A general instance-based learning framework for studying intuitive decision-making in a cognitive architecture

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ContentslistsavailableatScienceDirect

Journal

of

Applied

Research

in

Memory

and

Cognition

j ou rn a l h o m epa g e : w w w . e l s e v i e r . c o m / l o c a t e / j a r m a c

Original

Article

A

general

instance-based

learning

framework

for

studying

intuitive

decision-making

in

a

cognitive

architecture

Robert

Thomson

∗

,

Christian

Lebiere,

John

R. Anderson,

James

Staszewski

CarnegieMellonUniversity,UnitedStates

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received22October2013 Accepted11June2014 Availableonline19June2014

Keywords: Cognitivearchitecture Cognitivemodeling Decision-making Heuristics

a

b

s

t

r

a

c

t

Cognitivearchitectures(e.g.,ACT-R)havenottraditionallybeenusedtounderstandintuitive decision-making;instead,modelstendtobedesignedwiththeintuitionsoftheirmodelersalreadyhardcoded inthedecisionprocess.Thisisdueinparttoafuzzyboundarybetweenautomaticanddeliberative processeswithinthearchitecture.Wearguethatinstance-basedlearningsatisﬁestheconditionsfor intuitivedecision-makingdescribedinKahnemanandKlein(2009),separatesautomaticfrom delibera-tiveprocesses,andprovidesageneralmechanismforthestudyofintuitivedecision-making.Tobetter understandtheroleoftheenvironmentindecision-making,wedescribebiasesasarisingfromthree sources:themechanismsandlimitationsofthehumancognitivearchitecture,theinformationstructure inthetaskenvironment,andtheuseofheuristicsandstrategiestoadaptperformancetothedual con-straintsofcognitionandenvironment.Auniﬁeddecision-makingmodelperformingmultiplecomplex reasoningtasksisdescribedaccordingtothisframework.

Thisarticle describeshowcomputationalmodelsofintuitive decision-makingareexpressedwithintheconstraintsofthe ACT-Rcognitivearchitecture(Andersonetal.,2004).Thesemodelsare noteworthyfortheirabilitytoexplainavarietyofheuristicsand biasesintermsoftheprocessesandrepresentationsthatproduce them.Thesephenomenahavelargelybeencapturedanddeﬁned asresultsofexperimentalmanipulations(Kahneman&Tversky, 1996)butnotintermsofprocessmodelsjustiﬁedbyacognitive architecture(Dimov,Marewski,&Schooler,2013).Aconcernof modelingintuitivedecision-makingbehaviorusingcognitive archi-tecturesisconfoundedbytheexplicitdecisionsencodedbythe modelers.Thiscriticismcan bedescribedas: insteadof model-ingintuitivebehaviorperse,cognitivemodelsmakeexplicitthe intuitionsoftheirdesigners(Cooper,2007;Lewandowsky,1993; Schultheis,2009;Cooper,2007;Lewandowsky,1993;Schultheis, 2009; Shallice & Cooper, 2011). We address this criticism by showing that the instance-based learning mechanisms in the ACT-R cognitivearchitecture(Gonzalez,Lerch, &Lebiere, 2003) exhibitthecharacteristicsofintuitivedecision-makingasdescribed in Kahneman and Klein, (2009), and provide a clearer distinc-tionbetween automatic and implicit (System 1) processes and

∗Correspondingauthor.Tel.:+14126890536.

E-mailaddresses:[email protected],

[email protected](R.Thomson).

deliberative and explicit (System 2) processes. In addition, we speciﬁcallyaddressthismodelerselectioncriticismbyshowingthat theexplicitstrategiesofthemodelsinstantiatethetheoriesofthe modeldesignerandthusareamechanismfortheoryevaluation ratherthanaconfoundingfactorinmodeldevelopment.

Inmakingthisargument,werecommendadoptingatripartite explanationofdecision-makingandbiasesthatillustratesthe crit-icalroleofthetaskenvironmentinthedecision-makingprocess. Wearguethatdecision-makingshouldbeunderstoodintermsof: (1) themechanismsandlimitations ofthearchitecture; (2)the information structurein thetaskenvironment;and (3) theuse ofheuristicsandstrategiestoadaptperformancetothedual con-straintsofcognitionandenvironment.Fromexamplesofexisting models,weshowthatsimulatingbehaviorwithinacognitive archi-tectureisausefulmethodologyforthestudyofthemechanisms, variables,andtime-courseincomplexdecision-makingprocesses thatareimpossibleinexperimentationduetoexploding combina-torics.

1. Whatisintuitivedecision-making?

Simon(1992)characterizedintuitivedecision-makingskillas “nothing more and nothing less than recognition” (p. 155). In theirseminalworkonexpertise,Chaseand Simon(1973) iden-tiﬁed that chess expertsrequireupwards of a decade of study

http://dx.doi.org/10.1016/j.jarmac.2014.06.002

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toretain50,000–100,000distinctandrapidlyaccessiblepatterns ofchesspositions.Intuitivedecision-makinghasbeenstudiedin boththenaturalisticdecision-makingandheuristicsandbiases lit-erature,with theformer generally focused onthe successesof intuitivereasoning,whilethelattergenerallyfocusedonits fail-ures(Kahneman&Klein,2009).Adistinguishingfeatureofintuitive decision-makingisthatasingleplausiblesolutionrapidly‘comes tomind’initsentiretywithoutexplicitorconsciousawarenessof thecausalfactorsenteringintothedecision(i.e.,notbeing con-sciouslyderivedinapiecemeal,step-by-step,orina‘deliberative’ manner;Newell&Simon,1972;Simon,1995).Assuch,intuitive reasoningisconsideredSystem1.Forexample,Klein,Calderwood, andClinton-Cirocco(1986)foundthatﬁremarshalstendedtomake rapiddecisionsbygeneratingasinglealternative,mentally simu-latingitsoutcome,andeithermakingminorrevisionsoradopting thenextclosestalternative.Effectively,ﬁremarshalswere pattern-matchingbasedontheirpriorexperiences.Thisstrategyhasbeen termedrecognition-primeddecision-making.

Conversely,deliberativedecision-makingisoftencharacterized asstrategic,effortful,slow,andrule-oriented(Klein,1998),andas suchisconsideredSystem2thinking(Kahneman&Frederick,2005; Stanovich&West,1999).Interestingly,theactofverifyingan intu-itionisgenerallyseenasoptional,effortful,andthusafunctionof System2(Kahneman&Klein,2009).

Inordertogainintuitiveexpertise,twoconditionsfirstneedbe met.Thefirstconditionisthatpeoplereceiveextensivepracticein ataskenvironmentthatissufficientlystableandprovidescausal or statistical cues/structures that may at least theoretically be operationalized(Hogarth,2001;Hogarth,2001;Brunswik,1957). This need not be deterministic(e.g., playing poker is a proba-bilistic but stable environment; Kahneman& Klein, 2009).The secondconditionis thattheremustbesufficientfeedbackfrom thetaskenvironmentwhich providespeopleanopportunityto learntherelevantcues/structures.Inotherwords,feedbackmust besufficienttogeneratearelevantinternalproblemspace.This requirementoffeedbackandinteractionwiththetaskenvironment droveouradoptionofthetripartitelevelofdescription.

