Thinking About Evidence1

Thinking about Evidence1

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Evidence,InferenceandEnquiryPhilipDawid,WilliamTwining,andMimiVasilaki

Printpublicationdate:2011PrintISBN-13:9780197264843PublishedtoBritishAcademyScholarshipOnline:January2013DOI:10.5871/bacad/9780197264843.001.0001

ThinkingaboutEvidence1DAVIDLAGNADO

DOI:10.5871/bacad/9780197264843.003.0007

AbstractandKeywords

Thischapterarguesthatpeoplereasonaboutlegalevidenceusingsmall-scalequalitativenetworks.Thesecognitivenetworksaretypicallyqualitativeandincomplete,andbasedonpeople'scausalbeliefsaboutthespecificsofthecaseaswellastheworkingsofthephysicalandsocialworldingeneral.Akeyfeatureofthesenetworksistheirabilitytorepresentqualitativerelationsbetweenhypothesesandevidence,allowingreasonerstocapturetheconceptsofdependencyandrelevancecriticalinlegalcontexts.Insupportofthisclaim,thechapterintroducessomenovelempiricalandformalworkonalibievidence,showingthatpeople'sreasoningconformstothedictatesofaqualitativeBayesianmodel.However,people'sinferencesdonotalwaysconformtoBayesianprescripts.Empiricalstudiesarealsodiscussedinwhichpeopleover-extendthediscreditofoneitemofevidencetootherunrelateditems.Thisbiasisexplainedintermsofthepropensitytogrouppositiveandnegativeevidenceseparatelyandtheuseofcoherence-basedinferencemechanisms.Itisarguedthatthesecognitiveprocessesareanaturalresponse


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todealwiththecomplexityoflegalevidence.

Keywords:reasoning,legalevidence,qualitativenetworks,cognitivenetworks,alibievidence,Bayesianmodel

AbstractAretheregeneralprinciplesforhowpeopleupdatetheirbeliefsinthefaceofuncertainevidence?Howdotheserelatetoformaltheoriesofevidenceintegration?Inparticular,howdoeverydayreasonerssuchasjurorsdrawconclusionsfromlargebodiesofinterrelatedlegalevidence?Thischapterarguesthatpeoplereasonaboutlegalevidenceusingsmall-scalequalitativenetworks.Thesecognitivenetworksaretypicallyqualitativeandincomplete,andbasedonpeoplescausalbeliefsaboutthespecificsofthecaseaswellastheworkingsofthephysicalandsocialworldingeneral.Akeyfeatureofthesenetworksistheirabilitytorepresentqualitativerelationsbetweenhypothesesandevidence,allowingreasonerstocapturetheconceptsofdependencyandrelevancecriticalinlegalcontexts.Insupportofthisclaim,thechapterintroducessomenovelempiricalandformalworkonalibievidence,showingthatpeoplesreasoningconformstothedictatesofaqualitativeBayesianmodel.However,peoplesinferencesdonotalwaysconformtoBayesianprescripts.Wealsodiscussempiricalstudiesinwhichpeopleover-extendthediscreditofoneitemofevidencetootherunrelateditems.Thisbiasisexplainedintermsofthepropensitytogrouppositiveandnegativeevidenceseparatelyandtheuseofcoherence-basedinferencemechanisms.Itisarguedthatthesecognitiveprocessesareanaturalresponsetodealwiththecomplexityoflegalevidence.

(p.184) IntroductionLEONARDVOLEischargedwithmurderingarichelderlylady,MissFrench.Hehadbefriendedher,andvisitedherregularlyatherhome,includingthenightofherdeath.MissFrenchhadrecentlychangedherwill,leavingVoleallhermoney.Shediedfromablowtothebackofthehead.Therewerevariouspiecesofincriminatingevidence:Volewaspoorandlookingforwork;hehadvisitedatravelagenttoenquireaboutluxurycruisessoonafterMissFrenchhadchangedherwill;themaidclaimedthatVolewaswithMissFrenchshortlybeforeshewaskilled;themurdererdidnotforceentryintothehouse;VolehadbloodstainsonhiscuffsthatmatchedMissFrenchsbloodtype.

Asbefitsagoodcrimestory,therewerealsoseveralpiecesofexoneratingevidence:themaidadmittedthatshedislikedVole;themaidwaspreviouslythesolebenefactorinMissFrenchswill;VolesbloodtypewasthesameasMissFrenchs,andthusalsomatchedthebloodfoundonhiscuffs;Voleclaimedthathehadcuthiswristslicingham;Volehadascaronhiswristtobackthisclaim.Therewasoneothercriticalpieceofdefenceevidence:Voleswife,Romaine,wastotestifythatVolehadreturnedhomeat9.30p.m.ThiswouldplacehimfarawayfromthecrimesceneatthetimeofMissFrenchsdeath.However,duringthetrialRomainewascalledasawitnessfortheprosecution.Dramatically,shechangedherstoryandtestifiedthatVolehadreturnedhomeat10.10


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p.m.,withbloodonhiscuffs,andhadproclaimed:Ivekilledher.JustasthecaselookedhopelessforVole,amysterywomansuppliedthedefencelawyerwithabundleofletters.AllegedlythesewerewrittenbyRomainetoheroverseaslover(whowasacommunist!).InonelettersheplannedtofabricatehertestimonyinordertoincriminateVole,andrejoinherlover.Thisnewevidencehadapowerfulimpactonthejudgeandjury.Thekeywitnessfortheprosecutionwasdiscredited,andVolewasacquitted.

Afterthecourtcase,Romainerevealedtothedefencelawyerthatshehadforgedthelettersherself.Therewasnoloveroverseas.Shereasonedthatthejurywouldhavedismissedasimplealibifromadevotedwife;instead,theycouldbeswungbythestrikingdiscreditoftheprosecutionskeywitness.

