.uk/16/3/4.html 16 15/10/2015

1. ArgumentativeRedistributioninfluencesReputationDistributionpositivelyandSpatialDistributionnegatively.2. ReputationDistributioninfluencesAverageBeliefnegativelyandAverageImportancepositively.3. SpatialDistributioninfluencesAverageBeliefpositivelyandAverageImportancenegatively.

5.31 ThecorrelationmatricesalsoshowastrongnegativecorrelationbetweenAverageBeliefandBeliefDistribution(0.99).Moreover,thereisanegativecorrelationbetweenAverageImportanceandImportanceDistribution(-0.80)whenNormativeRedistributionislow.Thissupportsourmostimportantconclusion,namelythatastrongAverageBeliefandlowAverageImportanceimplyaunevendistributionofthesevaluesamongtheagents.Exactlythisisthecauseoftheemergenceofextremeopinionsinthismodel.

5.32 Whenwelookattherelationbetweenthebeliefandimportanceparameters,weseethestrongestcorrelation(0.71)betweenAverageBeliefandImportanceDistribution,whiletheweakestcorrelation(-0.50)isbetweenBeliefDistributionandAverageImportance.Thisbondbetweenbeliefandimportanceisaresultoftherulethattherepetitionofastatementincreasesitsevidence,butdecreasesitsimportance.

Figure24:CorrelationoftheparameterswhenNormativeRedistributionislow.

Figure25:CorrelationoftheparameterswhenNormativeRedistributionishigh.

CorrelationMaps

5.33 Inanattempttovisualizethecausalrelationsbetweentheparameters,wedrawtwocorrelationmaps:Figure26and27,basedonthecorrelationmatrices.Nowcorrelationbetweentwovariablesmayindicatecausation,butthedirectionofcausationisunknown.Thereforeweonlydrawarrows(indicatingapossiblycausalrelation)fromindependentparameters:inallothercases,wedrawonlylines.Thicknessofthelinesisproportionaltothecorrelation.Blacklinesindicatepositivecorrelation;negativecorrelationisdenotedbyredlines.

5.34 Itturnsoutthat,whenNormativeRedistributionislow(Figure26),alldependentvariablesdependonjustoneindependentvariable,viz.NormativeRedistribution.Sowehaveinfactaone-dimensionalsystem.ArgumentativeRedistributionhasaminorpositiveinfluenceonReputationDistribution.WhenNormativeRedistributionishigh(Figure27),itsinfluenceislow,andthecorrelationofNormativeRedistributionwithallvariablesexceptReputationDistributionhasachangedsignincomparisonwiththelowNormativeRedistributionruns.Notallcorrelationsareweakenedhowever:thecorrelationbetweenReputationDistributiononAverageBeliefandBeliefDistributionisstrongerthaninthelowNormativeRedistributioncase.ThecorrelationmapsuggeststhatthechainofcausesstartswithNormativeRedistribution,whichinfluencesReputationDistribution,whichonitsturninfluencesAverageBeliefandBeliefDistribution;andtheyinfluenceAverageImportance,ImportanceDistributionandSpatialDistribution.

http://jasss.soc.surrey.ac.uk/16/3/4.html 17 15/10/2015

Figure26:CorrelationMapforlowNormativeRedistribution.

Figure27:CorrelationMapforhighNormativeRedistribution.

5.35 Forthefollowingobservationweintroducetheconceptofacorrelatedtriplet.Thisisasetofthreeparameterswhereallthreepairsarecorrelated.Itisexpectedthatthenumberofnegativecorrelationsinacorrelatedtripletiseither0or2.Toseethis,imagineacorrelatedtriplet{A,B,C}:whenAandBarenegativelycorrelatedandalsoBandC,itseemsplausiblethatAandCarepositivelycorrelated;sothreenegativecorrelationsareveryunlikely.Similarly,supposeAandBarepositivelycorrelatedandalsoBandC:nowitseemsplausiblethatAandCarepositivelycorrelated;soexactlyonenegativecorrelationisunlikely,too.WeobservethatallcorrelationtripletsinFigure26obeythisrestriction.

5.36 However,whenNormativeRedistributionishigh(Figure27)therearetwocorrelationtripletswhereallcorrelationsarenegative,viz.

{NormativeRedistribution,ReputationDistribution,SpatialDistribution},and{NormativeRedistribution,ReputationDistribution,AverageBelief}

Thisisonlypossibleifthecorrelationsareveryweak.Thismayexplainwhytheinfluenceoftheforce-of-Normsissurprisinglylowwhenitsvalueishigh.Allarrowsleavingfromforce-of-NormsaremuchthinnerthaninFigure26.Theforce-of-Normsvalueseemstohavereachedakindofsaturationlevelmeaningthatastrongerforce-of-Normsdoesnothaveastrongeroutput.

5.37 WeobserveaverystrongnegativecorrelationbetweenAverageBeliefandBeliefDistribution.Thecorrelationissostrongthatitseemsthatbothparametersarerecordersofthesamephenomenon,butthisisnotthecase.ItwouldbeverywellpossibletohaveasimulationstatewithlowAverageBeliefandlowBeliefDistribution,orastatewithhighlevelsforbothparameters,butthisneverhappensascanbeseeninFigure7to8.AsimilarnegativecorrelationexistsbetweenAverageImportanceandImportanceDistribution.Thiscorrelationisalsonon-trivial,andsoisthepositivecorelationbetweenBeliefDistributionandAverageImportance.

5.38 SinceBeliefDistributionispositivelycorrelatedtoAverageImportance,itfollowsthatAverageBeliefandImportanceDistributionarealsopositivelycorrelated.Andbyasimilarconsequence,AverageBeliefandAverageImportancearenegativelycorrelated,andsoareBeliefDistributionandImportanceDistribution.ThecorrelationbetweenAverageBeliefandBeliefDistributionmirrorsthecorrelationbetweenAverageImportanceandImportanceDistribution.Inadditiontothat,wehavethenegativecorrelationbetweenSpatialDistributionandReputationDistribution.SpatialDistributionhasapositivecorrelationwithAverageBeliefandwithImportanceDistribution.

5.39 ThiscorrelationmapsofFigures26andFigure27raisethefollowingquestion:

IsthereahiddenfactorthatmakesNormativeRedistributionloseandinvertitsinfluence?

Searchingforahiddenfactor

5.40 Iftherearehiddenfactors,thequestionis:howmany?Inanattempttoanswerthisquestion,weappliedPrincipalComponentAnalysis(asembodiedintheFactoMineRpackageofR:Lêetal.(2008)).

5.41 Figure28showsthepercentageofthevariancethatcanbeexplainedbythedifferentparameters,assumingtheexistenceof8latentparameters(asisusual).TheplotsshowthatforlowNormativeRedistribution(left)onlythefirstprincipalcomponentisreallyimportant:itexplains64%ofthetotalvariance.ForhighNormativeRedistributiontheimportanceofthemaincomponentdecreases,andfourauxilarycomponentsbecomemoreimportantasexplainingfactors.

5.42 ApplyingPrincipalComponentAnalysis,whichisaformofFactorAnalysis,isjustifiedbyaBartletttest,aKaiser-Meyer-OlkintestandtheRootMeanSquareerrors(ofthecorrelationresiduals).Thep-valueofthehypothesisthattwofactorsaresufficientforlowNormativeRedistribution(and4factorsforhighNormativeRedistribution)islowerthan0.05.TheRootMeanSquareforbothdatasetsarealsobelow0.05.ThenormfortheKaiser-Meyer-Olkintestisthatvalueshavetobehigherthan0.5,whichisthecaseforbothdatasets.TheresultsaregiveninTable2.

Table2:JustificationtestsforPrincipalComponentAnalysis.

Test lowNormativeRedistribution highNormativeRedistribution

factorsforBartletttest 2 4

p-valueBartlett 3.27e-58 1.41e-112

KMO 0.79082 0.65695

RMS 0.045764 0.011741

http://jasss.soc.surrey.ac.uk/16/3/4.html 18 15/10/2015

Figure28:OutcomeofPricipalComponentAnalysisappliedtothecorrelationmatricesforlowandhighNormativeRedistribution.Thedegreeofinfluence

of8postulatedindependentparametersisplotted.