2. Whyuseacognitivearchitecture?

Cognitive architectures model behavior using a setof com-monmechanismsandprocesses(i.e.,thearchitecture)whosegoal istonotonlyexplainhumanbehavior,buttheunderlying struc-turesandrepresentationssubsumingcognitionasawhole.These mechanismsshouldbebothpsychologicallyandneurally plausi-bletoaccountforhumanbehavior.Thislevelofdescriptionisnot generallycapturedbyeithermathematicalorinformalmodelsof decision-making.Beforegettingintofurtherdetailsofmechanisms, models,andresults;thereisanimportantargumenttobemadefor theroleofcognitivearchitecturesingeneral,whichisbest charac-terizedbyHerbertSimon(in1971,noless):

Theprogrammabilityofthetheoriesistheguarantoroftheir operationality,aniron-cladinsuranceagainstadmittingmagical entitiesintothehead.Acomputerprogramcontainingmagical instructionsdoesnotrun,butitisassertedofthese information-processingtheoriesofthinkingthattheycanbeprogrammed andwillrun.Theymaybeempiricallycorrecttheoriesabout thenatureofhumanthoughtprocessesorempiricallyinvalid theories;[but]theyarenotmagicaltheories.(p.148)

In modern terms, simulationsusing a cognitive architecture provideafalsiﬁablemethodologyforthestudyofcognitive pro-cessesandrepresentations,aparticularlyimportantcharacteristic whenstudyinglargelyimplicitprocessessuchasintuitive decision-making. They serve several theoretical functions including:

organizingandrelatingasubstantialnumberofcognitive mech-anisms,makingtestablepredictions,andexplainingthecognitive processesunderlyinghumanperformance.Inmanycases,cognitive modelscanperformtaskstoocomplextoanalyzewithtraditional experimentationduetothecombinatoricsofthepossibledecision space.Aswillbedescribed,asingleACT-Rmodelhasexplained anchoringandadjustment,conﬁrmation,andprobability match-ingbiasesacrossarangeofcomplexgeospatialintelligencetasks usingacommoninstance-basedlearningapproach(Lebiereetal., 2013).Similarly,MarewskiandMehlhorn(2011)wereableto spec-ify39processmodelsstudiedindecision-makingusingasmaller subsetof5ACT-Rmodels.Inshort,cognitivearchitecturesallowfor theoriestobeconstrainedbyscientiﬁcallyestablishedmechanisms and(hopefully)easilydescribableprocesses.

Thisisnottoarguethatcognitivearchitecturesareapanacea forstudyingdecision-making(orpsychologyingeneral),butwe doclaimthattheyareavaluabletoolinthegenerationand explo-ration of theories (c.f., models) which maybe toocomplex for traditionalpiecemeal experimentalmethods.Inparticular, intu-itivedecision-makingtendstobecognitively‘opaque’withlittle observableevidence,andwhatlittleevidencethereiscomingfrom highlyfallibleintrospection.Assuch,manydescriptionsofintuitive decision-making are inherently qualitative or are characterized usingrelativelysimpleexperimentalresults(Dimovetal.,2013). Anadvantageofcognitivearchitecturesis notonlytheirability toobjectively explainaccuracy and response timesin terms of theoperationofbothsymbolicelementsandtheirsub-symbolic activationstrengths(andinthecaseofACT-R,linkstoneural struc-ture),butalsotheabilitytogo‘underthehood’andactuallylook insidethemodeltoexplicitlyexaminecausalprocesses.Such com-putationalcognitivemodelsmaketestablepredictionsofwhatis goingoninsidethemindofsomeoneperformingintuitive decision-making.

Onemeasureforvalidatinginsidethemindpredictionsisto per-formmodeltracing.Modeltracingisatechniquewhereamodel is forced to respondwithsome or all of thesame values as a humanparticipant,andthentheinternalstatesofthemodelare examinedtodeterminetheinﬂuenceofthese‘forced’decisions.By examiningthecommonalitiesbetweenthemodel’sinternalstates andhumanbehavior,modelersarepotentiallyabletomakecausal claimsaboutthenatureofmentalprocesseswithinparticipants; thatis,toexplainhowhumanperformanceisproducedby vari-ouscognitivemechanismsandtheirinteraction.Thisperformance includestraditionalmeasuressuchasaccuracyandresponsetime, butalsopredictionsoffMRIboldresponseforspeciﬁcbrainareas associatedwiththefunctionalmodulesofthecognitive architec-ture(Anderson,2007).

Thebenefitsofcognitivearchitecturescanbeseenasbridging orsynthesizing formalmathematicaltheories(suchasBayesian modeling)andknowledge-levelstrategies(e.g.,heuristics).Assuch, cognitivearchitecturesactasalinkbetweenMarr’s(1982) compu-tationalandalgorithmiclevels,withthebenefitsofacorresponding bridgetothephysicallevel(i.e.,neural)implementation.Bayesian modelsbelongtoabroadclassofabstractmodelsthatformally (i.e.,mathematically)explainhumanbehaviorintermsofprocesses computing probabilities over a set of possibledecisions. While Bayesian(andrelatedprobabilistic)modelsdoprovidean expla-nationofbehavior,itisnotgenerallyacceptedtobeacognitively (i.e.,psychologically)plausibleoneastheunderlyingmechanisms drivingtheprocessesaresomewhatvagueornottractable(Bowers &Davis,2012).Assuch,Bayesiantheoriesbelongatthe computa-tionallevelofMarr’shierarchy.Thisisnotacriticismspecificto Bayesianmodels,butcanalsobeappliedtoothermathematical the-oriessuchasprospecttheory(Kahneman&Tversky,1979),decision theory(Berger,1985),andquantumprobabilitytheory(Busemeyer, Pothos,Franco,&Trueblood,2011).Similarly,explanationsinthe

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formofheuristics(i.e.,knowledge-levelexplanations)tendtobe vagueastotheunderlyingprocessesleadingtothebiased behav-ior.Togiveanotherexample,whilefast-and-frugalheuristics(see

Gigerenzer,Todd,&theABCResearchGroup,1999)areexplained intermsofprocessmodels,itiscontestedwhethertheunderlying cognitivemechanismsrequiredarepsychologicallyplausible(e.g.,

Dougherty,Franco-Watkins,&Thomas,2008;butseeGigerenzer, Hoffrage,&Goldstein,2008).

Wewouldliketobrieflydiscusswhatsomeconsiderare limita-tionsofthecognitivearchitectureapproach,butwemaintainthat theselimitationsareoutweighedbytheadvantagesofthismethod oftheorizing.Perhapsthemaincriticismofcognitivearchitectures isthedegreesoffreedomargument(e.g.,RobertsandPashler,2000; Griffiths,Chater,Norris,&Pouget,2012).Thisargumentrelieson thenotionthatthenumerousparametersofthearchitecture(and theextensibilityoftheparameterspace)addunnecessary complex-itywhileofferinglittleconstraintonthekindsofmodelsthatmay begeneratedtosolveagivenproblem.Whileitistruethatcognitive architecturessuchasACT-Rareparameterized,theseparameters arewell-documented,transparentinthemodel, andare gener-allydependentoneachothersuchthat itlimitstheircapability toover-fittothedata(i.e.,theyhaveaconstrainedeffectondata). Furthermore,thissamedegreesoffreedomargumentcanandhas beenappliedtoprobabilisticmodels(Bowers &Davis,2012).In fact,weargue thatinformal theoriesalsofallpreytothesame degreesoffreedomcriticism(Griffithsetal.,2012),however,these theoriesbenefitfromtheirlackofformalizationbyhavingless obvi-ouspointsofcriticism(i.e.,noobviousparameterstopointat). Oneotherconcernwithinformaltheoriesisthattheytendtoward binaryoppositions(e.g.,System1vsSystem2orexplicitvsimplicit processes)withoutaclearunderstandingofwheretheboundaries lieorhowtheymaybebehaviorallyorneurallyinstantiatedwithin themind(seeKruglanski&Gigerenzer,2011fora similar argu-ment).Inouropinion,thislackofformalizationcanstifleprogress byleadingourtheorizingtowardrelativelyarbitraryboundaries ratherthanforcingtheorizingtooccurinatestableandpredictive environment.

Tomore directly address thedegrees of freedom argument, weargue for two techniquesto mitigateits concerns:thefirst istolimit thefreedomof architecturalparameters throughthe useofscientificallyjustifieddefaultvalues,andthesecondisto developmodelswhicharerelativelyinsensitivetoparameter val-ues.Forinstance,thebase-levellearning(i.e.,memorydecay)rate of.5 inACT-R hasbeenjustifiedin over100publishedmodels (seetheACT-Rwebsite:http://act-r.psy.cmu.edu).Inadditionto architecturalparameters,therearewaysofcontrolling‘knowledge’ parameters(e.g.,knowledgerepresentation)throughapproaches like instance-based learning which use a common knowledge representation determined directlyby the interaction withthe external environment. Finally, there have beenefforts touse a single,moregeneralACT-Rmodeltoperformaseriesof decision-makingtasks (e.g., Lebiereet al., 2013; Marewski&Mehlhorn, 2011;Stewart,West,&Lebiere,2009;Taatgen&Anderson,2008, 2010).Usingmoregeneralmodelsofcognitionreducesthedegrees of freedom in the architecture by aligning a common set of mechanisms,parameters,andstrategiesintoacohesivemodeling paradigm.