Thiscrimestoryisaworkoffiction.ItisdrawnfromAgathaChristiesplayWitnessfortheProsecution.Thestorycontainstwistsandturnsthatarenotrepresentativeofatypicalcrimecase;however,itservestoillustratethepatternsofinferencethatrecurinreal-worldlegalcontexts.Thetaskofthefact-finder(e.g.investigator,judgeorjuror)istopulltogetherallthediversethreadsofevidenceandreachasingularjudgmentofinnocenceorguilt.Onethingthatmakesthistasksodifficultisthatthedifferentpiecesofevidenceareofteninterrelated.Youcannotsimplysumupthepositiveevidenceonthe(p.185) onehand,andthenegativeontheother.Theevidenceinteractsincomplexways.Forexample,intheabovestory,Volesenquiryaboutaluxurycruiseisnotrelevantonitsown;itbecomesrelevantbecausehehadrecentlybeenwrittenintotheoldladyswill.Moreover,itstronglysuggeststhatheknewthatshehadchangedherwill.Notonlydoesthisgivehimamotiveforthemurder,butitalsoshowsthathewaslyingwhenheclaimednottoknowthathestoodtobenefitfromherdeath.2

Thisiswhatmakescrimestoriessofascinating.Theycannotbesolvedsimplybyaddingorsubtractingbeliefs;rather,onemustnegotiatetheintricaciesofhowthedifferentpartsofthepuzzlefittogether.Further,thepressuretoreachadecisiveverdictinacriminalcasebeyondreasonabledoubt3meansthatasimpleleaningtowardsonesideortheotherisnogood.Oneneedstomentallybolsterthecasefororagainstthesuspect,sothatitclearlydominatesthealternativescrowdingoutotherpossibleconstrualsofthecase.Thiscompelsonetoconstructastorythatisbothone-sided4andcomprehensive,andthuslikelytofillinmanygapsleftunsupportedbytheevidenceathand.Thereisseldomtheleisuretotinkerawayslowly,asinscience,accumulatingsupportforeachstep;instead,onemustsketchapictureallinonego,andhopethatitcapturestheessentialtruthsofthecase.

Despitetheenormityofthetask,untrainedjurorsareexpectedtoreachverdictsthatcanhavelife-changingconsequences.Forthelargeparttheyachievethis(althoughmistakesaremade!).Howdotheydothis?Howshouldtheydoit?Thesearethequestionsthatthischapterwilladdress.

Beforewestart,itisimportanttoclarifytheintendeddomainofthechapter.Itisnotaboutthereasoningoflegalexperts,suchasjudges,barristers,orinvestigators.Itisaboutthereasoningoflaypeoplewhenconfrontedwithcomplexbodiesofevidence.This


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mightinvolveanindividualjuroronacriminalcase,butitcouldalsobeamemberofthegeneralpublicfollowingtheunfoldingofevidencethroughreadingsnippetsinthemedia.Moreover,it(p.186) istheindividualjurorthatisthefocusofattentionhere,notthegroupofjurorsthatparticipateinthejurydeliberationprocess.Thisisnottosaythatwhatwediscoveraboutthepsychologyoftheindividualjuror,ornon-expert,doesnothaveimplicationsforthejuryasawhole,orfortheexpertjudge(theyarehumanafterall).Butextrapolationtothesemorecomplexcaseswouldrequirealotmoreargumentandevidence.

NetworksofrelationsEvidenceistypicallysortedaspositiveornegativewithrespecttoaparticularhypothesis.Forexample,evidencecaneitherexonerateorincriminateasuspect.However,therearevariousdifferentwaysinwhichtheevidencecanexertitsinfluenceonahypothesis,andthesedifferentroutesaremaskedbythesimpledichotomyofpositiveversusnegative.Toillustrate,considerthedistinctionbetweenaffirmativeandrebuttalevidence(cf.BinderandBergman,1984).Affirmativeevidencedirectlysupportsthecasemadebyeitherprosecutionordefence.Forexample,themaidstestimonythatsheheardVoletalkingtoMissFrenchshortlybeforethemurderisaffirmativeevidenceforVolesguilt.Rebuttalevidenceislessdirect;itservestoundermineaclaimmadebytheopposingside.Forinstance,themaidstestimonyisrebuttedbytheevidencethatshedislikedVole,andsoughttoincriminatehim.Affirmativeandrebuttalevidencecanbepresentedbybothsidestothedispute,andthuscrosscutsthedistinctionbetweenincriminatingandexoneratingevidence.Indeedsomeevidenceisbothaffirmativeandrebuttal.Forexample,thewifesstatementthatVolereturnedhomemuchlaterthan9.30p.m.rebutshisalibi,andalsosupportstheclaimthathewaswithMissFrenchshortlybeforethemurder.

Moregenerally,acrucialdifferencebetweenaffirmativeandrebuttalevidenceisthatthelatterisonlyrelevanttoahypothesis(e.g.guiltorinnocence)becauseittargetsapieceofevidencepresentedbytheopposingside.5Withoutanitemofevidencetooppose,rebuttalevidenceexertsnoinfluenceonthetargethypothesis.ThusevidencethatthemaiddislikedVoleisonlyrelevanttohisguiltgivenhertestimonythathewaswithMissFrenchshortlybeforethetimeofhermurder.

Tocapturethedistinctionbetweenaffirmativeandrebuttalevidence,andvariousotherstructuralsubtleties,evidenceandhypothesesneedtobe(p.187) representedinanetwork.Itseldomsufficestogatherpositiveitemsononeside,negativeitemsontheother,andcomputeaweightedsum(asCharlesDarwinfamouslydidwhendecidingwhetherornottomarry).Instead,accountmustbetakenofhowtheseitemsofevidencemightinterrelate.

FormalmodelsofevidentialreasoningHowcancomplexinterrelationsbetweenevidenceandhypothesesberepresented?Beforelookingathowpeopledothisinpractice,itisinstructivetoconsiderhowitcanbedoneinprinciple.Therehavebeensubstantialadvancesinnormativemodelsofevidentialreasoningoverthepastdecade,andavarietyofnetworkmodelshavebeendeveloped,


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includingWigmorecharts(Wigmore,1913),cognitivemaps(Axelrod,1976),andBayesiannetworks(Pearl,1988).WewillfocusonBayesiannetworks.Theyhavewell-establishedfoundationsinprobabilitytheory,andarecurrentlyappliedinmanypracticalcontexts,includinglegalandforensicreasoning(DawidandEvett,1997;Dawid,MorteraandVicard,2007;FentonandNeil,2008;Hepler,DawidandLeucari,2007;Taroni,Aitken,GarbolinoandBiedermann,2006).

BayesiannetworksBayesiannetworks(BNs)consistoftwoparts:agraphstructureandasetofconditionalprobabilitytables.Thegraphstructureismadeupofasetofnodescorrespondingtothevariablesofinterest,andasetofdirectedlinksbetweenthesevariablescorrespondingtocausalorevidentialrelations.Inlegalcontextsthevariableswillincludehypothesesaboutthedetailsofthecrime,theculprit,thesuspectandnumerousevidencestatements.Thisyieldsadirectedgraphthatcompactlyrepresentstheprobabilisticrelationsbetweenvariables,inparticulartheconditionalandunconditionaldependencies.Thusthegraphcanbeusedtoreadoffwhichitemsofevidencearerelevanttoeachother,ortoparticularhypotheses.Forexample,thegraphinFigure7.1representsasmallportionoftheevidenceintheWitnessfortheProsecutionstoryoutlinedabove.