Component eigenvalue percentageofvariance cumulativepercentageofvariance

comp1 5.121246864 64.01558580 64.01559

comp2 1.030778625 12.88473282 76.90032

comp3 0.772543595 9.65679494 86.55711

comp4 0.468223808 5.85279760 92.40991

comp5 0.420790991 5.25988738 97.66980

comp6 0.126523345 1.58154181 99.25134

comp7 0.054744103 0.68430128 99.93564

comp8 0.005148669 0.06435836 100.00000

Figure29:LowNormativeRedistribution.Onlythefirsttwocomponentsaresignificantbecausetheyhaveeigenvalues>1.

Component eigenvalue percentageofvariance cumulativepercentageofvariance

comp1 3.3137638846 41.42204856 41.42205

comp2 1.2416895774 15.52111972 56.94317

comp3 1.1055887273 13.81985909 70.76303

comp4 1.0063573718 12.57946715 83.34249

comp5 0.8456376275 10.57047034 93.91296

comp6 0.3882566455 4.85320807 98.76617

comp7 0.0981938786 1.22742348 99.99360

comp8 0.0005122872 0.00640359 100.00000

Figure30:HighNormativeRedistribution.Components1-4haveeigenvalues>1andaresignificant.

Nowwewanttoknowtheidentityofthesecomponents.ForthelowNormativeRedistributioncaseweknowthatNormativeRedistributionisthemostimportantfactor,andthereforeitislikelythatNormativeRedistributionandthefirstprincipalcomponentareactuallythesame.HowthedependentparameterscanberetreivedfromthecalculatedcomponentsisreveiledintefactormapsofFigure31.ThefactorloadingsforthePrincipalComponentAnalysisofbothdatasetsaregiveninTable4.

5.43 TheleftfactormapofFigure31confirmsthisidea.Herethedependentvariablesarecorrelatedwithtwolatentcomponents.Highcorrelationwithonecomponentisexpressedasanarrowinthedirectionofthatcomponent.Ifbothcomponentsareequallyimportantforthedependentparameter,thearrowhasanangleof45owithbothcomponentaxes.WeseethatthefirstcomponentpositivelyinfluencesNormativeRedistribution,SpatialDistribution,ImportanceDistributionandAverageBelief,whileitinfluencesBeliefDistribution,AverageImportanceandReputationDistributionnegatively.WemayconcludethatthefirstcomponentisinfactNormativeRedistributionandthesecondcomponentisArgumentativeRedistribution,whichhasonlyaweakinfluenceonReputationDistributionandAverageImportance.

5.44 WhenNormativeRedistributionishigh,therightfactormapofFigure31showsthatNormativeRedistributionisnegativelycorrelatedwiththesecondprincipalcomponent.Thefirstcomponent,whichexplainstwicetheamountofvarianceincomparisonwiththesecondcomponent,isBeliefDistribution(ornegatively:AverageBelief).Sothefirstcomponentisatruelatentparameter,anditcorrespondshighlywithBeliefDistribution.Howeveritisnotthesameparameter,becauseBeliefDistributionisadependentparameterandthenewlyfoundlatentparameterisanindependentparameter(causingfactor).ThereforewewillnamethislatentindependentparameterPluriformity.Thisexpressesthedegreeofinequalityinthebeliefsoftheagentsinthepopulation,whichispreciselythemeaningofBeliefDistribution.

5.45 WhenwecomparePluriformitywiththecomponentsinthe(one-dimensional)lowNormativeRedistributioncase,weseethatitisnotorthogonalbutcontrarytotheNormativeRedistributionparameter.Buthowcanalatentorindependentparameteremergeinasimulationsystem?Thiscanbeansweredasfollows.WhenNormativeRedistributionhasreacheditssaturationlevel,thestochasticnatureofagentactionsinthesimulationmodelstillgeneratesvarietyinthemodelstates(thevaluesofthedependentvariablesafter200cycles)oftheexperiment.Thedependenciesthatemergeinthissituation,dependonlyonthepecularitiesoftheunderlyinggame.Principalcomponentanalysisrevealsapossibleexplanatorycomponent(causingforce)forthesedependenciesinDIAL.

5.46 MorecomponentsarerelevantinthecaseofhighNormativeRedistribution;wealsoplottedthefirstcomponentPluriformityagainsttwoothercomponents(Figure32).ItshowsthatthethirdcomponentistoadegreesynonymouswithImportanceDistributionandthefourthcomponentisArgumentativeRedistribution,whichishighlyindependentoftheotherparameters.Sotheotherprincipalcomponentsarethealreadyknownindependentparameters.

http://jasss.soc.surrey.ac.uk/16/3/4.html 19 15/10/2015

Figure31:Factormapcomputedbyforlow(left)andhighNormativeRedistribution(right).

(A)(B)

Figure32:Factormapfor(A)thefirstandthirdprincipalcomponentand(B)thefirstandfourthprincipalcomponent.

(A)(B)

Table3:FactorloadingslowNormativeRedistribution.

Parameter comp1 comp2 comp3 comp4

NormativeRedistribution -0.043130 0.816307 0.135318 0.073938

ArgumentativeRedistribution 0.023861 -0.016411 0.016871 0.115345

SpatialDistribution -0.304245 -0.132709 0.045772 -0.256649

ReputationDistribution 0.885499 -0.441814 0.054505 0.146949

AverageBelief -0.970050 -0.139624 -0.170281 0.044717

BeliefDistribution 0.966860 0.139989 0.180188 -0.039016

AverageImportance 0.689594 0.155347 -0.464526 -0.202780

ImportanceDistribution -0.084827 -0.100561 0.565485 -0.155203

Table4:FactorloadingshighNormativeRedistribution.

Parameter comp1 comp2

NormativeRedistribution 0.896677 0.279955

ArgumentativeRedistribution -0.023683 -0.033705

SpatialDistribution 0.635191 -0.144248

ReputationDistribution -0.861629 -0.283399

AverageBelief 0.928792 -0.387833

BeliefDistribution -0.910489 0.398225

AverageImportance -0.856628 -0.098496

ImportanceDistribution 0.755080 0.309945

http://jasss.soc.surrey.ac.uk/16/3/4.html 20 15/10/2015

Discussion

6.1 Inourmodelweobservethat,whendialoguesdonotplayanimportantroleintheagentsociety(highNormativeRedistributionandlowArgumentativeRedistribution),clustersareformedonthebasisofacommonopinion.Itturnsoutthatthelackofcommunicationbetweenclustersenablestheemergenceofextremeopinions.Ontheotherhand,whentheoutcomesofdialoguesdoplayanimportantrole(lowNormativeRedistributionandhighArgumentativeRedistribution),theformationofclustersbasedonacommonopinionissuppressedandavarietyofopinionsremainspresent.

6.2 PrincipalComponentAnalysishasprovidednewinformationinadditiontotheestablishedcorrelations:

1. Thedirectionofcausationcanbeestablished.NormativeRedistributiondecreasesReputationDistribution,whichhasanegativeinfluenceonAverageBeliefandapositiveinfluenceonBeliefDistribution.AndahigherAverageBelief(extremeness)leadstomoreSpatialDistribution.

2. PluriformityisalatentparameterwhichisthemostimportantfactorinthehighNormativeRedistributionruns.Thisiscounterintuitive;wewouldexpectthatNormativeRedistributionwouldbethemostimportantfactor.

3. WhenNormativeRedistributionislow,DIALprovidesaone-dimensionalmodelwithstrongdependenciesbetweenNormativeRedistributionandallthedependentparameters.4. InthehighNormativeRedistributionrunsthestrongcorrelationsbetweenNormativeRedistributionandthedependentparametersdisappearandtheworkingofalatentforceisrevealed,

whichcorrelatesstronglywiththestronglycoupledAverageBelief-BeliefDistributionpair,whichcorrespondstothenegativeextremismscale.WecalledthisforcePluriformity.5. ArgumentativeRedistributionisthesecondcomponent(explaining13%ofthevariance)inthelowNormativeRedistributionrange.IthasmoreinfluenceonReputationDistributionand

AverageImportanceinthehighNormativeRedistributionruns.6. SpatialDistributionseemstobedirectlyinfluencedbyNormativeRedistributioninthelowNormativeRedistributionarea,butthiseffectcompletelydisappearsinthehighNormative

Redistributionarea.Thenitiscorrelatedtoextremisminthepluralismscale.