Insummary,descriptionsateithertheformalorinformallevel areunder-constrained.Cognitive architecturestietogetherboth formalandinformallevelsofdescription(Gonzalez&Lebiere,2013) bycombiningsub-symbolicalgorithmsakintoformaltheorieswith symbolicknowledgestructurescontrolling thoseprocesses in a heuristicmanner.Assuch,theyprovidenotonlyexplanationsof existingbehavior,butpredictionsofthemechanisms,knowledge, andbehaviorsoffutureactionsbasedonamodel’spriorexperience (Thomson&Lebiere,2013).

Fig.1.AnoverviewofACT-R’sdefaultmodulesandtheirdependentbuffers.

3. WhyuseACT-R?

3.1. WhatisACT-R?

The following is a brief technical descriptionof ACT-R, and whileitishelpfultounderstandourlaterarguments,readersnot interestedin technicaldescriptionsshouldfeelfree toskipthis section. For those interested in a more in-depth descriptionof ACT-R,pleaseseeAndersonetal.(2004)andtheACT-Rwebsite:

http://act-r.psy.cmu.edu/.

ACT-Risacognitivearchitecturedeﬁnedasa setofmodules whichareintegratedandcoordinatedthroughacentralized pro-ductionsystem(seeFig.1).Eachmoduleisassumedtoaccessand depositinformationintobuffersassociatedwiththemodule,and theproductionsystemonlyrespondstothecontentsofthebuffers, nottheinternalprocessingofthemodules.Thedeclarativememory andproductionsystemmodules,respectively,storeandretrieve informationthatcorrespondstodeclarativeknowledgeand proce-duralknowledge.Declarativeknowledgeisthekindofknowledge thata personcanattendto,reﬂectupon, andusually articulate insomeway(e.g.,bydeclaringitverballyorbygesture). Proce-duralknowledgeconsistsoftheskillswedisplayinourbehavior, generallywithoutconsciousawareness.

Declarative knowledge in ACT-R is represented formally in terms of chunks. The information in declarative memory cor-responds to episodic and semantic knowledge that promotes long-termcoherenceinbehavior. Chunkshave anexplicittype, andconsistofslot-valuepairsofinformation(seeFig.2).Chunks areretrieved fromlong-termdeclarative memorybyan activa-tionprocess.Eachchunkhasabase-levelactivationthatreﬂects itsrecencyandfrequencyofoccurrence.Activationspreadsfrom thecurrentfocusofattentionthroughassociationsamongchunks

Fig.2.AnexampleofachunkinACT-R.ThenameofthechunkisRed-Player,itisof

typeplayer,andhasthreeslots:name,valueandmissioncontainingvaluesaggressive,

.8and2,respectively.Thischunkrepresentsthenameofahypotheticalopponent whothemodelassumesisaggressivewithaprobabilityof.8.Inthisexample,the valueof.8isderivedbythemodelbasedonevidenceaccumulatedduringthetask andisderivedbytheproportionoftrialsinwhichattacksoccurred.

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Table1

Thelistofsub-symbolicmechanismsintheACT-Rarchitecture.

Mechanism Equation Description

Activation Ai=Bi+Si+Pi+εi Bi:Base-levelactivationreﬂectstherecencyandfrequencyofuseofchunki

Si:Spreadingactivationreﬂectstheeffectthatbuffercontentshaveontheretrievalprocess

Pi:Partialmatchingreﬂectsthedegreetowhichthechunkmatchestherequest

εi:Noisevalueincludesbothatransientand(optional)permanentcomponent(permanent

componentnotusedbytheintegratedmodel)

Base-level Bi=ln

_n

j=1 t−d j

+ˇi

n:Thenumberofpresentationsforchunki

tj:Thetimesincethejthpresentation

d:Adecayrate(notusedbytheintegratedmodel)

ˇi:Aconstantoffset(notusedbytheintegratedmodel)

Spreadingactivation

Si=

k

j

WkjSji k:Weightofbufferssummedoverareallofthebuffersinthemodel

j:Weightofchunkswhichareintheslotsofthechunkinbufferk

Wkj:Amountofactivationfromsourcesjinbufferk

Sji:Strengthofassociationfromsourcesjtochunki

Sji=S−ln(fanji) S:Themaximumassociativestrength(setat4inthemodel)

fanji:Ameasureofhowmanychunksareassociatedwithchunkj

Partialmatching

Pi=

k

PMki P_M:Matchscaleparameter(setat2)whichreﬂectstheweightgiventothesimilarity

ki:Similaritybetweenthevaluekintheretrievalspeciﬁcationandthevalueinthe

correspondingslotofchunki

Thedefaultrangeisfrom0to−1with0beingthemostsimilarand−1beingthelargest

difference

Declarativeretrievals _Pi₌

eAi/s

je Aj/s

Pi:Theprobabilitythatchunkiwillberecalled

Ai:Activationstrengthofchunki

Aj:Activationstrengthofallofeligiblechunksj

s:Chunkactivationnoise

Blendedretrievals

V=argmin

i

Pi(1−Simij)2 P_Simi:Probabilityfromdeclarativeretrieval

ij:Similaritybetweencompromisevaluejandactualvaluei

Utilitylearning Ui(n)=Ui(n−1)+˛[Ri(n)−Ui(n−1)] Ui(n−1):Utilityofproductioniafteritsn−1stapplication

Ri(n):Rewardproductionreceivesforitsnthapplication

Ui(n):Utilityofproductioniafteritsnthapplication

Pi=

eUi/s je

Uj/s

Pi:Probabilitythatproductioniwillbeselected

Ui:Expectedutilityoftheproductiondeterminedbytheutilityequationabove

Uj:istheexpectedutilityofthecompetingproductionsj

indeclarativememory.Theseassociationsarebuiltupfrom experi-ence,andtheyreﬂecthowchunksco-occurincognitiveprocessing. Chunksarecomparedtothedesiredretrievalpatternusingapartial matchingmechanismthatsubtractsfromtheactivationofachunk itsdegreeofmismatchtothedesiredpattern,additivelyforeach componentofthepatternandcorrespondingchunkvalue.Noiseis addedtochunkactivationstomakeretrievalaprobabilisticprocess governedbyaBoltzmann(softmax)distribution.

Whilethemostactivechunkisusuallyretrieved,ablending pro-cess(i.e.,ablendedretrieval;seeLebiere,1999;Wallach&Lebiere, 2003a)canalsobeappliedthatreturnsaderivedoutput reﬂect-ingthesimilaritybetweenthevaluesofthecontentofallchunks, weightedbytheirretrievalprobabilitiesreﬂectingtheiractivations andpartial-matchingscores(seeTable1foralistofsub-symbolic activationsinvolvedinchunkretrievalandproductionselection). Thisprocessenablesnotjusttheretrievalofpreviously encoun-teredsymbolicvaluesbutalsothegenerationofcontinuousvalues suchasprobabilityjudgmentsinaprocessakintoweighted inter-polation.

Productionrulesareusedtorepresentproceduralknowledgein ACT-R.Theyspecifyproceduresthatrepresentandapplycognitive skillinthecurrentcontext,includinghowtoretrieveandmodify informationinthebuffersandtransferittoothermodules.In ACT-R,eachproductionruleisasetofconditionsandactionswhichare analogoustoanIF-THENrule.Conditionsspecifystructuresthatare matchedinbuffers,andcorrespondtoinformationfromthe exter-nalworldorotherinternalmodules.Actionsrepresentrequests andmodiﬁcationstothecontentsofthebuffers,including queu-ingperceptual-motorresponses(e.g.,speaking,typing,orlooking togivenlocation).Matchingproductionruleseffectivelymeans: iftheconditionsofagivenproductionmatchthecurrentstateof

affairs(i.e.,thestateofthemodulesandcontentsofthebuffers) thenperformthefollowingactions(seeFig.3).

ACT-Rusesamixofparallelandserialprocessing.Modulesare encapsulatedandmayprocessinformationinparallelwithinone another.However,therearetwoserialbottlenecksinprocessing. First,onlyoneproductionmaybeexecutedatatime.Second,a buffercanonlycontainonechunkatatime.Ingeneral,multiple productionrulescanmatch,butonlyonecanbeactive–in ACT-Rparlanceﬁred–atanypoint.Productionutilities,learnedusinga

Fig.3. AnexampleofaproductioninACT-R.Thenameoftheproductionis get-feedback,anditteststhegoalbuffers(the=sign)andqueries(the?sign)thestate oftheretrievalmoduleontheleft-handsideoftheequation(everythingbefore the==>).Theproductionalsomodiﬁesthechunkinthegoalbuffer(the=sign)and makesarequest(the+sign)foranewchunktobeplacedintheretrievalbufferon theright-handsideoftheequation.