Thisgraphhasfourbinaryvariables,eachtakingvaluesofeithertrueorfalse.ThevariableVoleGuiltyrepresentswhetherornotVolemurderedMissFrench.ThevariableVolePresentrepresentswhetherornotVolewaswithMissFrenchat9.30p.m.onthenightofthemurder.ThevariableMaidTestimonyrepresentswhetherornotthemaidtestifiedthatVolewaspresent(p.188) atthattime.ThevariableMaiddislikesVolerepresentswhetherornotthemaiddislikedVole.

Figure7.1 .AsimpleBayesianNetworkcapturingafewvariablesintheWitnessfortheProsecutionstory.

ThelinkfromVolePresenttoVoleGuiltyindicatesthatVolescommittingthemurderthatnightdependsonhisbeingwithherat9.30p.m.ObviouslythislinkisprobabilisticVolemighthavebeenpresentatthattimebutnotguiltyofthesubsequentmurder.Moreover,VolespresenceatthecrimesceneisclearlynotasufficientcauseofhismurderingMissFrench.Variousadditionalcausalfactors,suchasmotiveandintentarenecessaryforVoletohavemurderedher.SomeofthesevariablesarerepresentedinthefullerBayesianNetworkinFigure7.3.NeverthelessVolespresenceatthecrimesceneisevidenceofopportunity,andthusraisestosomedegreetheprobabilitythathedidmurderMissFrench.ThisexplainsthelinkfromVolePresenttoVoleGuilty.

ThelinkfromVolePresenttoMaidTestimonyindicatesthattheMaidsclaimthatshe


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heardVolespeakingtoMissFrencharound9.30p.m.dependsonwhetherornotVolewasactuallythereatthattime.Thislinkisalsoprobabilistic.PerhapsthemaidmisidentifiedVolesvoice.Indeedthedefencelawyersuggestedthatshemighthaveheardvoicesfromtheradio.AnotheralternativecauseofthemaidstestimonyisthatshefabricateditbecauseshedislikedVole.Afterall,inthetrialsheexpressedastrongdislikeforhim.ThispossibilityisexplicitlyrepresentedinthenetworkbythelinkfromMaiddislikesVoletoMaidTestimony.

Inadditiontothegraph,aBayesiannetworkalsorequiresaconditionalprobabilitydistributiontableforeachvariable.Thisdictatestheprobabilityofthevariableinquestionconditionalonthepossiblevaluesofitsparents(thenodeswithdirectlinksintothatvariable).Whenanodehasnoparents,thistablesimplycontainsthebase-ratevalueforthatvariable.Thisbase-ratecorrespondstothepriorprobabilityofthevariablebeforeanyofthecaseevidenceistakenintoaccount.Insomecasestheexactvaluesoftheseconditional(p.189) probabilitiesarenottooimportant,solongastheyobeythequalitativerelationsencapsulatedbythelinksinthegraph.Forexample,thepresenceofalinkfromVolepresenttoMaidTestimonyrequiresthattheprobabilityofthetestimonygiventhatVoleispresentisgreaterthan(orlessthan)theprobabilityofthetestimonygiventhatVoleisnotpresent.However,therearevariousaspectsthatarenotgivenbythegraphstructurealone,butarefurnishedbytheprobabilitiesthemselves:forexample,whetherthelinkispositiveornegative;howthevaluesofdifferentparentnodescombinetodictatethevalueofthechildnode.Inaddition,mostofthealgorithmsthatallowaBNrepresentationtobeusedforinferencerequireexactnumbers.

RepresentationandinferenceAsignificantbonusofBayesiannetworksisthatoncetherepresentationisconstructed,itcanbeusedforinference.Thissetsitapartfrommostotherformsofnetworks(e.g.WigmorechartsandCognitivemaps),whichservemainlyasdescriptivetools.IndeedrepresentationisintertwinedwithinferenceinaBN.Thearrangementofnodesandlinks,plustheconditionalprobabilitytablesforeachnode,dictatewhatinferencesarelicensed(viathelawsofprobability).Onewaytodrawnovelinferencesistosetasubsetofvariablestoparticularvalues(instantiatethevariables),andthenseewhateffectthishasontheothervariablesofinterest(e.g.thecrimehypothesis).Thiscorrespondstostandardcasesofinferentialreasoninginlegalcases.Moreover,itenablesseveralkindsofinference:inferencebasedonevidencethatisknownforsure(e.g.theMaidstestimony),evidencethatisbelievedwithsomeprobability(e.g.thatVolewaspoor),andevidencethatispresumedforsakeofargument(e.g.ifwesupposethatVolewaspresentat9.30p.m.,whatelsefollows?).Thelattercanbeveryusefulattheinvestigativestageofenquiry,whennewpiecesofevidencearesought.Forexample,adetectivemightsupposethatVolewasindeedpresentat9.30p.m.,andtheninferthelikelyconsequencesofthis,suchasVolebeingseenandheardbythemaid,orleavingsometraceevidence.

PatternsofinferenceThenetworkstructurecapturesseveralpatternsofinferencecriticaltoevidentialreasoning.


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(p.190) Screening-off(conditionalindependence)AbasicfeatureofBNsisthescreening-offrelation.Thisholdswhentwovariablesthatareprobabilisticallydependentarerenderedindependentbytheknowledgeofthestateofathirdvariable.Forexample,themaidstestimonydependsonVolesguilt,butifweknowforcertainthatVolewaswithMissFrenchat9.30p.m.,hertestimonybecomesindependentofhisguilt.Inotherwords,ifwealreadyknowthatVolewaswithMissFrenchat9.30p.m.,themaidstestimonydoesnotaddanythingtoourknowledgeofwhetherornotVoleisguilty.Ofcoursesuchcertaintyisoftenhardtocomeby.EvenCCTVfootageconfirmingVolespresenceat9.30p.m.isopentodoubt.WasitreallyVole?Couldthefootagehavebeentamperedwith?Isthetimingcorrect?Neverthelesstherearemanysituationswhereapropositionisassumedoracceptedastrue(orfalse).

TheBNrepresentationrestsupontheassumptionthattheparentnodesofavariablescreenitofffromallothervariablesinthenetwork(exceptforvariablesthatthemselvesdependonthatvariable).6Thisisapowerfulcondition:itcangreatlysimplifythecomputationsneededtodrawinferences,allowingvariousitemsofevidencetobeignoredalltogether.Forexample,ifitisestablishedthatVolewaswithMissFrenchat9.30p.m.,thennootherwitnesstestimonyaboutthiseventcaninfluencetheprobabilitythatVoleisguilty.Thisscreening-offassumptioncanalsoaidfutureinvestigationandinformationgathering.Thus,ifaneventEisestablishedforcertain,thereisnoadditionalinferentialbenefittobegainedfromfurtherwitnesstestimoniesthatattesttoE.Ofcourseinmanycasesthetruthofakeyeventwillremainindispute;hencetheaddingofextrawitnessestothesameeventwillbeareasonablepolicy.