6.3 SocialJudgementTheory(Sherif&Hovland1961)describestheconditionsunderwhichachangeofattitudestakesplacebyassimilationandcontrasteffects.InDIALassimilationtotheenvironmentisthesourceofchangesinopinions.Werewardwell-adaptedagentsand/oragentswhowindebateswithahigherreputationstatus.Togetherwithhomophily(Sulsetal.2002;Lazarsfeld&Merton1954),whichisimplementedinthemovebehaviour,itresultsinclustering.Contrasteffectsemergeindirectlyasaresultofthisformofsegregation.Infutureworkwewillinvestigateanagentmodelwithanacceptance-rejectionstrategyforutterancesbasedon(Huetetal.2008;Hegselmann&Krause2002).

6.4 InDIALthedevelopmentofextremizationofopinionsFranksetal.(2008);Deffuantetal.(2002);Deffuant(2006)iscausedbythewaytheacceptancefunctionisdefined.Oncesegregation(spatialdistribution)hastakenplaceandagentsarenotconfrontedanymorewithutterancesofdifferentmindedagents,theagent'sopinionisboundtoextremizewitheachutteranceofaneighbouringagent.ThisexplainsthenegativecorrelationbetweenSpatialDistributionandBeliefDistribution(pluraliformity)(seeFigures26and27).Inourexperimentsweconsideronlyoneproposition.Whenweextendthesimulationtomorethanoneproposition,itwillbemorecomplicatedforagentstoavoiddifferent-mindedagents,whichwillhindertheextremizationprocess(Dykstraetal.2010).

ReputationDistributionanditsrelationwithnormswasstudiedbySabater-Miretal.(2006)andConte&Paolucci(2003).DIALshowsthatReputationDistributionisinhibitedbytheinfluenceofnormsinthelow-force-of-Normscase.Thisnegativeinfluenceevenexistsinthehighforce-of-Normsruns,althoughtheinhibitionbypluraliformityismoreimportant(Figures26and27).ReputationDistributioncannotbeconsideredasanincentivetocooperationasinSabater-Miretal.(2006),becausethereisanegativecorrelationwithSpatialDistribution.Brandtetal.(2003)andMcElreath(2003)notethatingamesagent'sreputationservestoprotecthimfromattacks.ReputationDistributionhasthesameresultinDIAL.ThenumberofattacksdropsinrunswhenReputationDistributionstatusishigh.

6.5 Theinteractionbetweenopinion-andsocialnetwork-dynamics,whichisthebasisofCarley(1986)andFestinger(1954),functionsalsoinDIAL,butincircumstanceswithalowdegreeofSpatialDistributionasocialstructureispracticallyabsentandsocialcontactsarealmostrandom.

ConcludingRemarksandFutureWork

7.1 WehavepresentedDIAL,acognitiveagent-basedmodelofgroupcommunication.Agentsareinvolvedinadialoguegameinwhichtheygamblereputationpointsonthetruthofastatement.Dialogueconflictsareresolvedbyappealtosurroundingagentsinsuchawaythatthemoresupportedstatementwinsthedialogue.OurmodelshowstheradicalisationinclustersthroughextremizationofindividualopinionsofagentsinNormativeRedistributionmodelsandthisphenomenonispreventedinArgumentativeRedistributionmodels.Thisprocessisbasedontwosimpleingredients:movementintopicspace,andcommunicationwithothersindialogues.Themovementintopicspaceensuresthatagentsinteractwithothersdynamicallyandthattheyareabletoalignthemselveswithothersofsimilaropinions.Extremeopinionsaretypicalforisolatedclusters.Toextrapolatetheresultsfromourmodelsimulationstocurrentsociety,wemaytentativelyconcludethat,asfarassocialmedialikeTwitterandFacebookareaboutcreatinganopensociety,theymightbeaneffectiveweaponinfightingextremism.

7.2 Animportantquestionis:

IsDIALrealisticenoughtoreflectthesocialprocessesinhumansociety?

Infutureresearchweplantoanswerthisquestionbytestingmoresocial,psychologicalandcommunicationalaspectsinDIAL.

7.3 Thispaperisthefirstpartofatrilogy.InthesecondpartwewillinvestigatetheextensionofDIALwithFuzzyLogictorepresentagentattitudes(Dykstraetal.2010).Wewillintroduceasetofapartialorderingsonstatements,whichservesasthedomainofthelinguisticvariablesforthecorrespondingfuzzysets.Withthisextension,changesofopinionscanbeexpressedaccordingtoSocialJudgementTheory(Sherif&Hovland1961).

7.4 Inathirdpartofourresearchprogram,wewillinvestigatehowawareagentsneedtobeoftheirrôleinthesocialprocess,inordertoexplainphenomenasuchastheextremizationofopinionsinsociety.Doesitreallymakeadifferencewhethertheypossesstheabilitytoreasonaboutotheragents'beliefsornot?Afteraddingthesenewingredients,weintendtoinvestigatewhatwouldhappeninanormativesociety,whichhasmovedtoanextremeposition,whenitissuddenlyconfrontedwithpreviouslyunusedinformationflowslikethoseprovidedbysocialmedia.Forexample,wouldthissuddenopencommunicationresultinastrongforcetowardsapluriformsociety,ornot?Rephrasedinactualterms:couldtheNorth-Africanrevolutions,whichwerefacilitatedbysocialmedia,resultinastrongforcetowardsapluriformsocietyornot?

AppendixA

The2-dimensionallogicofBelnap&Anderson

A2-dimensionalBelnap&Andersonlogichasbeendesignedforaslightlysimplercase(Belnap3).Supposeanagenthasnopriorknowledgeaboutacertainstatementandaskstwoormoreagentsayes-or-noquestionaboutthematter.Whatareinformationstatestheagentmayachieve?BelnapandAndersonconsideredfouroutcomesthattheagentcouldget:

1. noansweratall({}),alsodenotedby -theagentstillhasnoclue,2. someanswerswereyesandthereweren'tanyno's({true})-theagentbelievesit'strue,3. someanswerswerenoandthereweren'tanyyes's({false})-theagentbelievesit'sfalse-and

4. someansweredyesandsomeansweredno({false,true}),alsodenotedby -theinformationiscontradictory.

Asimilarfour-valuedlogicisalsousedasastartingpointby(Sźałas&Sźałas53)forthedefinitionofaparaconsistentlogic.

Whenwerepresenttheinformationstatesbypairs(p,k)withp,k {0,1},withp=1meaning''thereisayes''andp=0meaning''thereisnoyes''andsimilarfork,thenwehaveour2-

dimensionallogicreducedtofourvalues.Ginsberg,in(Restall45),noticearelationbetweenthesevaluesalongtwoparameterssimilartowhatwedidabove.Hecallsittheamountofbeliefinavalue(t)andtheamountofinformationk(forknowledge).tcorrespondswithournotionofevidence,thedegreeofbeliefanagenthasinthestatement,andkcorrespondswithi-importance-,

althoughithasadifferentinterpretation.Bothrelationsarepartialorders,denotedby and .

InFigure33(a)theareainsidethesquarerepresentsthepossiblebeliefvaluesanagentmayassigntoastatement.Thearrowshaveaspecialmeaning:increasingbeliefandincreasingimportanceasasimultaneousmoveontheR-andP-axis.

http://jasss.soc.surrey.ac.uk/16/3/4.html 21 15/10/2015

Figure33:Thesquareofpossiblebeliefassignments.Belnap'sdiamond(a)andourtwodimensionalbeliefspace(b).k=(amountof)knowledge,t=truthP=Pay,R=Reward.