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reinforcementlearningscheme,areusedtoselectthesinglerule thatﬁres.Asfordeclarativememoryretrieval,production selec-tionisaprobabilisticprocess.Basedonexperienceandmatching certaincriteria,twoproductionrulesmaybeautomatically com-piledtogetherintoanewandmore-efﬁcientrule,whichaccounts forproceduralizationofbehavior.

3.2. WhatdoesACT-Rhavetodowithintuitivedecision-making?

CognitivemodeldevelopmentinACT-Risinpartderivedfrom therationalanalysisofthetask(Anderson,1982)andinformation structuresintheexternalenvironment(e.g.,thedesignofthetasks beingsimulated),theconstraintsoftheACT-Rarchitecture,and guidelinesfrompreviousmodelsofsimilartasks(Taatgen,Lebiere, &Anderson,2006).Asuccessfuldesignpatterninspecifying cogni-tiveprocesssequencinginACT-Ristodecomposeacomplextask tothelevelofunittasks.Card,Moran,andNewell(1983)suggested thatunittaskscontrolimmediatebehavior.Unittasksempirically takeabout10s.Toan approximation,thestructureof behavior abovetheunittasklevellargelyreflectsarationalstructuringof thetaskwithintheconstraintsoftheenvironment,whereasthe structurewithinandbelowtheunittasklevelreflectscognitiveand biologicalmechanisms,inaccordancewithNewell’s(1990)bands ofcognition.Accordingly,inACT-R,unittasksareimplementedby specificgoaltypesthatcontrolasetofproductionswhichrepresent thecognitiveskillsforsolvingthosetasks.

There are a broad range of ACT-R models studying prob-lem solving, decision-making (including intuitive decision-making;Kennedy &Patterson, 2012),and implicitlearning (see

http://act-r.psy.cmu.edu/publicationsforexamplesofeach;also, see Anderson (2007) and Lebiere and Anderson (2011) for an overview).Speciﬁcexamples(all usinginstance-basedlearning) include a model of how batters predict baseball pitch speed (Lebiere,Gray,Salvucci,&West,2003),amodelpredictingrisk aver-sioninarepeatedbinarychoicetask(Lebiere,Gonzalez,&Martin, 2007),amodelofsequencelearning(Lebiere&Wallach,2001),and amodel ofplaying PaperRockScissors(West&Lebiere,2001). AnothermodelofrepeatedbinarychoicealsowontheTechnion Predictioncompetitionovermachine-learningalgorithms(Stewart etal.,2009).These modelsallworkbystoringproblem-solving instances in declarative memory, then they make decisions by retrievingthoseinstancesbyleveragingthecognitivearchitecture’s activationprocessestoextractregularitiesinthetaskenvironment. Thereis amisconceptionthat intuitiveprocessesinACT-R – as implicit – are governed using only procedural memory pro-cesses,whiledeliberativeprocesses–asexplicit–aregoverned byonlydeclarativememoryprocesses(thisimplicit/explicit dis-tinction has been mistakenly attributed to Wallach & Lebiere, 2003b).In fact, whileeach declarative chunkis usually consid-eredapieceofconsciousknowledge,thesub-symbolicactivations thatcontroltheretrievalprocess(e.g.,base-levelactivationsand strengthsof associations)are consciouslyinaccessible and con-stitutetheimplicitknowledgeofthemodel(Gonzalez&Lebiere, 2005;Lebiere,Wallach,&Taatgen,1998).Inessence,theactivation calculusinvolvedinretrievingachunkistheimplicitpartofthe declarativesystem,whilethecontentsofthechunkitselfarethe explicitpartofthedeclarativesystem.

AninterestinginterplaybetweenSystem1andSystem2 pro-cessesoccursduringaretrievalrequest.Whenaproductionmakes aretrievalrequestitspeciﬁesthetypeofchunktoretrieveand potentiallyasetofslot-valuepairsfromwhichtomatch,whichis essentiallythespeciﬁcationofwhattoretrieve.Whilethe produc-tionsystemisgenerallyseenasanimplicit(System1)process,the constraintsin matchingtheretrievalrequestcomefrom explic-itlysettingwhichslot-valuepairstomatchagainst.Sincethisis somethingcodedbythemodeler,it couldbearguedthatitis a

totallyexplicitstrategy(i.e.,System2)basedonthemodelers intu-ition(c.f.,theory)ofhowtheretrievalshouldfunction.Thisisabit ofafalsedichotomybecauseeverymodelisablendofboth Sys-tem1andSystem2processes,andtheretrievalrequestlinksboth strategic(e.g.,requestingaspeciﬁcchunk)andimplicitprocesses (e.g.,spreadingactivation).Intermsofacognitivearchitectureand theno-magicdoctrine(Anderson&Lebiere,1998),wearguethat theretrievalspeciﬁcationisinsteadbestdescribedasanimplicit heuristic(asopposedtoaconscious/strategicheuristic),albeitstill beingeffectivelythemodeler’stheoryofhowtheretrievalprocess shouldunfold.

Itispossibletomakeretrievalsdrivenmorebyimplicit pro-cessesbyusingatechniquethatwecall‘open’retrievals.Aretrieval isconsideredopenwhenonlythetypeofchunkisrequestedand

no(orinarelaxedcase,minimal)slot-valuepairsareusedinthe speciﬁcationoftheretrievalrequest.Anexamplewouldbewhen oneisgivenasetofindirectcluesabouttheidentityofaperson andthenameofthepersonpopsupinone’smindfromthe con-vergenceofthecluesratherthananyspeciﬁcinformationretrieval process.Effectively,openretrievalsareakindofcontext-drivenfree association.Byusingopenretrievals,themodelisrelyingmoreon sub-symbolicactivations–which aredrivenbyexperience–to controltheretrievalprocess.Forinstance,performingaretrieval byspecifyingonlythecontextanddoingfreeassociationonthe outcomeallowsthemodeltomatchthebestoutcomebasedonthe recencyandfrequencyofprioroutcomesandspreadingactivation fromthecurrentcontext.Thisstandsincontrasttospecifyinga par-ticularoutcomeintheretrievalrequest,whichismoreanalogous tothemodelengaginginamorestrategicretrievalstrategy.

AsimilarthemebetweenSystem1andSystem2processesis thenatureofheuristicsindecision-making.Areheuristicsexplicit becauseoftheirsymbolicnature,orimplicitbecausethedecision makerisoftenunawareofthem?Thechoiceofwhich simplify-ingheuristicsareavailabletothemodeltendstobeaconscious strategyofthemodeler(asopposedtobeingchosenbythemodel;

Lewandowsky,1993).Thismaybeconsideredexplicit,although thisisanuncharitableviewofthemodeler’sselectionof heuris-tics/strategies(e.g.,themodeler’stheoryofwhich heuristicsare available;Taatgen&Anderson,2008).It ispossibletoviewtask instructionas akindof heuristic imposedby thetask environ-ment, thus byparsing thetaskinstructions themodel chooses fromasetof(generally)implicitheuristics(e.g.,recognition heuris-tic;ﬂuencyheuristic;Marewski&Link,2014)andperformsthe appropriateaction.Twosuchtheoriesaretherelatednotionsof

cognitiveniches(Marewski&Schooler,2011)andtheadaptive tool-box(Gigerenzer&Selten,2002).Acognitivenicheisasimplifying frameworkwhichdescribeshowonlyalimitednumberof appli-cablestrategiesmaybeconsideredinagivensituationbasedon theinterplaybetweenavailablestrategies,limitedhuman capaci-ties,andthetaskenvironment.Similarly,theadaptivetoolboxisa psychologicallyvalidatedsetofheuristicsfromwhichthemodel mayselect.Ofcourse,thesesolutions stillleaveopentotheory theunderlyingbasisforstrategyselectionofthemodel(Marewski, Gaissmaier,Schooler,Goldstein,&Gigerenzer,2010).

Oneofthedifﬁcultiesin providing amore completeanswer comesfromthetraditionaldichotomyofautomaticversus deliber-ative(orproceduralversusdeclarative)beinginsufﬁcienttoexplain thesourceofheuristics(mainlyfromthetaskenvironment),which isakeyindicatorofwhethertheheuristicshouldbeseenas pri-marilyimplicit,explicit,orboth.