Inlegalinvestigations,asineverydaylife,itiscrucialtodistinguishbetweenwhatpeopleclaimandwhatactuallyhappened.Thenetworkstructure(p.191) isideallysuitedtothis,andreadilydistinguisheswitnessreportsfromtheeventsorsituationsthatthesereportsareabout.ThusthemaidstestimonythatVolewaswithMissFrenchat9.30p.m.isrepresentedseparatelyfromtheeventthathewasinfactwithheratthattime.OneadvantageinrepresentingthereportE*andthereportedeventsEseparatelyisthattheprobativeforceoftheevents(iftrue)iskeptdistinctfromthecredibilityofthewitnesssource.7ThisisimportantbecausethefactorsrelevanttotheprobativeforceofEonthetargethypothesisHarequitedifferentfromthoserelevanttotherelationbetweenthereportE*andE.Forexample,therearevariousreasonswhyVolespresenceat9.30p.m.doesnotguaranteethathekilledMissFrench;perhapssomeoneelsewastheretoo,orbrokeinshortlyafterwards.Butadifferentsetoffactorspotentiallyunderminethereliabilityofawitnessreport,andthustheinferencefromE*toE.Thisisaplacewhererebuttalevidencecanexertitsforce.Perhapsthemaidmisidentifiedthevoice,orheardtheradio,orsimplylied.ThedistinctionbetweenE*andEalsogreatlyfacilitatesinferenceinsituationswherethereareseveralwitnesstestimoniestothesameevent,andclarifiesthedifferencesbetweencorroborating,conflicting,orcontradictorytestimony.8

ExplainingawayThescreening-offrelationholdswhenthreevariablesareinachain(ABC)9oradivergentstructure(ABC).Inbothcases,AandCaredependent,butbecome


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independentconditionalonB.Theconversesituationoccurswithaconvergentstructure(ABC).Inthiscase,AandCareindependent,butbecomedependentconditionalonB(orconditionalonavariablethatitselfdependsonB).Thisencapsulatesadistinctivepatternofinferencetermedexplainingaway.10

Explainingawaytypicallyoccursinsituationswheretherearemultipleindependenthypotheses(explanations)foranobserveditemofevidence.Theobservedevidenceleadstosomeincreaseinprobabilityforallthesehypotheses;however,ifoneoftheseisfoundtobetrue,theothersthendecreaseinprobability.Theevidencethatpreviouslysupportedthemisexplained(p.192) away.Anotablefeatureofthissituationisthatthepossiblehypothesesareindependentwhenthestatusoftheevidenceisunknown,butbecomeconditionallydependentgivenknowledgeofitsstatus.Thisisdistinctfromcaseswherehypothesesaremutuallyexclusive.

Toillustrate,consideragainthenetworkinFigure7.1.ThereisnodirectlinkbetweenVolepresentandMaiddislikesVole.Thisindicatesthatthesetwovariablesareunconditionallyindependent.WhetherornotVolewaspresentatthattimeisirrelevanttowhetherornotthemaiddislikedVole,andviceversa.However,oncethemaidgiveshertestimony,thesetwovariablesbecomeconditionallydependenttheycompeteasalternativeexplanationsofhertestimony.SupposefurtherthatwearesurethatthemaiddoeshaveastrongdislikeforVole,andwishestoincriminatehim.Thishypothesiswillexplainawaythemaidstestimony.

ConsideranotherexamplefromtheWitnessfortheProsecution.Volescuffswerefoundtohavetracesofbloodonthem(typeO).ThiswasadvancedasevidencethatVolehadmurderedMissFrench(whohadbloodtypeO).11However,thedefencesoughttoexplainawaythisevidencebyclaimingthatthebloodbelongedtoVole(alsotypeO),whohadcuthimselfwhenslicingham.Thisclaiminturnwasbacked-upbyarecentscaronVoleswrist.ClearlytherearetwocompetingexplanationsforthepresenceofbloodonVolescuffs.Moreover,theseexplanationswereindependentpriortothediscoveryofbloodonthecuffs.

Legalscenarios,andevidentialcontextsingeneral,arerepletewithexplainingawayinferences,anditisasubstantialadvantageoftheBNframeworkthatitmodelsthisinferencesonaturally.Thisalsoexplicatesthedistinctionbetweenaffirmativeandrebuttalevidencementionedearlier.Rebuttalevidenceservestoexplainawayanopposingpieceofaffirmativeevidence.Forinstance,thebloodonVolescuffsisaffirmativeevidencethathemurderedMissFrench,whereastheclaimthathecuthimselfslicingham(andthescaronhiswrist)isrebuttalevidence.WhetherornotVolecuthimselfisonlyrelevanttothequestionofhisguiltbecauseitrebuts(explainsaway)theevidenceprovidedbythebloodonhiscuffs.BNsprovideanaturalformatforrepresentingthiskindofevidentialsubtlety.

(p.193)


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Figure7.2 .WitnessvsAlibimodels.ModelAisanimpartialwitnesstestimonyinwhichEscreens-offHfromE*.ModelBisapartialalibitestimonywhereEdoesnotscreen-offHfromA,andModelCrepresentsthesamesituationasmodelBbutwiththedeceptionvariableDexplicitlyrepresented.

Alibitestimonyandfailureofscreening-offInthesimplestcaseofwitnesstestimony,theeventtestifiedto(E)willscreen-offthewitnessreportE*fromthetargethypothesisH(seeFig.7.2,modelA).Thisscreening-offrelationcanholdevenifthereareseriousreasonstodoubtthereliabilityofthemaidstestimony,ortheprobativenessoftheeventE.However,thiswillnotalwaysbethecase.SometimesthewitnessreportE*willexertanindependentinfluenceonH.Thisismostclearlyillustratedbyconsideringalibitestimony.

Analibiinvolvestheclaimthatthedefendantwassomewhereelseatthetimethecrimewascommitted.Assumingthatnobodycanbeintwoplacesatthesametime12analibiispotentiallyverystrongevidenceinfavourofthedefendant.Thisisbecausetheprobabilitythatthedefendantcommittedthecrime,onthesuppositionthathewasnotatthecrimescene,isverylow,andmuchlowerthantheprobabilitythathecommittedthecrime,giventhathewasatthecrimescene.However,alibievidenceisoftenconsideredweakevidence,especiallyifitisonlythedefendantsword,andthereisnocorroboratingevidence(Gooderson,1977).

ThealibicontextisdepictedbymodelBinFigure7.2.ThevariableHcorrespondstothehypothesisthatthedefendantisguilty;variableEtothe(p.194) defendantspresenceatthecrimescene;variableAtothedefendantsclaimthathewassomewhereelse.ThelinkfromEtoHindicatesthathiscommittingthecrimedependsonhispresenceatthecrime-scene;thelinkfromEtoAindicatesthathisalibistatementdependsonwhetherornothewasatthecrimescene.InthecaseofalibitestimonytheinferencefromHtoEisusuallytakentobemuchstrongerthantheinferencefromAtoE.