AppendixB

Computingtheacceptancefunction

WecandistinguishtwoauxiliaryfunctionsAE:[0,1]×[0,1] [0,1]andAI:[0,1]2×[0,1]2 [0,1]with

A((e1,i1),(e2,i2))=(AE(e1,e2),AI((e1,i1),(e2,i2))).

BeforewegivethedefinitionofAEandAI,weformulatesomerequirements:

1. Aiscontinuous,i.e.smallchangesinitsindependentvaluesleadtosmallchangesintheresult;2. AEismonotonic,i.e.whenitsindependentvaluesincrease,theresultincreases;3. Aissymmetric,i.e.A((e1,i1),(e2,i2))=A((e2,i2),(e1,i1));4. AEcommuteswiththenegationfunctionn(x)=1-x,i.e.AE(1-e1,1-e2)=1-AE(e1,e2);5. AEisconfirmative:similarevidenceisreinforced,contradictingevidenceisweakened,i.e.

AE(e1,e2) e1,e2ife1,e2 0.5,

AE(e1,e2) e1,e2ife1,e2 0.5,

e1 AE(e1,e2) e2ife1 0.5 e2;

6. AIiscontroversial:similarevidenceleadstoweakeningofimportance,contradictingevidenceleadstostrengtheningofimportance,so

AI((e1,i1),(e2,i2)) 0.5(i1+i2)ife1,e2 0.5ore1,e2 0.5,

AI((e1,i1),(e2,i2)) 0.5(i1+i2)ife1 0.5 e2.

Theserequirementsaremetbythefollowingdefinitions:

AE(e1,e2) = 2e1e2 ife1,e2 0.5

= 2e1+2e2-2e1e2-1 ife1,e2 0.5

= e1+e2-0.5 otherwise

and

AI((e1,i1),(e2,i2))=0.5(i1+i2)+0.125(2e1-1)(2e2-1)(2i1i2-i1-i2).

CheckingtherequirementsforAEisstraightforward,exceptforthesecondcaseintheconfirmativityrequirements.Forthis,weobserve:ife1,e2 0.5thenAE(e1,e2)=2e1+2e2-2e1e2-1=e1

+(1-e1)(2e2-1) e1,andsimilarforAE(e1,e2) e2.

ForabetterunderstandingofthedefinitionofAI,weobservethat0.25(2e1-1)(2e2-1)playstheroleofagreemementfactor ,rangingfrom-1to1:itispositivewhene1,e2>0.5ore1,e2<

0.5,negativewhen0.5isbetweene1ande2andzerowhene1ore2equals0.5.WecandefineAIalsousing :

AI((e1,i1),(e2,i2))=

Dependingonthevalueofthisagreementfactor,thevalueofAI((e1,i1),(e2,i2))rangesfromi1+i2-i1i2whenc=-1via0.5(i1+i2)whenc=0toi1i2whenc=1.

Moreover,wehavethefollowinglimitpropertiesofA.Supposewehaveasequence(e0,i0),(e1,i1),(e2,i2),...,abbreviatedby((en,in)|n N).Weconsidertheresultsequence((rn,sn)|n

N),obtainedbyrepeatedlyapplyingA:

(r0,s0) = (e0,i0)

(rn+1,sn+1) = A((rn,sn),(en+1,in+1)) foralln N

Whendoes((rn,sn)|n N)convergetoalimit?Toformulatesomeproperties,weusethefollowingnotion:

http://jasss.soc.surrey.ac.uk/16/3/4.html 22 15/10/2015

sequence(xn|n N)iswellbelowaifthereisab<aandam Nsuchthatxn bforalln m;

and'wellabovea'isdefinedsimilarly.Nowwehave:

1. if(en|n N)iswellbelow0.5,thentheresultsequenceof((en,in)|n N)convergestothelimit(0,0);

2. if(en|n N)iswellabove0.5,thentheresultsequenceof((en,in)|n N)convergestothelimit(1,0).

AppendixC

DescriptionoftheModelParameters

Abriefdescriptionoftheindependentanddependentparametersisgivenhere.fortheimplementationdetailsseethelistingoftheDIALprogram.

Independentpararameters:

1. number-of-agents.Thenumberoftheagentsinasimulation.2. number-of-propositions.Thenumberofthepropositionstheagentstalkaboutinasimulation.Inthiscasenumber-of-propositions=1.3. Force-of-Arguments(informational-conformity).Determinesthedegreeinwhichtheagent'sreputationisdeterminedbywinningandlosingdebates.4. Force-of-Norms(normativeconformity).Thedegreeinwhichthereputationisdeterminedbythesimilaritywithitsenvironment.

Parametersinfluencingthechoiceofactions:

Thefolowingparametersdeterminetheprobabilitythatanagentwillchosethecorrespondingaction:

1. chance-announce.Utteranannouncement.2. chance-walk.Movementinthetopicspace.3. chance-attack.Attackarecentlyheardannouncement.(Themostdifferentonefromtheownopinionwiththehighestprobability)4. chance-question.Askanotheragentaboutitsopinion.5. chance-change-stategy.Probabilityofchangingthewalkingdirection(awayfrom,ortowardsfriendsorperpendiculartothebestfriends'position).6. chance-learn-by-neighbour.Learnfromthenearestneighbour.7. chance-learn-by-environment.Learnfromtheaverageopinionontheagents'location.8. chance-mutation.Change(e,i)–valuesofanopiniontoarandomvalue.

Parametersinfluencingbehaviour:

1. loudness.Determinesthedistancethatamessagecantravelforanonymouscommunication.Anonymouscommunicationaffectstheenvironment(patches)andindirectlyitsinhabitantsthroughthelearn-by-environmentaction.

2. visual-horizon.Determinesthemaximumdistancetootheragentswho'smessagescanbeheard(includingthesender,whichisnecessaryforattacking.3. undirectedness.Randomnessofthedirectionofmovement.4. stepsize.Maximumdistancetraveledduringawalk.

Parametersinfluencingreputation:

1. inconspenalty.Penaltyforhavinginconsistentopinions.2. lack-of-principle-penalty.Penaltyforutteringstatementsthatdonotreflecttheagent'strueopinion.

Parametersinfluencingopinion:

1. neutral-importance.Thelevelofimportancetheenvironmentreturnstowhennoannouncementsaremadeandpastannouncementswillbeforgotten.(Typically0.5)2. attraction.Thelargestdistanceintheevidencevalueofanutteredpropositionandtheevidencevalueofthesamepropositionofareceivingagentforwhichthereceiverisinclinedto

adjustitsopinion.3. rejection.Theshortestdistanceintheevidencevalueofanutteredpropositionandtheevidencevalueofthesamepropositionofareceivingagentforwhichthereceiverisinclinedto

attacktheutteredproposition.4. winthreshold.Theminimaldifferencebetweentheevidencevalueoftheproponent's-andtheopponent'spropositionthatforcestheloserofthedebatetochangeitsopinionimmediately

(insteadofindirectlyvialearningbyenvironmentorlearningbyneighbour).

Parametersinfluencingmemory:

1. forgetspeed.Thespeedtheevidence-andimportance-valuesoftheagents'opinionconvergestoneutralvalues(typically0.5).2. neutral-importance.(Maydifferfrom0.5.)

Dependentparameters:

1. ReputationDistribution.Theunequality(gini)ofthedistributionofreputationovertheagentpopulation(report-authority).2. SpatialDistribution.Degreeofclusteringoftheagents(report-clustering).3. AverageBelief.Meandeviationoftheevidencefromtheneutralvalue(0.5)(report-eopop).4. BeliefDistribution.Gini-evidenceofthedeviationoftheevidencefromtheneutralvalue(0.5)(report-ginievid).5. AverageImportance.Meanimportanceoftheopinion(report-iopop).6. ImportanceDistribution.Gini-importanceoftheopinion(report-giniimp).