3.3. Howdoesinstance-basedlearningtieintointuitive decision-making?

Instance-basedlearningtheory(Gonzalezetal.,2003;Taatgen etal.,2006)istheclaimthatimplicitexpertiseisgainedthroughthe

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accumulationandrecognitionofexperiencedeventsorinstances. Unlike instance-based machine learning algorithms (Gagliardi, 2011)thatareessentiallystrictexemplarmodelsofcategorization appliedtobigdata(Erickson&Kruschke,1998),instance-based learningtheoryallows forgeneralizationand thebootstrapping of learning with weak methods. Weak methods are relatively knowledge-freeheuristicmethodsofactionandexploration(such as random choice) that are procedurally driven when there is insufﬁcientdomainknowledge(i.e.,instances)tomakeeffective decisions.Onceenoughinstancesarestored,theseweakmethods aresupplantedbytheretrievalofdecisionsbasedontheseprior instances.

Similartotheoriesofintuitiveexpertise(Kahneman&Klein, 2009),instance-basedlearningtheoryarguesforthenecessityof receivingeffectivefeedback.Feedbackisrequiredtodeterminethe relativepayoffsfromnotonlyexpectedoutcomes,butfromthe actualoutcome.Thiseffectivelytunesinstancestorealexperiences asopposedtosimplyexistinginthecognitiverealmof expecta-tions.Thecombinationofcontextualinformationandthecurrent goal,theselectedaction,andtheoutcomeofthatactionresultin acommoncondition→action→outcomerepresentational struc-ture.Thisstructurereﬂectsthenecessaryrequirementsforeffective learningandsubsequentperformance.Supportingthisstructure,

Lebiere,Gonzalez,andWarwick(2009)haveshownhowKlein’s (2009) recognition-primed decision-making and instance-based learningusesimilarmechanismsandmakesimilarpredictionsin thecontextofnaturalisticdecision-making.Instance-based learn-ing,havingbeenformulatedwithintheprinciplesandmechanisms ofcognitioninACT-R,makesuseofthedynamicsofchunkretrieval torecall instances and alsomakes useof blended retrievalsto generalizeknowledge.Thisinstance+generalizationprocess pro-videsanadditionallevelofexplanationandpredictivepowerto complement the process speciﬁed in Klein’s analysis. As such, recognition-primeddecision-makingandothersimilarnaturalistic processescan beseenasa macrocognitivesubstratethat natu-rallycomplementsthemicrocognitivemechanismsofacognitive architecture(Lebiere&Best,2009).

The main claim of instance-based learning is that implicit knowledgeisgeneratedthroughthecreationofinstances.These instancesarerepresentedinchunkswithslotscontainingthe con-ditions(e.g., a set of contextualcues), the decision made (e.g., anaction), and theoutcome of thedecision (e.g.,the utilityof thedecision).Beforethereissufﬁcienttask-relevantknowledge, decision-makersimplicitlyevaluatealternativesusingheuristics (e.g.,randomchoice,minimizeloss,maximizegain).Oncea suf-ﬁcientnumberofinstancesarelearned,decision-makersretrieve andgeneralizefromtheseinstancestoevaluatealternatives,make adecision,andexecutethetask.Theprocessoffeedbackinvolves updating the outcome slot of the chunk according to thepost hocgeneratedutilityofthedecision.Thus,whendecision-makers areconfronted withsimilarsituations whileperforming a task, theygraduallyabandongeneralheuristicsinfavor of improved instance-baseddecision-makingprocesses(GonzalezandLebiere, 2005).

Comparinginstance-basedlearningwiththenecessityclaims of intuitivedecision-making fromKlein and Kahneman(2012), bothconsiderintuitiveknowledgetobelearnedviainstances.Also, inbothcasesdecisionsaremadebypattern-matchingoverprior instances(and/orsupplementedbyheuristics)andthenretrieving thebestfit.Inthecaseofinstance-basedlearning,however,this bestfitiscomputedusingageneralizationacrosstheclosest neigh-borsusingpartialmatchingorblendedretrievals.Bothrequirethe taskenvironmenttobesufficientlyregulartobeableto implic-itlylearnthestatisticalcorrelationsbetweencondition,action,and –througheitherinternalorexternalfeedback–outcome. How-ever,instance-basedlearningoffersconstraintsonexplanationby

groundingimplicitlearningwithinthemechanismsofacognitive architecture. For instance, the dynamics of an instance’s sub-symbolicactivations(e.g.,frequencyandrecencyinthebase-level learningequation) provideatheoretically groundedmechanism fordetermining whichinstances arelikelytoberetrieved fora givensituation,andalsocanexplainwhytheywereretrievedand what factorscame intoplay. Thisprovidesa much more rigor-ousexplanationofintuitivedecision-makingthancase-studiesand introspectionofexperts.

IBL–asinstantiatedinACT-R–alsoprovidesforaclearer dis-tinctionbetween automaticand deliberative processes. Theact ofencodingandretrievinginstancesisafullyautomaticprocess, guidedbyeither(hopefullyopen)retrievalorimplicitheuristics. However,oncetheretrievaliscompleted,whatthemodeldoes withtheretrievedchunk(e.g.,thestructureofthesubsequent pro-ductions)isanexplicitheuristic/strategy.Forinstance,whilethe retrievedchunkmightprovidearecommendedaction,itisuptothe model(throughtheproductionsystem)todeterminewhetherto verifytheaction,discardtheaction,performtheaction,orsimulate possibleotheroutcomes.

InACT-R, overthepast10years modelsrelatedto decision-making and problem-solving have seen increasing use of instance-based learning (whether explicitly referred-to as such or otherwise; e.g., Kennedy & Patterson, 2012) to learn intu-itiveknowledgestructures.ThisisunsurprisinggiventhatACT-R’s declarativememorymoduleandchunkstructureisanexcellent matchforthestorageandretrievalofinstances,whicheffectively guidespeopletosomeformofinstance-basedlearning.Inother words,thedesign andconstraintsof thearchitecturelead peo-pletoadoptaninstance-basedlearning-likeapproachbyusingthe architectureinthemostdirectandintuitiveway.

4. Whyatripartitedescription?

An essential feature in being able to explain how a model performsdecision-makingistoexaminenotonlythesourcesof generatingexpertise(e.g.,therole ofinstance-basedlearningin naturalistic decision-making), but also to examine both where

heuristicscome fromand howtheyare applied;and how they potentially leadto biasedbehavior. Theimplicit versus explicit argumentignoresthequestionofwhereheuristicsmaycomefrom –suchasthestructureofthetaskenvironment–somethingwhich isessentialfortheimplicitlearningofexpertise.Wearguethata tripartitedescriptionissufﬁcienttoexplainthesourceofboth suc-cessesandfailuresindecision-making.Thesethreelevelsinclude adescriptionofthemechanismsandlimitationsofthe architec-ture,theinformationstructureinthetaskenvironment,andthe useofheuristicsandstrategiestoadaptperformancetothedual constraintsofcognitionandenvironment.

We arenot theﬁrsttoargue forthree levelsof description. Forinstance,inthefast-and-frugalheuristics(Gigerenzer&Selten, 2002;Gigerenzeretal.,1999;Todd&Gigerenzer,2003)framework, heuristicsweredeterminedfromtheinterplayofbasiccognitive capacitiesandtheenvironment.Fast-and-frugalheuristicsexploit commonalitiesinthestructureofthetaskenvironmenttonotonly supportcapacitylimitationsinthemind(e.g.,short-term mem-ory), butshowhowtheselimitationmaybeadaptivegiven the environment.

Similarly,thegeneralargumentofecologicalrationalityisthat rationalityis context- andsituation-dependent, thus something considering irrational in one context may be fully rational in another.Forinstance,ifthegoalistomakeaccurateinferences, thenusingtherecognitionheuristicisecologicalrationalin envi-ronmentswhereone’srecognitionofanobject(e.g.,acityname) correlateswiththecriteriontobeinferred(e.g.,citysize). Ecologi-calrationalityiscomposedofthreefocuses:afocusonthemind,a

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focusontheworld(thestudyofregularitiesandconstraintsinthe environment),andafocusonputtingmindandworldtogether(the studyofecologicalrationality).Whatwehavedoneisadopta sim-ilarframeworkforthestudyofcognitivearchitectures,andfocus onexplainingbehaviorintermsofthemoretransparentcognitive constraintsofthearchitecture(inthatyoucanpointtothe under-lyingmechanisminthearchitecture),taskenvironment,andmodel structure.However,wearguethatbysituatingourtripartitelevel ofdescriptionwithinacognitivearchitecture,wemaymakemore causalclaimsastotheunderlyingstructureoftheheuristicsand howtheymayresultinbiasedbehaviorbasedonthecomplexityof theenvironment.