ThereisalsoadirectlinkfromHtoA.ThisrepresentsourclaimthattheeventEdoesnotscreen-offHfromA.Whyisthisthecase?Recallthatthescreening-offrelationstatesthatonceyouknowthevalueoftheintermediatevariableE,knowledgeofAtellsyounothingmoreaboutH(andviceversa).Butconsiderthesituationinwhichthedefendantgiveshisalibi,butyouhaveindependentevidence(e.g.CCTVfootage)thathewasinfactatthecrimescene.Doesthefactthathesaidhewasnotatthecrimescenetellyouanythingmoreaboutwhetherornotheisguilty?Wellnowyouknowthathelied.13Andthis


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informationseemsincriminating,over-and-abovethefactthatyouknowthathewasatthecrimescene.Ofcoursehemightbelyingforotherreasons:perhapshewashavinganaffair;orcommittingadifferentcrime.Butitseemsreasonabletoassumethattheprobabilitythathewilllieinhisalibiisgreaterwhenheisguiltythanwhenheisinnocent.

Onthisreadingofthesituation,theeventEnolongerscreens-offHfromA.Theprobabilitythatthedefendantisguilty(H)giventhathewasatthecrimescene(E)islowerthantheprobabilitythatheisguilty(H)giventhathewasatthecrimescene(E)andsaidhewasnotatthecrimescene(A).Innumbers,P(H|E&A)P(H|E).Forscreening-offtohold,thesetwoprobabilitieswouldhavetobeequal.14

Inotherwords,findingoutthatthedefendanthasliedinhisalibitellsyoumoreabouthisguiltthansimplyknowingthathewasatthecrimescene.Thepossibilitythatthealibiproviderislyingcanitselfberepresentedinthegraph(seeFigure7.2modelC)withanadditionalnodeDrepresentingwhetherornotthedefendantismotivatedtolie.ThelinkfromHtoDcorrespondstotheassumptionthatthemotivationtoliedependsonwhetherornotthedefendantisguilty(i.e.heismorelikelytoliewhenguiltythanwheninnocent).ThelinkfromDtoAindicatesthatwhetherthedefendantsayshewaspresentatthecrimescenedependsonwhetherheismotivatedtolie(i.e.heismorelikelytosayhewasnotatthecrimesceneifheismotivatedtolie).

(p.195) ThisalibinetworkisreadilyappliedtoVolesalibi.RecallthatVoleclaimedthathereturnedtohishomeat9.30p.m.,andthereforewasnotwithMissFrenchatthattime.However,ifVoleisindeedguiltyhewouldhavestrongmotivationtolieaboutthis.Thisfurnishesanalternativeexplanationforhisalibi.Thereforeitisnottoosurprisingthatadefendantsalibiisoftentreatedwithscorn.Thealternativeexplanationintermsofdeceptionexplainsawaythealibitestimony.

Thesituationchangesifsomeoneelsecorroboratesthealibi.Animpartialwitness,withnothingtogain,mightbolsterthealibiconsiderably(althoughnotalwaysasmuchasexpected).15Apartialwitness,suchasafriendorrelative,islessconvincing.Afterall,theytoohaveamotivetolie.Romaineknewthis,andrealisedthatthejurywouldnotbeoverlyimpressedbyasupportingalibifromVolesbelovedwife.

Anintriguingconsequenceofthealibinetworkisthatthefailureofscreening-offonlyseemstoapplywhenthealibi-providerknowswhetherornotthedefendantcommittedthecrime.ThisisbecausethelinkfromHtoDisonlypresentiftheguiltofthedefendantinfluencesthealibi-providersmotivationtolie.Butifthealibi-providerdoesnotknowwhetherornotthedefendantisguilty,thereisnosuchlink.Thisisnottosaythatthealibi-providerisnotmotivatedtolieinhisfavour,butjustthatthismotivationisnotdependentonthedefendantactuallybeingguilty.Forexample,onemightexpectawifetolieforherbelovedhusbandevenifshedoesnotknowwhetherheisguiltyorinnocent.ButinthiscasetheeventEwillscreen-offHfromA.Ifweknowthatthedefendantwasatthecrimescene(E),findingoutthatthealibi-providerliedtoprotectthedefendantdoesnotaddanythingextratoourassessmentofguilt.Theirmotivationtoliewasnotaffectedbywhetherornotthedefendantwasindeedguilty.


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Thistwistdemonstratestheconsiderablesubtletiesthatcanariseinreasoningaboutwitnessoralibievidence,andreiteratestheneedforanetworkrepresentation.Inalatersectionwewillpresentanempiricalstudyshowingthatpeoplearesensitivetothissubtletyintheirinferencesaboutalibievidence.

ThusfaritappearsthatBNsprovideapromisingframeworktorepresentthecomplexinterrelationsbetweenbodiesofevidenceandhypotheses.Inparticular,BNscaptureimportantpatternsofreasoningsuchasscreening-offandexplainingaway,andelucidatesomeofthesubtletiesinvolvedinalibi(p.196) andwitnesstestimony.16Moreover,itisthegraphstructureratherthantheexactconditionalprobabilitiesthatplaythekeyrole.Thenetworkrepresentationsandthequalitativerelevancerelationsbetweenvariablesdomuchoftheinferentialwork.

HolisticvsatomisticapproachesBayesianapproachestolegalreasoningareoftencriticisedfortheiratomisticevaluationofevidence(e.g.PardoandAllen,2008).Incontrast,proponentsofaholisticapproacharguethatevidenceshouldbeassessedasawholenotpiecemeal.Thisclaimalsodrawsonpsychologicalresearchthatjurorscomposecoherentstoriestomakesenseoftheevidencepresentedattrial(PenningtonandHastie,1986,1992).However,thiscriticismisbasedonarestrictednotionoftheBayesianapproachthatdoesnottakeintoaccounttheholisticrelationsimplicitinBayesiannetworks.Thenetworkmodeldefendedinthischaptermaintainsthatpeopleorganiseevidenceandhypothesesincoherentnetworks,andthatthisisoftentherightthingtodofromarationalviewpoint.Thus,anitemofevidencecanonlybeevaluatedwithrespecttoitsrelationtootheritemsofevidenceandrelevanthypotheses.Forexample,thescaronVoleswristisonlyrelevanttothehypothesisofhisguiltgivenhisclaimthathecuthimselfslicingham,andtheevidenceofbloodonhiscuffs.Thisisnottosaythatsmallersubsetsofevidencecannotbeanalysedinisolationfromothersubsets.PresumablythecomplexitiesofthebloodevidencearelargelyindependentoftheissuesthatsurroundthemaidstestimonyaboutVolespresenceonthenightofthecrimethesesubsetsareonlylinkedviathesuperordinatepropositionthatVolecommittedthecrime.Indeeditisthepossibilityofisolatingsmallsubsetsofevidencethatmakesanetworkapproachtractabletothehumanmind.