AppendixD

extensions [array]

turtles-own [ props ; a list of pairs: < evidence importance > ; the evidence of the p-th proposition is: first item p props ; the importance of the p-th proposition is: second item p props init-props ; a list of pairs: < evidence importance > the initial values announcements ; a list of 4-tuples: < key <evidence importance> ticks reputation> attacks ; a list of pairs: < attacking-agent prop > questions ; a list of pairs: < requesting-agent prop > profit-strategy ; list of learned profits for each strategy prior-size ; prior size for profit ; the reputation of an agent is represented by its size ]patches-own [pprops]

globals [

http://jasss.soc.surrey.ac.uk/16/3/4.html 23 15/10/2015

delta ; a small value action-prob-pairs ; a list of odds-action pairs, ; one for each behavioral alternative current-prop ; the proposition which is pictured in the world number-of-props total-odds ; the sum of the odds of all behavioral alternatives change-reputation ; the change of the sum of the reputation of all agents ; during one cycle total-reputation ; the sum of the reputation of all agents filename agentsorderedatstart ; for reporting purposes strategy-shapes ; a list of shapes, one for each strategy ]

; Utility functionsto-report second [l] report item 1 lend

to-report zip [l m] ifelse empty? l [report l] [report fput (list (first l) (first m)) (zip (butfirst l) (butfirst m))]end

to-report sign [x] ifelse x >= 0 [report 1] [report -1]end

; The Acceptance of Announcements

to-report agreementfactor [e1 e2] report (2 * e1 - 1) * (2 * e2 - 1)end

to-report accepte [e1 e2] ifelse e1 < 0.5 [ ifelse e2 < 0.5 [ report 2 * e1 * e2 ][ report e1 + e2 - 0.5 ] ][ifelse e2 < 0.5 [ report e1 + e2 - 0.5 ][ report 2 * e1 + 2 * e2 - 2 * e1 * e2 - 1 ] ] end

to-report accepti [agree i1 i2] report (i1 + i2 + agree * (2 * i1 * i2 - i1 - i2)) / 2end

; environment oriented procedures for accepting announcements and; forgetting. the patches are used for anonymous communication. ; the information of announcements are accumulated in the patches; according to the accept function. forgetting is a; a gradual move towards neutral values ((e,i) = (0.5, 0.5))

to announce-patch [agnt loc evid imp]; patch procedure; input agent is a turtle; update the patches with the information of the announcement; this is proportional to the distance from the agent that made the announcement. let rsquared (distance agnt + 1) ^ 2 let pevid first item loc pprops let pimp second item loc pprops let agree (agreementfactor evid pevid) set pevid 0.5 + ((accepte evid pevid) - 0.5 + rsquared * (pevid - 0.5)) / (rsquared + 1) set pimp ((accepti agree imp pimp) + rsquared * pimp) / (rsquared + 1) set pprops replace-item loc pprops (list pevid pimp)end

; Forgetting means changing gradually the pevidence and pimportance; to a neutral value (which is 0.5)to-report forget-pevidence [pevidence] report pevidence - sign (pevidence - 0.5) * forgetspeed end

to-report forget-pimportance [pimportance] report pimportance - sign (pimportance - neutral-importance) * forgetspeed end

; Agent-agent communication, used in announcements, questions and; replies on attacks.

to update-announcement [w p ev i ] ; w = sender, p = proposition ; update memory

http://jasss.soc.surrey.ac.uk/16/3/4.html 24 15/10/2015

let key number-of-agents * p + w let loc find-location key announcements ifelse loc != false [ set announcements replace-item loc announcements (list key (list ev i) ticks) ; do something with reputation ][ set announcements fput (list key (list ev i) ticks) announcements] ; now the SJT type attraction and rejection let evidence first item p props let importance second item p props let agree (agreementfactor evidence ev) if agree > 1 - attraction [ setopinion p (list (accepte evidence ev) (accepti agree importance i)) ] ; accept p if agree < rejection - 1 [ setopinion p (list (accepte evidence (1 - ev)) (accepti (agreementfactor evidence (1 - ev)) importance i)) ] ; attack agent w on pend

to-report find-location [a b] report position a (map [first ?] b)end

to forget-announcements; all announcements older than 10 ticks are forgotten let yesterday ticks - 10 set announcements filter [ yesterday < item 2 ?] announcementsend

; initialization and the main loop;;to-report random-prop ; to create a proposition with random evidence ; and importance values, used in setup;;report list (random-float 1) (random-float 1);;end

to setup clear-all reset-ticks set delta 1e-5 set number-of-props number-of-propositions set current-prop min (list (position current-proposition ["a" "b" "c" "d" "e" "f" "g" "h" "i" "j"]) (number-of-props - 1)) ;; create turtles with random locations, evidence and importance values set strategy-shapes ["circle" "default" "face happy"] set-default-shape turtles "circle" ask patches [ set pcolor blue set pprops[] repeat number-of-props [ set pprops fput (list 0.5 neutral-importance) pprops] ] crt number-of-agents [ setxy random-xcor random-ycor set props generateopinions set init-props props set announcements [] set attacks [] set questions [] set color scale-color yellow first (item current-prop props) 1 0 set label who set label-color 66 set size (random-float 2) + 1 set profit-strategy [0 0 0] ] set total-reputation sum [size] of turtles setup-plot ;update-plotfile ;; !!!!!!!end

to-report incr-total-odds [ee] set total-odds total-odds + ee report total-oddsend

to-report find-action [c l] while [c > first (first l) ] [set l but-first l] report first lend

to go; Determine the chances of all agent actions according to the values; of the global parameters, chance-announce, chance-question, chance-attack,; chance-walk, chance-learn-by-neighbour, chance-learn-by-environment,; chance-mutation and chance-change-strategy set total-odds 0 set action-prob-pairs (map [list (incr-total-odds ?1) ?2] (list chance-announce chance-question chance-attack chance-walk chance-learn-by-neighbour chance-learn-by-environment chance-mutation chance-change-strategy)

http://jasss.soc.surrey.ac.uk/16/3/4.html 25 15/10/2015

(list "announce" "question" "attack" "walk" "learn-by-neighbour" "learn-by-environment" "mutate" "change-strategy" )) set change-reputation 0 ask turtles [act] ; The forgetting of anonymous information ask patches [ ; to forget set pprops map [ list (forget-pevidence first ?) (forget-pimportance second ?)] pprops ] ; Rounding off: forget announcements, answer some questions which were put ; in this cycle and reply some attacks made by other agents in this cycle. ; These three actions are different from the previous ones by the fact that ; they are performed each cycle, so they are not subject to some choice ; constrained by global parameters. ask turtles [ forget-announcements answer-questions reply-attacks ] ; The change of reputation is normalized so that the sum of the reputations ; of all agents (total-reputation) remains constant over time. let f total-reputation / (total-reputation + change-reputation) ask turtles [set size max (list 0 (size * f))]

show-world tickend

to-report similar-attitude [a b] report sum (map [agreementfactor first ?1 first ?2] a b )end

to act set prior-size size run second (find-action (random-float total-odds) action-prob-pairs) let sim normative-conformity * similar-attitude props pprops / number-of-propositions - lack-of-princ-penalty * similar-attitude props init-props / number-of-propositions if size + sim > delta [ set size size + sim set change-reputation change-reputation + sim ] foreach [0 1 2] [ ifelse item ? strategy-shapes = shape [ set profit-strategy replace-item ? profit-strategy (size - prior-size) ][ set profit-strategy replace-item ? profit-strategy (item ? profit-strategy + delta) ] ]end