Thefirstlevelof descriptionentailsanunderstandingofthe constraintsimposedbythemechanismsandlimitationsofthe cog-nitivearchitecture.InACT-R,theseincludeanunderstandingofthe impactofrecencyandfrequencyofthelikelihoodofaninstance beingretrieved,whichalsoinfluencestheabilityofthemodelto generalizetonewsituationswhenusingblendedretrievalsto gen-erateaderivedoutputratherthanaspecificinstance.Othersources ofconstraintincludetheserialnatureoftheproductionsystem, onlyasinglechunkbeinginabufferatatime,andmatchinghuman time-courseof responses.Acommonsourceofbiased behavior ininstance-basedlearningdecision-makingmodelsistheuseof blendedretrievals,whichhaveatendencytoretrievevaluesthat arepulledtowardthemeanofallvaluesinmemory.Thiscommon mechanismcanleadtobothanchoringand confirmationbiases basedonhowfartheanchoredvaluevariesfromthemeanacross allinstancesinmemory(Lebiereetal.,2013).Itisimportanttonote thatthiswhollyimplicitprocessisnotconsciouslyavailabletothe model.

The second level of description entails an understanding of theconstraints imposedby the taskenvironment. Thiskind of descriptionhasbeensomewhatneglectedin discussions ofthe validityof cognitivemodels; however, it isa critical feature in understandingboththeconsistencyoflearningandthenatureof biases.Anunderstandingofthestatisticalandquantiﬁable regu-laritieswithinthetaskenvironmentdrivestheoverallabilityand rateoflearning,and thenatureofenvironmentalfeedback pro-videsfurtherevidence.Using anexamplefromSimon(1990);if youwanttostudythemovementofanantacrossthebeachyou needlooknofurtherthanthehillsandvalleysinthesandto deter-mineitspath.Tofurtherpushthisissue,Simon(1990)arguedthat “[h]umanrationalbehavior...isshapedbyascissorswhosetwo bladesarethestructureofthetaskenvironmentsandthe com-putationalcapabilitiesoftheactor”(Simon,1990,p.7).Someof themechanismsofACT-Rwerecreatedfollowingarational anal-ysis(Anderson, 1990), which assumes that cognitive processes areoptimally adaptedtotheenvironment. Therefore, ifwe are abletocapturetheessentialstructureoftheenvironmentin ACT-R,weshouldbeabletopredictwhat kindof heuristicsmaybe availableorusedinagivensituation.Thislevelofdescriptionis alsotheleveloftheunittask(Cardetal.,1983),andisgenerally capturedinACT-Rbyspeciﬁcgoaltypesthatdriveasetof pro-ductionsthatrepresentthecognitiveskillsrequiredforsolvingthe task.

Thethirdlevelofdescriptionentailsanunderstandingofhow thejointconstraintsofarchitectureandtaskenvironment influ-encethekindsofheuristicsandstrategiesavailabletothemodel. InACT-Rterms,thisistheexplanationoftheselectionandsequence ofproductionsfiring.Thislevelismostimportanttodescribeasit entailsmostofthechoicesofthemodelerindesigningthemodel. Instrategyselection,evensimpleheuristicstructurescangreatly influence theoutput of themodel, which in turn couldoverly constraindecision-makingwhilealsomakingcomplexproblems tractable.In otherwords, thedetection of affordances (Gibson, 1977)provided bythetaskenvironment influencethekinds of

informationthatthemodelcanaccumulateandtheactionsthat themodelmayperform.

OneuseofaffordancesinACT-Ristothinkofthemintermsof cognitiveniches(Marewski&Link,2014; Marewski&Schooler, 2011).Aspreviouslydiscussed,cognitivenichesareaffordances thatconstrainthesetofavailablestrategiesthatthemodelmay choosefrombasedontheinterplaybetweenpriorexperiencesand thetaskenvironment.Theselectionofwhichheuristicstoapplytoa givencontextmayalsobelearnedbythemodelthroughproduction utilitiesviareinforcementlearning,withearlylearningoccurring asa trial-and-errorprocessuntilsufﬁcientreinforcementoccurs throughexperienceorisinferredbyexplicittaskinstruction.This isanalogoustohow,ininstance-basedlearning,themodel transi-tionsfromreasoningviaheuristicstoreasoningviainstanceswith enoughexperience.Themechanismforhowthemodelmovesfrom heuristic-toinstance-based reasoningcan beseenasa kindof metacognitiveawareness(whichitselfdoesnottotallyescapethe strategyselectionargument).

Nowthatwearearmedwithatheory(instance-basedlearning) andameansofdescribingmodeloutput(thetripartitedescription), wecandelveintoanexample.

5. Intuitivedecisionsinsensemaking

Ratherthanprovideanoverviewofmanyexamples,wewould liketofocusonanin-depthanalysisofa singleACT-Rmodelof sensemakingthatusesinstance-basedlearningtoperformsix com-plexgeospatialintelligencetasksandprovidesbothanexplanation oftheoriginofbiasesandaclosefittohumandata(seeLebiereetal., 2013foramorecompletedescriptionofthetasksandfor quanti-tativemodelfits).Sensemakingisaconceptthathasbeenusedto defineaclassofactivitiesandtasksinwhichthereisanactive seek-ingandprocessingofinformationtoachieveunderstandingabout somestateofaffairsintheworld,whichhasalsobeenappliedin organizationaldecision-making(Weick,1995).

Oursensemakingmodeliscomposedofthreerelated compo-nents.Theﬁrst(Tasks1–3)learnsstatisticalpatternsofeventsand thengeneratesprobabilitydistributionsofcategorymembership basedonthespatiallocationandfrequencyoftheseevents(e.g. howlikelydoesagiveneventbelongtoeachofthecategories). Thesecond(Tasks4–6)appliesprobabilisticdecisionrulesinorder togenerateandreviseprobabilitydistributionsofcategory mem-bership(e.g.,ifa givenfeatureispresentatanevent,thenthat eventistwiceaslikelytobelongtocategoryA).Thethird(Tasks 1–6)involvesmakingdecisionsabouttheallocationofresources basedonthejudgedprobabilitiesofthecausesofperceivedevents, andiseffectivelyametacognitivemeasureofconﬁdenceinone’s judgment.

Theremainderofthissectiondescribesthemethodsandresults ofthesixtasksfromLebiereetal.(2013).Weusetheterm par-ticipants to reﬂect both human subjects and the ACT-R model performingthetask.

ForTasks1–3,theﬂowofanaveragetrialproceeded accord-ingtothefollowinggeneraloutline(seeFig.4foranexampleof thetaskinterface).First,participantsperceivedaseriesofevents labeledaccordingtowhichcategorytheeventbelonged.After per-ceivingtheseriesofevents,participantswereaskedtogeneratea centerofactivity(e.g.,prototype)foreachcategory’sevents,reﬂect onhowstronglytheybelievedtheprobebelongedtoeachcategory, andgenerateaprobabilityestimateforeachcategory(summedto 100%acrossallgroups).Scoringwasdeterminedbycomparing par-ticipants’distributionstoanoptimalBayesiansolution.Usingthese scoresitwaspossibletodeterminecertainbiases.Forinstance, participants’probabilityestimates thatexhibited lowerentropy thanafullyrationalBayesmodelwouldbeconsideredtoexhibita

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Fig.4. Asampleofthetaskinterface.Totheleftisalegendexplainingallthe sym-bolsonthemap(center).Totherightaretheprobabilitydistributionsforthefour eventcategories.Thepaneacrossthetopprovidesstep-by-stepinstructionsfor participants.

conﬁrmation bias, while probability estimates having higher entropy than an optimal Bayesmodel would be consideredto exhibitananchoringbias.Themodelwascomparedtrial-by-trial againsthumanstodeterminewhetherbothexpressedthebiases orotherwise.