Arelatedissueiswhetherpeoplesultimatefocusisontheprobabilityoftheissueinquestion,forexample,theprobabilitythatthedefendantisguilty,oronsomethingmoreholistic,suchastheprobability(orplausibility)oftheprosecutionsaccountasawhole(ascomparedtothedefendantsaccount).TheBayesianaccountisusuallyportrayedasconcentratingontheformertheprobabilityofthecrimehypothesisgivenalltheevidence.Andastandardobjectionisthatincontrastfact-findersareconcernedwithholisticjudgements,suchashowbelievabletheprosecutionstoryisascomparedtothe(p.197) defencestory.However,thelatterkindofjudgementisreadilyaccommodatedwithinthebroaderBayesianframework.Thus,Pearldiscussesinferencemechanismsthatrevisetheprobabilityofcompositesetsofbeliefsratherthanupdatingindividualprobabilities(Pearl,1988).Inshort,theBayesiannetworkframeworkisnotrestrictedtoprobabilityjudgementsaboutsingularpropositions,butcanextendtojudgementsabout


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setsofpropositions.Itsuppliesthetoolsforassessingtheprobabilityofaconnectedsetofbeliefs,aswellasindividualbeliefs.

Bayesiannetworksasmodelsofhumanreasoning?Bayesiannetworkshaveconsiderableappealasnormativemodelsofevidentialreasoning,especiallyindomainswithquantitativedata(Aitken,TaroniandGarbolino,2003;Dawid,MorteraandVicard,2007;HeplerandWeir,2008).However,fullyfledgedBNsareunlikelytoprovideacomprehensivemodelforhumanreasoning.Thespecificationofpreciseconditionalprobabilities,andthecomplexcomputationsrequiredtodrawinferences,seembeyondthecapabilitiesofhumanreasoners,especiallywhenlargenumbersofvariablesareinvolved.Forexample,evenapartialBNfortheWitnessfortheProsecution,includingonlyasubsetoftheavailableevidence,wouldpresentanintimidatingpicturefortheuninitiatedjuror(seeFig.7.3).Indeedmanypsychologicalstudiessuggestthatpeoplearepooratestimatingandcalculating(p.198) withprobabilities(Gilovich,GriffinandKahneman,2002;Kahneman,SlovicandTversky,1982).

Figure7.3 .PartialBayesianNetworkcoveringsomeofthemajorpiecesofevidenceinWitnessfortheProsecution.Notethatnotalltheitemsofevidencehavebeenincludedinthisnetwork.

ItthusappearsthatBNsareanon-starterasadescriptivemodel.However,thisconclusionispremature.ItoverlooksthefactthatkeyaspectsoftheBNformalismarequalitativeratherthanquantitative,andthatBNscanbehierarchicallystructuredtoovercomehumanprocessinglimitations.

QualitativenetworkmodelsThenetworkstructureofaBNispurelyqualitative,representingthepresenceorabsenceofdependenciesbetweenvariables.ThusalinkfromAtoBtellsusthatcertainvaluesofAwillchangetheprobabilityofcertainvaluesofB,withoutneedingtospecifyexactlyhowmuch.AndalthoughthestandardBNframeworkrequiresaprecisesetofconditionalprobabilities,manyoftheimportantcharacteristicsofthenetworkareretainedwithoutafullandexactsetofprobabilities(BiedermannandTaroni,2006;WellmanandHenrion,1993).

ThismeansthatsomeonecanconstructthegraphicalpartofaBNwithouthavingaccesstoanypreciseprobabilities.Moreover,inmanycasestheywillstillbeabletodrawinferencesbasedsolelyonthisqualitativestructure,albeitlesspreciseonesthanwitha


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quantitativenetwork.Indeedmostofourexamplesanddiscussionssofarhavereliedonthisqualitativesenseofprobabilisticrelations.

Thereforethefactthatpeoplecannotestimateorcalculatewithexactprobabilitiesdoesnotunderminethepossibilitythattheyusenetworkstorepresentrelationsbetweenevidenceandhypotheses.Furthermore,suchqualitativerepresentationscanapplyequallywellindomainswherenoprecisefiguresareavailable.Thisisparticularlysignificantinthelegalcontext,wheremuchoftheevidencedoesnotadmitofquantification.Forexample,itmightnotbepossibletoquantifytheexactprobativeforceofawitnesstestimonythatplacesthedefendantatthecrimescene;butmostpeoplewouldagreethatitraisestheprobabilityofguilt,howeverslightly.Moreover,peoplewilloftenbeabletomakecomparativeprobabilityjudgements;forinstance,judgingthatacertainpieceofforensicevidence(e.g.tracesofthevictimsbloodfoundonthedefendantscoat)raisestheprobabilityofguiltmorethanthetestimonyofapartialwitness.

Theimportantpointisthatevenifpeoplelackafullyspecifiedprobabilisticmodel,theycanstillexpresstheiruncertainknowledgeintermsofaqualitativenetwork.Inasimilarvein,evenifpeopleareunabletoperformexactBayesiancomputationsoverthisnetwork,theycanstilldrawapproximate(p.199) inferences(perhapsusingheuristicmethods).Andthismightnotbesuchabadthing,especiallyincontextswhereexactfiguresareunavailable,orwheretherearelargenumbersofinteractingvariables,sothatexactinferenceisintractable.Therestrictiontoqualitativenetworksmightactuallyincreasetheapplicabilityandfeasibilityofthesenetworkstotheproblemsfacedinlegalcontexts.

Theideathatpeopleutilisequalitativenetworksisnotnew.Andincomputersciencetherearevariousqualitativereasoningsystemsdesignedtomeshwiththenaturalpropensitiesofhumanusers(Druzdzel,1996;Keppens,2007;Parsons,2001).Theseprovideanimpressivearrayofrepresentationalformatsandinferencealgorithms.Therearealsoseveralconsiderationsfrompsychologythatspeakinfavourofqualitativeapproaches.

First,psychophysicalstudiesshowthatforarangeofsensoryphenomenapeoplearepooratmakingabsolutejudgements,andinsteadmakeordinalcomparisons(e.g.Stewart,BrownandChater,2005).Estimatesoflikelihoodorstrengthofevidenceseemnoexceptiontothis.Thus,althoughsomeonemightnotbeabletojudgethepreciseprobativeforceofevidenceE1onhypothesisH,theymightbeabletojudgethatE1makesHmoreprobable,andperhapsthatE1isstrongerevidenceforHthanE2is.