; The Agent's Actions

to announce if size > announce-threshold [ ; select a proposition with likelihood proportional to importance let announce-odds sum map [second ?] props let choice random-float announce-odds let p 0 let choice-inc second first props while [choice > choice-inc] [ set p p + 1 set choice-inc choice-inc + second item p props ] let w who let evidence (first item p props + firmness-of-principle * first item p init-props) / (firmness-of-principle + 1) let importance (second item p props + firmness-of-principle * second item p init-props) / (firmness-of-principle + 1) let loud random-float loudness * size ask other turtles with [distance myself < loud] [ update-announcement w p evidence importance] ask patches with [distance myself < loud] [ announce-patch myself p evidence importance] ]end

to question let imp map [second ?] props let max-imp-question position max imp imp ; my most important proposition let candidate one-of other turtles with [distance myself < visual-horizon] if candidate != nobody ; ask a passer-by [ask candidate [

http://jasss.soc.surrey.ac.uk/16/3/4.html 26 15/10/2015

set questions fput (list myself max-imp-question) questions]]end

to answer-questions if not empty? questions [ let q one-of questions let ag first q let ag-dist distance ag let w who; let pps props let evidence first (item (second q) props) let importance second (item (second q) props) ask other turtles with [distance myself <= ag-dist] [ update-announcement w (second q) evidence importance]; ask patches with [distance ag < loud ]; [ announce-patch ag (second q) evidence importance] set questions [] ]end

to-report agrees [v] let i floor (first v / number-of-agents) let t (first v) mod number-of-agents ifelse [size] of turtle t < announce-threshold or distance turtle t < visual-horizon [report 1] [report agreementfactor (first item i props) first second v]end

to attack; attack an agent who made an announcement this agent disagrees with most if size > announce-threshold and not empty? announcements [ ; rank the announcements for attack let agree (map [agrees ?] announcements) let loc position (min agree) agree let key 0 if item loc agree < 0 [ set key first (item loc announcements) ask turtle (key mod number-of-agents) [ set attacks fput (list myself floor (key / number-of-agents)) attacks] show (word self " attacks " (key mod number-of-agents)) ] ]end

to reply-attacks; select one of the attacks for a replyif size > 1 [ let pr filter [[size] of first ? > 1] attacks ; only attacks one ofthe agents who have sufficient reputation if not empty? pr [ let a one-of pr ; win == s (Epro) = s (Eopenv + Eprenv) let p second a let epro first item p props let ipro second item p props let eop first item p [props] of first a let iop second item p [props] of first a let eprenv (first item p pprops + [first item p pprops] of first a) / 2 let win 0 ifelse agreementfactor epro eprenv > agreementfactor eop eprenv [ set win ipro * epro * informational-conformity][ set win (-( ipro * (1 - epro) * informational-conformity)) ] ifelse win > 0 [set win min (list win (delta + [size] of first a))] [set win max (list win (-(size + delta)))] set size size + win ask first a [set size size - win] ifelse win > 0 [ ask patches with [distance first a < loudness] [announce-patch first a p epro ipro] ][ ask patches with [distance myself < loudness] [announce-patch myself p eop iop] ] ; update the beliefs of the proponent and the opponent let agree (agreementfactor epro eop) ifelse win > 1 - winthreshold [; setopinion p (list (accepte epro epro) (accepti agree ipro ipro)) ask first a [setopinion p (list (accepte epro eop) (accepti agree ipro iop))] ][ if win < winthreshold - 1[ setopinion p (list (accepte eop epro) (accepti agree iop ipro)); ask first a [setopinion p (list (accepte epro eop) (accepti agree ipro iop))] ] ] show (word self "replies attack on " p " of " first a " and wins " win) ]]set attacks [] ; ask my-in-links [die]end

http://jasss.soc.surrey.ac.uk/16/3/4.html 27 15/10/2015

to walk find-direction rt random undirectedness - random undirectedness fd random-float stepsizeend

to find-direction ; find a direction according to the selected strategy; 1: (shape = circle) towards the area that corresponds best with the agent's; opinion; 2: (shape = default) perpendicular towards the most corresponding area; 3: (shape = face happy) away from the most corresponding area let p props let b 0 ifelse (shape = "face happy") [set b min-one-of patches in-radius visual-horizon [similar-attitude p pprops]] [set b max-one-of patches in-radius visual-horizon [similar-attitude p pprops]] if b != nobody [face b] if shape = "default" [ifelse random 2 = 0 [right 90][left 90]]end

to change-strategy; select the first strategy with the highest profit for the its reputation let i position max profit-strategy profit-strategy set shape item i strategy-shapesend

to learn-by-neighbour let nb one-of turtles-on neighbors if nb != nobody [ let i random number-of-props let evidence first item i props let importance second item i props let ev first (item i [props] of nb) let imp second (item i [props] of nb) let agree (agreementfactor evidence ev) setopinion i (list (accepte evidence ev) (accepti agree importance imp)) ]end

to learn-by-environment; adapt belief values of a proposition to the values of the environment; with a chance proportional it the importance of the propositions let prop-odds sum map [second ?] props let choice random-float prop-odds let p 0 let choice-inc second first props while [choice > choice-inc] [ set p p + 1 set choice-inc choice-inc + second item p props ] setopinion p (item p pprops)end

to mutate; change the belief values of a random proposition to random values setopinion (random number-of-props) (list (random-float 1) (random-float 1))end

to setopinion [p evi] ; p = prop, evi = (evidence importance) set props replace-item p props evi end

to-report generateopinions let evids [] repeat number-of-props [ set evids fput (random-float 1) evids] let imps [] repeat number-of-props [ set imps fput (random-float 1) imps] report zip evids impsend

; Computation of Dependent Parameters.

; Average Belief.to-report report-eopop report mean [abs (2 * first item preferredopinion props - 1)] of turtlesend

; Average Importance.to-report report-iopop report mean [ second item preferredopinion props] of turtlesend

; Belief Distribution.to-report report-ginievid report gini [abs (2 * first item preferredopinion props - 1)] of turtlesend

; Importance Distribution.to-report report-giniimp

http://jasss.soc.surrey.ac.uk/16/3/4.html 28 15/10/2015

report gini [ second item preferredopinion props] of turtlesend

; Reputation Distribution.to-report report-authority report gini [size] of turtlesend

to-report gini [Lin] ;; expects a list of values.; Orders by the lowest rank first (or highest value) let L sort-by [?1 > ?2] Lin let N length L if N <= 1 [report 0] let i 0 let numerator 0 while [i < N ] [ set numerator numerator + (i + 1) * (item i L) set i i + 1 ] let u mean L ifelse u = 0 [report 0] [ report (N + 1) / (N - 1) - 2 * numerator / (N * (N - 1) * u) ] end

; Spatial Distribution.to-report clustering ;; Spatial Distribution report 1 - mean [avg-dist] of turtles / visual-horizonend

to-report avg-dist let m mean [distance myself] of turtles in-radius visual-horizon ifelse m = 0 [report 1][report m]end

to-report ranks [n L] ; n = number of classes, L = data; if L = [] [set L [1]] let al n-values n [0] let c 1 if max l != 0 [set c 0.999 * n / max L] let ar array:from-list al foreach L [ let v floor (c * ?) array:set ar v (array:item ar v) + 1] report array:to-list arend

to update-plot ;; Plot the parameter values for each cycle. ;; (For Figures 6 to 9)

let tmp 0 set-current-plot "Distribution of Evidence" histogram [first item current-prop props] of turtles set-current-plot "Importance Distribution" histogram [second item current-prop props] of turtles set-current-plot plottitle set-current-plot-pen "Reputation Distribution";; black set tmp report-authority plot tmp set-current-plot-pen "Spatial Distribution" ;;"friend ratio" ;; green set tmp clustering plot tmp set-current-plot-pen "Average Belief" ;; blue set tmp report-eopop plot tmp set-current-plot-pen "Belief Distribution" ;; yellow set tmp report-ginievid plot tmp set-current-plot-pen "Average Importance" ;; green set tmp report-iopop plot tmp set-current-plot-pen "Importance Distribution" ;; yellow set tmp report-giniimp plot tmp end

906

Notes

1

DexiareferstoaFranco-Belgianfinancialinstitution,whichwaspartiallynationalizedbytheBelgianstateinOctober2011.

2

In2008,JeremyClarksonshowedatracktestofaTeslaRoadstercarontheBBCprogramTopGear,whichincludedabatterythatwentflatafter55miles,justoveraquarterofTesla'sclaimedrange;theprogramledtoalibelchargebythemanufacturerin2011.

3

Overanumberofyears,in2006-2011,anumberofTurkishimmigrantswerekilledinGermany,andthepolicethoughtthattheperpetratorsmightformamysteriousTurkishcriminalnetwork.Finallyitturnedoutin2011thatthemurderersactuallywereasmallgroupofNeo-Nazis.