Participantswerethenaskedtoallocateresourcestoeach cat-egorywiththegoalofmaximizingtheirresourceallocationscore, whichwastheamountofresourcesallocatedtothecorrect cate-gory.ForTasks1–3,theresourceallocationresponsewasaforced choicedecisiontoallocate100%oftheirresourcestoasingle cat-egory, and participantsreceivedfeedback whetheror not their categorizationwascorrect.

ForTasks4–6,theﬂowofanaveragetrialwasstructurally dif-ferentasintelligence‘features’,governedbyprobabilisticdecision rules,werepresentedinsequential layersonthedisplay.These Tasksrequiredreasoningbasedonrulesconcerningtherelationof observedevidencetothelikelihoodofanunknownevent belong-ingtoeachoffourdifferentcategories.Participantsupdatedtheir beliefs(i.e.,likelihoods)aftereachlayerofinformation(i.e., fea-ture) waspresented. For instance,in Task 4, afterdetermining the center of activity for each category (similar in mechanism toTasks 1–3) and reporting aninitial probabilityestimate,the SOCINT(SOCialINTelligence)layerwouldbepresentedby display-ingcolor-codedregionsonthedisplayrepresentingeachcategory’s boundary,wherethelikelihoodoftheeventbelongingtoagiven categoryistwiceaslikelyifitwaswithinthatcategory’s bound-ary.AfterreviewingtheinformationpresentedbytheSOCINTlayer, participantswererequiredtoupdatetheirlikelihoodsbasedonthis informationandthecorrespondingprobabilisticdecisionrule.

Whenallthelayershavebeenpresented(twolayersinTask 4,ﬁve layersin Task5, and fourlayersin Task6), participants wererequiredtogeneratearesourceallocation.IntheseTasks,the resourceallocationresponsewasproducedusingthesame inter-faceasprobabilityestimates.Forinstance,assumingthatresources wereallocatedsuchthat{A=40%,B=30%,C=20%,D=10%},ifthe probebelongedtocategoryA(i.e.,thatAwasthe‘groundtruth’)

thentheparticipantwouldreceiveascoreof40outof100,whereas iftheprobeinsteadbelongedtocategoryB,theywouldscore30 points.

Twoseparateexamswerecollectedfromtwoseparate popu-lations.Themodelperformedthefirstexamand wascompared against45participantswhowereemployeesoftheMITRE Corpo-ration.Allparticipantscompletedinformedconsentanddebriefing questionnairesthatsatisfiedIRBrequirements.Withoutgoinginto extensivedetailovertheresults,theACT-Rmodelsignificantly pre-dictedmanyofthetrial-by-trialvariationsinhumanperformance, andnotonlythepresenceorabsenceofabias,butalsothequantity ofthebiasmetric,reflectedinanoverallr2₌_.645_for_negentropy

scoresacrossalltasks.

Theresultsofthemodelwerethencomparedtotheresultsofa novelsamplegatheredfrom103studentsatPennStateUniversity. Thisnewdatasetwasnotavailablebeforethemodelwasrun,and noparametersorknowledgestructureswerechangedtofitthis dataset.Unliketheoriginal45-participantdataset,thePennState sampleusedonlypeoplewhohadtakencoursecredittowarda graduateGeospatialIntelligenceCertificate.Themodel correctly predictedboththepresenceanddegreeofbiasesoneverytrial inTasks1–3,andfollowedsimilartrial-by-trialtrendsforbiasesin Tasks4–5.Thequantitativefitsofthemodelwerealsosimilar,with anoverallr2₌_.591_for_negentropy_scores_across_all_tasks.

6. Wewillnowprovideanoverviewofthemodelfunction

6.1. Biasesingroupcentergeneration

Intheﬁrsttaskcomponent,theﬂowofanaveragetrialbegan withparticipantsperceivingaseriesofeventslabeledaccordingto whichcategorytheeventbelonged,eachcorrespondingtoagroup icononthecentralmap,afterwhichaprobewasdisplayed. Par-ticipantswerethenrequiredtogenerateacenterof activityfor eachcategory’sevents,andgenerateaprobabilityestimateforeach category(summedto100%).

Whengroupcentersweregenerateddirectlyfromaretrieval ofeventsrepresentedinmemory, theblended retrievalprocess inACT-Rreflectedadisproportionateinfluenceofthemostrecent eventsgiventheirhigherbase-levelactivation.Astrategytocombat thisrecencybiasconsistedofgeneratingafinalresponseby per-formingablendedretrievaloverallthegroupcenters(bothcurrent andpastcentersgeneratedforprevioustrials)storedinmemory, therebygivingmoreweighttoearliereventsbycompoundingthe influenceofearliercentersoverthesubsequentblendedretrievals. Thissecond-orderblendedretrievalisdoneforeachcategoryacross theirpriorexistingcenters,whichwerefertoasthegenerationof acentroid-of-centroids.Thiseffectivelyimplementsan anchoring-and-adjustmentprocesswhereeachnewestimateisacombination ofthepreviousonestogetherwiththenewevidence.

Afundamentaldifferencewithtraditional implementationof anchoring-and-adjustmentheuristicsisthatthisprocessisentirely constrainedbythearchitecturalmechanisms(especiallyblending) and doesnot involveanyadditional degreesof freedom. More-over,becausethereareanequalnumberofcentroid-of-centroids chunks (one per category createdafter each trial), there is no effectofbase-rateonthemodel’slaterprobabilityjudgments,even thoughthebase-rateforeachcategoryisimplicitlyavailableinthe modelbasedonthenumberofrecallableevents.Thisillustrates themetacognitivenatureofheuristicsinourtripartite organiza-tion:giventhatthenatureofcognitivemechanismsgivesriseto a recency biasthat is incompatible withthe taskenvironment (assumingastabledistribution),thecentroid-of-centroids heuris-ticisusedtogivemoreweighttoolderinstancesandcircumvent therecencybias.Notethatthebiastowardrecencyinarchitectural

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mechanismsarosebecauseitindeedreﬂectedthenatureofmany environments(Anderson&Schooler,1991),makingitwelladapted tothosesettings.Thereisnosuchthingassuboptimalbias:just a mismatch between assumptions and environment that occa-sionally needs to be supplemented with the proper heuristic adjustment.

6.2. Biasesinprobabilityadjustment

Inthistaskcomponent,eventfeatures–suchasthelocation orcontextofevents–werepresentedinsequentiallayersonthe display.Initialdistributionsforeachcategorywereprovidedto par-ticipants,afterwhichparticipantsupdatedtheirbeliefsaftereach featurewasrevealed.Beliefswereupdatedbasedonasetof pro-videdprobabilisticdecisionrules:e.g.,iftheMOVINT(movement intelligence)featureshowsdensetrafﬁc,thengroupsAandCare fourtimesaslikelyasgroupsBandD.Whenallthelayerswere presented,participantswererequiredtoallocateresourcestoeach category.

Toleverageaninstance-basedlearningapproachforprobability adjustment,theACT-Rmodel’smemorywasseededwitharange ofinstancesconsistingoftriplets:aninitialprobability,an adjust-mentfactor,andtheresultingprobability.Thefactorissetbythe explicitrulesofthetask.Whenthemodelisaskedtoestimatethe resultingprobabilityforagivenpriorandmultiplyingfactor,it sim-plyperformsablendedretrievalspecifyingpriorandfactor,and thenoutputstheposteriorprobabilitythatrepresentstheblended consensusoftheseededchunks.

Whenprovidedwithlinearsimilaritiesbetweenprobabilities (and factors), the primary effect is an underestimation of the adjustedprobabilityformuchoftheinitialprobabilityrange(i.e., ananchoringbias),withanoverestimationonthelowerend of therange (i.e., conﬁrmation bias). While themagnitude of the biasescanbemodulatedsomewhatbyarchitecturalparameters, theeffectsthemselvesareaprioripredictionsofthearchitecture, inparticularitstheoreticalconstraintsonmemoryretrieval.