Second,analysesofawiderangeofpredictivetasks(e.g.clinicalandmedicaldiagnosis)suggestthatstatisticalmodelsthatuseunitweightsoftenoutperformmorecomplexmodels(Dawes,1979).Thekeyrequirementforthesesimplermodelsisthatthesignofeachvariableinthemodeliscorrect;theexactweightsplacedonthesevariablesisnotcritical.Whilethegeneralisabilityofthesefindingsisopentoquestion,thesuccessofunitweightmodelsinthesespecificenvironmentsremainsimpressive.Onelacunaisthatthemodelstypicallyassumeasimplisticstructure,wheretherelevantpredictorvariables


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areindependent.Thisassumptionmightworkwellincertainenvironments,butisunlikelytosucceedinmorecomplexcontexts,suchasthelegaldomain,wheretheinterrelationsbetweenevidenceandhypothesesarecrucial.Theproposedqualitativenetworksthusgobeyondsimplelinearmodels,butsharetheintuitionthatprecisionintheweightsisnotanecessaryconditionforsuccessfulinference(andinfactmightimpairperformance,byaddingaspuriousdegreeofprecision).17

Third,psychologicalresearchoncausalreasoning(GriffithsandTenenbaum,2005;Lagnado,Waldmann,HagmayerandSloman,2007;Sloman,2005)suggeststhatpeopleareinitiallyconcernedwithjudgementsabout(p.200) causalstructure(istherealinkbetweenAandB?)ratherthancausalstrength(howstrongisthelinkbetweenAandB?).Peoplefocusonqualitativecausalrelations,andusethesecausalmodelstoguidetheirinferenceandactions.ThereisalsogrowingempiricalevidencethatpeoplereasoninaccordancewiththequalitativeprescriptsofcausalBNs(KrynskiandTenenbaum,2007;SlomanandLagnado,2005).Clearly,causalbeliefsarecriticalintheconstructionofourmodelsoftheworld.Ifthesearepredominantlyqualitative,thensotoowillbethenetworkstructuresthattheyunderpin.Indeedithasbeenarguedthatpeoplesnetworkrepresentationsoftheworldarecausalthrough-and-through.Pearl(2000)advancesanargumentfortheprimacyofqualitativecausalbeliefsthatalsoservesasastrongempiricalhypothesisabouthumancognition.Hearguesthatthebestwayforpeopletoorganisetheirknowledgeoftheworldisintermsofinvariant(stable)qualitativecausalrelations.Theserelations,onceknownorassumed,willnotchangeaccordingtotheparticularitiesoftheinformationwehave,whereasprobabilisticrelationscan.Forexample,considerachainABC.ThereisaprobabilisticdependencybetweenAandC,butthisdisappearswhenweknowB(screening-off).Conversely,consideracommoneffectmodelABC.OnthismodelAandCareprobabilisticallyindependent,butbecomedependentconditionalonourknowingB(explainingaway).Whatremainsconstantacrossallthesechangesintheprobabilisticrelationsaretheunderlyingcausalrelationsinthemodels.Ofcoursewemighthavethestructurewrong,butthisisaseparateissue.Inessence,theargumentisthatpeopleshouldprefertoorganisetheirknowledgeonthebasisofinvariantratherthanunstableaspectsoftheworld.Thisisnottosaythatcausalrelationsdonotchange.Theyoftenwill,especiallywhenweinteractwiththeworld.Butunlikewithprobabilisticrelations,thesechangeswillreflectchangesintheworldratherthanchangesinourknowledgeaboutit.Thisisapowerfulconjectureabouthumancognition,andpsychologistsareexploringitsimplications.However,itisnotanessentialpartofthecurrentargument,whichemphasisesthequalitativenatureofourmentalnetworks.

TheproposalthatthefundamentalbuildingblocksofhumanreasoningarequalitativefitswithGilbertHarmansclaimthatpeoplethinkandreasonprimarilyintermsofbeliefs(all-or-none)ratherthandegreesofbelief(Harman,1986).Tospeculate,onereasonforthecentralroleofcategoricalbeliefsmightderivefromthecloserelationbetweenthoughtandaction.Eventsintheworld,includingactionsandoutcomes,aretypicallyall-or-none;soourrepresentationsoftheseeventsarelikelytofollowsuit.Forinstance,thesuspectwaseitheratthecrimesceneornothecannothavebeen67percentpresent.


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Consequently,whenreasoningaboutthispossibilityweeither(p.201) supposethathewaspresent,orsupposethathewasnot.Itseemslessplausiblethatwecansupposeandreasonwithsomemixedstateinwhichheispartiallythere,andpartiallyelsewhere.Thisisnottosaythatmorecomplexsituationscannotadmitofgradations,orthatwecannotassignprobabilitiesordegreesofbelief.Theclaimisthatourcognitivesystemshaveprimarilydevelopedtoreasonwithsituationsinvolvingcategoricalevents,actionsandoutcomes.

Small-scalenetworksNotonlydopeoplereasonqualitatively,theyalsoseemtoreasonwithjustafewvariablesatatime.Thisisnottoarguethattheycannotbuilduplarge-scaleknowledgesetscontainingmanyvariables;buttheactivereasoningprocessislikelytoinvolveonlyafewvariablesatatime.Thisseemstobeanaturalconsequenceofourlimitedworkingmemorycapacity(Cowan,2001;Halford,CowanandAndrews,2007;Miller,1956).Thisrestrictionsuggeststhatactiveevidentialreasoningtakesplacewithnetworkfragments(e.g.themodelinFig.7.1)ratherthanthefull-scalenetworks(e.g.thelargermodelinFig.7.3).Thesesmall-scalenetworksaresufficienttocarryoutkeyinferencepatternssuchasexplaining-awayorscreening-off,butmayrequirethatsomevariablesbechunkedtogetherorignoredentirely.Reasoningwithnetworkfragmentscanleadtomodificationsintheimplicitlystoredknowledgebase,sothatinthelongtermpeopleeffectivelyrepresentlargerstructures.Inotherwords,peopleconstructandreasonwithnetworkfragments,andthesearestitchedtogethertoyieldalarge-scalepictureoftheworld.Onthisview,workingmemoryactsasabottleneckbetweentheworldandourlarge-scalerepresentationofthisworld.