4

TheHofstadNetwork(inDutch:Hofstadgroep)isanIslamistgroupofmostlyyoungDutchMuslims,membersofwhichwerearrestedandweretriedforplanningterroristattacks.

5

ThemodelisavailableatopenABM.

6

http://jasss.soc.surrey.ac.uk/16/3/4.html 29 15/10/2015

Infull-fledgedcomputationalcognitivemodelssuchasACT-R,memoryandforgettingarebasedonelaboratedecayfunctions,relatedtofrequencyandrecencyofuseofmemorychunks(Anderson&Schooler2).

7

Inthecaser=0,anagentispreparedtopaywhenlosing,butdoesnotgetareturnincaseofwinningthedialogue.Thismakessenseonlyincasetheagentbelievesthatitstatedanabsolute(logical)truth.

8

Inrecentyearsinalgorithmicsocialchoicetheory,therehasbeenalotofattentionfordifferentvotingmethods,seeforexample (Saari46).

References

AJZEN,I.&FISHBEIN,M.(1980).UnderstandingAttitudesandPredictingSocialBehavior.EnglewoodCliffs,NJ:Prentice-Hall,1sted.

ANDERSON,J.R.&SCHOOLER,L.J.(1991).Reflectionsoftheenvironmentinmemory.PsychologicalScience2,396-408.[doi:10.1111/j.1467-9280.1991.tb00174.x]

BELNAP,N.D.(1977).Ausefulfour-valuedlogic.In:ModernUsesofMultiple-ValuedLogic(DUNN,J.M.&EPSTEIN,G.,eds.).Dordrecht:D.ReidelPublishingCo.,pp.5-37.[doi:10.1007/978-94-010-1161-7_2]

BRANDT,H.,HAUERT,C.&SIGMUND,K.(2003).Reflectionsoftheenvironmentinmemory.Proc.R.Soc.Lond.B270,1099-1104.[doi:10.1098/rspb.2003.2336]

BRATMAN,M.E.(1987).Intention,Plans,andPracticalReason.Cambridge,MA:HarvardUniversityPress.

BREIGER,R.,CARLEY,K.M.&PATTISON,P.(2003).Dynamicsocialnetworkmodellingandanalysis:Workshopsummaryandpapers.J.ArtificialSocietiesandSocialSimulation6(4).

BROERSEN,J.,DASTANI,M.&TORRE,L.V.D.(2001a).Resolvingconflictsbetweenbeliefs,obligations,intentionsanddesires.In:SymbolicandQuantitativeApproachestoReasoningwithUncertainty,6thEuropeanConference,ECSQARU2001,Toulouse,France,September19-21,2001,Proceedings(BENFERHAT,S.&BESNARD,P.,eds.),LectureNotesinComputerScience.Berlin:Springer,pp.428-447.[doi:10.1007/3-540-44652-4_50]

BROERSEN,J.,DASTANI,M.&TORRE,L.V.D.(2005).Beliefs,obligations,intentionsanddesiresascomponentsinanagentarchitecture.InternationalJournalofIntelligentSystems20(9),893-920.[doi:10.1002/int.20098]

BROERSEN,J.,DASTANI,M.,HUANGZ.,HULSTIJN,J.&TORRE,L.V.D.(2001b).TheBOIDarchitecture:Conflictsbetweenbeliefs,obligations,intentions,anddesires.In:ProceedingsofFifthInternationalConferenceonAutonomousAgents(AA'01)(ANDRé,F.,SEN,S.,FRASSON,C.&MüLLER,J.,eds.).NewYork,NY:ACMPress,pp.9-16.

CARLEY,K.,REMINGA,J.&KAMNEVA,N.(2003).Destabilizingterroristnetworks.In:NAACSOSConferenceProceedings(PENN,O.W.,ed.).Pittsburgh,PA.

CARLEY,K.M.(1986).Knowledgeacquisitionasasocialphenomenon.InstructionalScience14(4),381-438.[doi:10.1007/BF00051829]

CIALDINI,R.B.&GOLDSTEIN,N.J.(2004).Socialinfluence:Complianceandconformity.AnnualReviewofPsychology55,591-621.[doi:10.1146/annurev.psych.55.090902.142015]

CONTE,R.&PAOLUCCI,M.(2003).Socialcognitivefactorsofunfairratingsinreputationreportingsystems.In:Proceedingsofthe2003IEEE/WICInternationalConferenceonWebIntelligence(WI'03).Washington,DC:IEEEComputerSociety.[doi:10.1109/WI.2003.1241210]

DEATON,A.(1997).AnalysisofHouseholdSurveys.BaltimoreMD:JohnsHopkinsUniversityPress.[doi:10.1596/0-8018-5254-4]

DEFFUANT,G.(2006).Comparingextremismpropagationpatternsincontinuousopinionmodels.JournalofArtificialSocietiesandSocialSimulation9(3).

DEFFUANT,G.,NEAU,D.,AMBLARD,F.&WEISBUCH,G.(2002).Howcanextremismprevail?Astudybasedontherelativeagreementinteractionmodel.JournalofArtificialSocietiesandSocialSimulation5(4).

DEUTSCH,M.&GERARD,H.B.(1955).Astudyofnormativeandinformativesocialinfluencesuponindividualjudgment.JournalofAbnormalandSocialPsychology51(3),629-636.[doi:10.1037/h0046408]

DIGNUM,F.,DUNIN-KEPLICZ,B.&VERBRUGGE,R.(2001).Agenttheoryforteamformationbydialogue.In:ATAL'00:Proceedingsofthe7thInternationalWorkshoponIntelligentAgentsVII.AgentTheoriesArchitecturesandLanguages(CASTELFRANCHI,C.&LESPéRANCE,Y.,eds.).Berlin:Springer-Verlag.[doi:10.1007/3-540-44631-1_11]

DUNIN-KEPLICZ,B.&VERBRUGGE,R.(2010).TeamworkinMulti-AgentSystems:AFormalApproach.Chichester:Wiley.[doi:10.1002/9780470665237]

DYKSTRA,P.,ELSENBROICH,C.,JAGER,W.,RENARDELDELAVALETTE,G.&VERBRUGGE,R.(2009).Adialogicallogic-basedsimulationarchitectureforsocialagentsandtheemergenceofextremistbehaviour.In:The6thConferenceoftheEuropeanSocialSimulationAssociation(EDMONDS,B.&GILBERT,N.,eds.).ElectronicProceedings1844690172.

DYKSTRA,P.,ELSENBROICH,C.,JAGER,W.,RENARDELDELAVALETTE,G.&VERBRUGGE,R.(2010).Alogic-basedarchitectureforopiniondynamics.In:Proceedingofthe3rdWorldConongressonSocialSimulationWCSS2010(ERNST,A.&KUHN,S.,eds.).(CD-ROM)CentreforEnvironmentalSystemsResearch,UniversityofKassel,Germany.

FAGIN,R.&HALPERN,J.Y.(1987).Belief,awareness,andlimitedreasoning.ArtificialIntelligence34(1),39-76.[doi:10.1016/0004-3702(87)90003-8]

FESTINGER,L.(1954).Atheoryofsocialcomparisonprocesses.HumanRelations7(2),117-140.[doi:10.1177/001872675400700202]

FRANKS,D.W.,NOBLE,J.,KAUFMANN,P.&STAGL,S.(2008).Extremismpropagationinsocialnetworkswithhubs.AdaptiveBehavior-Animals,Animats,SoftwareAgents,Robots,AdaptiveSystemsArchive16(4),264-274.[doi:10.1177/1059712308090536]

GILES,R.(1978).Formallanguagesandthefoundationofphysics.In:PhysicalTheoryasLogico-OperationalStructure(HOOKER,C.A.,ed.).Dordrecht:ReidelPublishingCompany.

HARTMANN,S.&SPRENGER,J.(2010).Theweightofcompetenceunderarealisticlossfunction.LogicJournaloftheIGPL18(2),346-352.[doi:10.1093/jigpal/jzp061]

HEGSELMANN,R.&KRAUSE,U.(2002).Opiniondynamicsandboundedconfidence:Models,analysisandsimulation.JournalofArtificialSocietiesandSocialSimulation5(3).