Asimplerandmoreimplicitmodelofprobabilityadjustmentcan beproducedbyrepresentingthevarioushypothesesaschunksin memoryandusingtheiractivationasanestimateoftheirstrength ofsupport.Whenevidenceisreceived,itismatchedagainst pat-ternslinkingittovarioushypothesesandthebestmatchingoneis retrieved,leadingtoaboostinactivation.Ifcontradictoryevidence startsaccumulating,twobiaseswillemerge.First,newevidence willsometimesbemisinterpretedbecausethecurrentdominant hypothesisismostactiveandcanovercomesomedegreeof mis-match.Second,eveniftheevidenceiscorrectlyinterpretedandthe correcthypothesisreinforced,forthenewhypothesistoattain pri-macyitwilltakesometimetosufﬁcientlybuildactivationandfor theactivationofthepreviouslydominanthypothesistosufﬁciently decayovertime.Thisprocesshasbeengivenanumberofnames, fromanchoringbiastopersistenceofdiscreditedevidence.

Anumberofstructuredanalytictechniqueshavebeenproposed toremedythesebiasesemergingfromthedynamicsofour cog-nitivesystem(Heuer&Pherson,2010).Themostprominentone mightbeAnalysisofCompetingHypotheses,whichproposesa pro-cessbywhichallcompetinghypothesesareevaluatedagainsteach pieceofevidenceandthesumoftheirsupportonlycomputedand comparedattheend.Thisisdonetopreventtheearlyemergence ofafavoredhypothesisandtheresultingbiases.Ananalogtothe AnalysisofCompetingHypotheseshasbeenimplementedinour modelandcanbeshowntodirectlyaffecttheactivation dynam-icsdescribedabove.Eachhypothesischunkreceivesarehearsalat eachstep,equalizingtheinﬂuenceofbase-ratefromtheir activa-tionandpreventingawinner-take-alldynamic.Theresultisthat theiractivationovertime willsimplyreﬂect thedegreeof sup-portthattheyhavereceived.Inthisexample,structuredanalytic

techniquescanalsobeseenasmetacognitiveheuristicsthat lever-agethebeneﬁcialaspectsofcognitivemechanismswhiledefeating oratleastlimitingtheirpotentialbiasesandthusprovideexternal aidstoourintuitivedecision-making.

6.3. Biasesinresourceallocation

Resource allocation makes use of the same instance-based learningparadigmasprobabilityadjustment.Thisuniﬁed mech-anism hasno explicit strategies, but instead learns to allocate resourcesaccordingtotheoutcomesofpastdecisions.Themodel generatesaresourceallocationdistributionbyfocusingonthe lead-ingcategoryanddetermininghowmanyresourcestoallocateto thatcategory.Theremainingresourcesaredividedamongstthe remainingthreecategoriesinproportiontotheirassigned proba-bilities.Representationofatrialinstanceconsistsofthreeparts:a decisioncontext(i.e.,theprobabilityoftheleadingcategory),the decisionitself(i.e.,theresourceallocationtotheleadingcategory), andtheoutcomeofthedecision(i.e.,thepayoff).

The model’s control logic takes a hybrid approach between choice(Lebiere&Anderson,2011)anddecisionmodels(Wallach &Lebiere,2003a),involvingtwostepsofaccesstoexperiencesin declarativememoryratherthanasingleone.Whendetermining howmanyresourcestoapplytotheleadcategory,themodel ini-tiallyhasonlytheprobabilityassignedtothatcategory.Thefirst stepisdonebyperformingablendedretrievalonchunks repre-sentingpastresourceallocationdecisionsusingtheprobabilityas acue.Theoutcomevalueoftheretrievedchunkistheexpected outcomeforthetrial.Thesecondstepistogeneratethedecision thatmostlikelyleadstothatoutcomegiventhecontext.Notethat thisprocessisnotguaranteedtogenerateoptimaldecisions,and indeedpeopledonot.Rather,itrepresentsaparsimoniouswayto leverageourmemoryofpastdecisionsinthisparadigmthatstill providesfunctionalbehavior.Asignificanttheoreticalachievement ofourapproachisthatitunifiescontrolmodelsandchoicemodels inasingledecision-makingparadigm.

Afterfeedbackisreceived,themodellearnsaresource alloca-tiondecisionchunkthatassociatestheleadingcategoryprobability, thequantityofresourcesassignedtotheleadingcategory,andthe actualoutcomeofthetrial(i.e.,theresourceallocationscorefor thattrial).Additionally,uptotwocounterfactualchunksare com-mittedtodeclarativememory.Thecounterfactualsrepresentwhat wouldhavehappenedifawinner-take-allresourceassignmenthad beenapplied,andwhatwouldhavehappenedifapure probability-matchedresourceassignment(i.e.,usingthesamevaluesasthe ﬁnalprobabilities)hadbeenapplied.Theactualnatureofthe coun-terfactualassignmentsisnotimportant;whatisessentialistogive themodelabroadenoughsetofexperiencerepresentingnotonly thechoicesmadebutalsothosethatcouldhavebeenmade.The useofacounterfactualstrategytogenerateadiversityofoutcomes, experiencedorimagined,canbeseenasaverygeneralandeffective metacognitiveheuristic.

Theadvantageofthisapproachisthatthemodelisnotforced tochoosebetweenadiscretesetofstrategiessuchas winner-take-allorprobabilitymatching;rather,variousstrategiescanemerge from instance-based learning. By priming the model with the winner-take-alland probability matching strategies (essentially theboundaryconditions),itispossibleforthemodeltolearnany strategyinbetweenthem,suchasatendencytomoreheavilyweigh theleadingcandidate,orevensuboptimalstrategiessuchas choos-ing25%foreachofthefourcategories(assuringascoreof25on thetrial)ifthemodelreceivesenoughnegativefeedback(i.e.,poor scores)soastoencourageriskaversion.Instance-basedlearning canthus beseen in this instanceas a highlyﬂexible metacog-nitivestrategyfromwhichanumberofmorelimited,hardwired strategiescanemerge.

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7. Discussion

Sofar,wehavearguedthatcognitivearchitecturesaidinthe studyofintuitivedecision-makingbyprovidingafalsifiable the-oryforthestudyofmechanisms,processes,andrepresentations involvedindecision-making.Byusingacognitivearchitecture,one isadoptingconstraintsinvolvedinmanagingtheflowofknowledge andprocessesinvolvedintheseknowledgeoperations. Architec-tures expand ourability to gobeyond‘just-so’ explanationsto describetheunderlyingprocessesand knowledgeleadingupto decisions.Theyalsoprovidemoreflexibilitybeyondtheconstraints ofexpertise-basedsystemswhenoperatingoutsideofvery con-strainedand/orverystableenvironments.Inmanycases,models basedinacognitivearchitecturecanperformtasksandprovide testablepredictionsthataretoocomplextoanalyzewith tradi-tionalexperimentalmethodsduetothecombinatoricsofpossible decisions.

Thenextstep in thedevelopmentof cognitivearchitectures shouldbemechanismstosupportthegeneralizabilityofmodels andreducedegreesoffreedom.Somepreliminarythrustsinclude: theintegrationofneurallyplausibleassociativelearningtodrive implicitstatisticallearningofregularitieswithintheenvironment (Thomson&Lebiere,2013),thedevelopmentofexpectation-driven cognitiontocueepisodicmemoryformation(Kurupetal.,2012), and more generally the development of strategy selection (or metacognitive awareness) withinthe architecture to guidethe selectionof featuresusedin therepresentation andretrievalof instances(Lebiereetal.,2009;Marewski&Link,2014;Marewski &Schooler,2011;Reitter,Juvina,Stocco,&Lebiere,2010;Reitter, 2010).

Ideally,thestrategiesandheuristicsimplementedinthe archi-tectureshouldbeselected(ifnotcreated)bythemodelitselfrather thanprovided bythemodeler.Themodel (drivenby the archi-tecture)shouldberesponsiblefortheselectionandevolutionof strategies.Togetstarted,however,severalgeneralproceduresare neededtobootstraplearninguntilsufﬁcientknowledgeislearned, atwhichpointprocessesimplicatedingeneratingexpertiseshould lead tointeresting emergent behaviors (andnovel predictions) withinthemodel.Thequestionofwhichminimalsetofprocedures bestcaptureshumanperformanceisanempiricalone,andonethat needstobeacenteroffocus.Theadoptionofgeneralframeworks suchasinstance-basedlearningandtheadoptionofacommonset ofheuristicsacrosstasksappeartobethenextstepintheright direction.

ConﬂictofInterestStatement

The authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest(such ashonoraria; educationalgrants; participationin speakers’bureaus;membership,employment,consultancies,stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such aspersonalorprofessionalrelationships,affiliations,knowledge or beliefs) in the subject matter or materialsdiscussed in this manuscript.

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