HELMHOUT,J.M.(2006).TheSocialCognitiveActor.Ph.D.thesis,UniversityofGroningen,Groningen.

HELMHOUT,J.M.,GAZENDAM,H.W.M.&JORNA,R.J.(2005).Emergenceofsocialconstructsandorganizationalbehavior.In:21stEGOSColloquium(GAZENDAM,H.,CIJSOUW,R.&JORNA,R.,eds.).Berlin.

HUET,S.,DEFFUANT,G.&JAGER,W.(2008).Arejectionmechanismin2Dboundedconfidenceprovidesmoreconformity.AdvancesinComplexSystems(ACS)11(04),529-549.[doi:10.1142/S0219525908001799]

JAGER,W.&AMBLARD,F.(2005).Uniformity,bipolarizationandpluriformitycapturedasgenericstylizedbehaviorwithanagent-basedsimulationmodelofattitudechange.Computational&MathematicalOrganizationTheory10(4),295-303(9).[doi:10.1007/s10588-005-6282-2]

http://jasss.soc.surrey.ac.uk/16/3/4.html 30 15/10/2015

KAMLAH,W.&LORENZEN,P.(1973).LogischePropädeutik.München,Wien,Zürich:B.I.-Wissenschaftsverlag.

KELMAN,H.(1958).Compliance,identification,andinternalization:Threeprocessesofattitudechange.JournalofConflictResolution2(1),51-60.[doi:10.1177/002200275800200106]

KELMAN,H.(2006).Interests,relationships,identities:Threecentralissuesforindividualsandgroupsinnegotiatingtheirsocialenvironment.AnnualReviewofPsychology57,1-26.[doi:10.1146/annurev.psych.57.102904.190156]

LAWLER,R.W.&CARLEY,K.M.(1996).CaseStudyandComputing:AdvancedQualitativeMethodsintheStudyofHumanBehavior.Norwood,NJ,Ablex.

LAZARSFELD,P.&MERTON,R.K.(1954).Friendshipasasocialprocess:Asubstantiveandmethodologicalanalysis.In:FreedomandControlinModernSociety(BERGER,M.,ABEL,T.&PAGE,C.,eds.).NewYork:VanNostrand,pp.18-66.

Lê,S.,JOSSE,J.&HUSSON,F.(2008).Factominer:AnRpackageformultivariateanalysis.JournalofStatisticalSoftware25(1),1-18.[doi:10.18637/jss.v025.i01]

LEHRER,K.&WAGNER,C.(1981).RationalConsensusinScienceandSociety.Dordrecht:D.ReidelPublishingCompany.[doi:10.1007/978-94-009-8520-9]

MACY,M.&FLACHE,A.(2002).Learningdynamicsinsocialdilemmas.ProceedingsoftheNationalAcademyofSciencesU.S.A.99(3),7229-36.[doi:10.1073/pnas.092080099]

MCELREATH,R.(2003).Reputationandtheevolutionofconflict.JournalofTheoreticalBiology220(3),345-357.[doi:10.1006/jtbi.2003.3166]

PARSONS,S.,SKLAR,E.&MCBURNEY,P.(2011).Usingargumentationtoreasonwithandabouttrust.In:ArgumentationinMulti-AgentSystems.Taipei,Taiwan,May2011.InconjunctionwithAAMAS2011.(MCBURNEY,P.,PARSONS,S.&RAHWAN,I.,eds.).

PRAKKEN,H.,REED,C.&WALTON,D.(2003).Argumentationschemesandgeneralizationsinreasoningaboutevidence.In:Proceedingsofthe9thInternationalConferenceonArtificialIntelligenceandLaw(ICAIL'03).NewYork,NY:ACM.[doi:10.1145/1047788.1047794]

RAO,A.S.&GEORGEFF,M.P.(1991).ModelingrationalagentswithinaBDI-architecture.In:KR'91.SanMateo,CA:MorganKaufmannpublishersInc.

RAO,A.S.&GEORGEFF,M.P.(1995).BDIagents:Fromtheorytopractice.In:ProceedingsoftheFirstInternationalConferenceonMult-AgentSystems(ICMAS-95)(LESSER,V.&GASSER,L.,eds.).Cambridge,MA:MITPress.

RESTALL,G.(2006).Relevantandsubstructurallogics.In:HandbookoftheHistoryandPhilosophyofLogic(GABBAY,D.&WOODS,J.,eds.),vol.7.Amsterdam,Boston:Elsevier,pp.289-398.[doi:10.1016/s1874-5857(06)80030-0]

SAARI,D.G.(2001).DecisionsandElections:ExplainingtheUnexpected.CambridgeUniversityPress.[doi:10.1017/cbo9780511606076]

SABATER-MIR,J.,PAOLUCCI,M.&CONTE,R.(2006).Repage:REPutationandimAGEamonglimitedautonomouspartners.JournalofArtificialSocietiesandSocialSimulation9(2).

SCHELLING,T.C.(1971).Dynamicmodelsofsegregation.JournalofMathematicalSociology1(2),143-186.[doi:10.1080/0022250X.1971.9989794]

SHERIF,M.&HOVLAND,C.(1961).SocialJudgment:AssimilationandContrastEffectsinCommunicationandAttitudeChange.NewHaven:YaleUniversityPress.

SUBAGDJA,B.,SONENBERG,L.&RAHWAN,L.(2009).Intentionallearningagentarchitecture.AutonomousAgentsandMulti-AgentSystems18(3),417-470.[doi:10.1007/s10458-008-9066-5]

SULS,J.,MARTIN,R.&WHEELER,L.(2002).Socialcomparison:Why,withwhomandwithwhateffect?CurrentDirectionsinPsychologicalScience11(5),159-163.[doi:10.1111/1467-8721.00191]

SUN,R.(2008).Prolegomenatointegratingcognitivemodelingandsocialsimulation.In:CognitionandMulti-AgentInteraction:FromCognitiveModelingtoSocialSimulation(SUN,R.,ed.).NewYork,NY:CambridgeUniversityPress,pp.3-26.

SŹAŁAS,A.S.&SŹAŁAS,A.(2009).Paraconsistentreasoningwithwords.In:AspectsofNaturalLanguageProcessing(MARCINIAK,M.&MYKOWIECKA,A.,eds.),vol.5070ofLectureNotesinComputerScience.Berlin:Springer.

VANBENTHEM,J.(2001).Gamesindynamic-epistemiclogic.BulletinofEconomicResearch53(4),219-48.[doi:10.1111/1467-8586.00133]

VERBRUGGE,R.(2009).Logicandsocialcognition:Thefactsmatter,andsodocomputationalmodels.JournalofPhilosophicalLogic38(6),649-680.[doi:10.1007/s10992-009-9115-9]

VERBRUGGE,R.&MOL,L.(2008).Learningtoapplytheoryofmind.JournalofLogic,LanguageandInformation17(4),489-511.[doi:10.1007/s10849-008-9067-4]

VERHEIJ,B.(2000).Dialecticalargumentationasheuristicforcourtroomdecision-making.In:Rationality,InformationandProgressinLawandPsychology.LiberAmoricumHansF.Crombag(KOPPEN,P.J.V.&ROOS,N.H.M.,eds.).Maastricht:MetajuridicaPublications.

WALTON,D.&KRABBE,E.(1995).CommitmentinDialogue.Albany,NY:StateUniversityofNewYorkPress.

WIJERMANS,N.,JAGER,W.,JORNA,R.&VLIET,T.V.(2008).Modellingthedynamicsofgoal-drivenandsituatedbehavior.In:TheFifthConferenceoftheEuropeanSocialSimulationAssociation(ESSA2008).Brescia,Italy.

ZOETHOUT,K.&JAGER,W.(2009).Aconceptuallinkagebetweencognitivearchitecturesandsocialinteraction.Semiotica175,317-333.[doi:10.1515/semi.2009.052]

http://jasss.soc.surrey.ac.uk/16/3/4.html 31 15/10/2015