HierarchicalrepresentationsThenotionofchunkingiswidelyrecognisedtobeakeyfeatureofhumanmemory,butithasnotbeenconnectedwithinferenceandreasoninginalegalcontext.18Inthecontextofevidentialreasoning,itseemsthatpeopleuserichlystructuredrepresentationsthatcanbeunpackedatvariouslevelsofgrain.Inthiswaypeoplecannegotiateacomplexproblemdomainwithmultipleinteractingvariables,whilerespectingthelimitationsofworkingmemoryand(p.202) activereasoning.19Forexample,inmanycrimecasestheinitiallevelofrepresentationisintermsofindividualpeople(e.g.victim,perpetrator,suspect,accomplices,witnesses),objects(e.g.weapons,bloodtraces,fibres),andthespatiotemporalrelationsandinteractionsbetweenthem.Atafinerlevelofgrain,eachindividualpossessesvariousattributes(age,race,gender,personalitytraits,dispositionsetc.),alongwithbeliefs,desiresandintentionsthatservetoexplainandpredicttheirbehaviour.Whenreasoningaboutacrimecasethefact-findercanswitchbetweentheselevelsofabstraction,atonemomentreasoningabouttheinteractionsbetweenseveralindividuals(e.g.thelocationsofVole,MissFrenchandthemaidonthenightofthecrime),atanothermomentreasoningaboutthemotives,beliefsandintentionsofaspecificindividual(e.g.themaid).Thekeypointisthatbyusingrichhierarchicallystructuredrepresentationshumanreasonerscanovercomethelimitationsimposedbytheirlimited-capacityworkingmemory.


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HowdoesthisabilitytochunkinformationfitwiththeideathathumanreasonersuseBayesiannetworks?Atfirstsightitwouldseemthatthehierarchicallystructuredrepresentationsusedinhumanreasoningarefar-removedfromBayesiannetworks,whichrepresentallvariablesatthesamelevel.However,recentworkincomputerscience(KollerandPfeffer,1997;Hepler,DawidandLeucari,2007)hasdevelopedprobabilisticsystemsthatintroducehierarchicalstructures(objects)todealwithmorecomplexreal-worlddomains.ThesesystemsarestillbaseduponBayesiannetworks,andexploitthenotionofconditionalindependence,butallowforricherrepresentationsandmoreefficientinferenceprocedures.Thishighlightsanintriguingparallelbetweenthehumanreasoningsystemandartificialsystemsdevelopedincomputerscience.Inordertocopewiththecomputationaldemandsoflargeandcomplexdomains,bothsystemsmakeuseofhierarchicalstructuredrepresentations,andsimplifyinferencebyusingnetworkstructuresthatexploitconditionalindependencerelations.Thusfutureresearchintohumanevidentialreasoningcanprofitablydrawonadvancesinprobabilisticgraphicalframeworks.

Ourguidinghypothesisisthatpeoplereasonaboutlegalevidenceusingsmall-scalequalitativenetworks.Thesenetworksaregeneratedonthebasisofbackgroundassumptions,genericcausalknowledge,andcase-specificinformation,andutilisehierarchicallystructuredrepresentationstoovercomecomputationallimitationsandsupportefficientinference.Suchnetworksoftenrequireonlycomparativejudgementsofrelevanceandprobability,ratherthanpreciseprobabilityestimates.Inaddition,itislikelythatpeopleflexiblyadopt(p.203) theformatthatbestsuitsthedataavailabletothem.Forexample,combiningquantitativeevidencesuchasthatprovidedbyaDNAmatchwithqualitativeevidencesuchasthatfurnishedbyawitnesstestimony.Reasoningandinferencemightalsobeconductedinanapproximatefashion,ratherthanthroughfull-scaleBayesiancomputation.Thereisarangeofpossibleinferencemechanisms,includingsignpropagation,beliefpropagation,spreadingactivationandconstraintsatisfaction.Hereagainthechoiceofmechanismmightdependontheavailabledataandtheformatofthenetwork.Forexample,ifallnetworklinkshavesigns(positiveornegative),20butnostrengthvalue,thensignpropagationisthemostappropriateinferencemechanism.Ifthestrengthoflinkscanberankedorquantified,thenotheralgorithmsmightbemoresuitable.

Anotherimportantfeaturetonoteisthatthequalitativenetworkmodelsthatpeopleconstructaresubjective.Thesemodelsdependonanindividualsbackgroundknowledgeandassumptions,theevidenceavailabletothem,theirinterpretationofthisevidence,andmyriadotherfactors.Andofcoursethesecandiffersubstantiallyfromindividualtoindividual.Presumablytheprosecutionsmodelwillbeverydifferentfromthatofthedefence.However,thisdoesnotmeanthattheyareunconstrained,orthatreasonablepeoplecannotendupagreeingonasharedmodel.Therequirementsofconsistencyandcoherence(andfitwithreal-worldcausalknowledge),andtheneedtoaccommodatetheundisputedelementsofthecase,willplaceconstraintsontheviablemodelsandinferencesthatcanbelegitimatelydrawnfromtheavailableevidence.Thetrialisasocialstructurethatwillideallyconvergeonamodelthatisanappropriatereflectionofwhat


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actuallyhappenedinthecase.

SourcesofreasoningerrorsThecentralclaimisthatqualitativenetworkslieattheheartofpeoplesevidentialreasoning.Thisisnottosaythatpeoplewillconformperfectlytothedictatesofanyspecificqualitativereasoningsystem.Rather,theclaimisthatthefundamentalvehicleforrepresentationandinferenceisqualitative,andoftenderivedfromcausalunderstanding.Indeed,therewillbemanywaysinwhichevidentialreasoningcanfallshortofnormativetheory.Withregardtorepresentation,peoplecanerrduetoinadequatemodels,failuretoincludecrucialvariablesorlinks,inappropriatecollapsingorgroupingofvariables.(p.204) Withregardtocomputation,peoplecanerrbecauseofshort-cutheuristicproceduresthatcanleadtosuboptimalinference.Inbothcaseserrorswilltypicallyarisefromcapacityandprocessinglimitations,andthereasonersattemptstoovercomethesebysimplifyingrepresentationandinference.Aswithmanycognitivebiases,theseerrorsareanecessarypricetopayinordertomaintainanduseworkablemodelsoftheworld.

DynamicnetworksAkeyfeatureofhumancognitionisthatitadaptstoachangingenvironment.Thesechangesmightinvolvenovelevidence,hypothesesandgoals.Thusnetworkconstructioninthefaceofevidenceisdynamic.Peopleadapttheirnetworkonlineasinformationisreceivedandhypothesesaredevelopedorthoughtup.ThisisnotastrictlyBayesianprocess(inwhichacompletesetofhypothesesarecontinuallyupdated).Rather,peopleseemtointroduceandeliminatehypothesesinamoreall-or-nothingmanner.Thissavesgreatlyonstorageandcomputation,butcanleadtobiasesanderrors.Forexample,anearlypieceofevidencemightbeignoredbecausetherighthypothesishadnotyetbeenentertained.Andtheinterpretationofambiguousevidencewilldependonwhathypothesesareentertainedatthattime.Thiscanleadtosubstantialordereffectsthefinalevaluationofabodyofevidencebeingheavilydependentontheorderinwhichthatevidenceisprocessed(HogarthandEinhorn,1992).

Aparallelcanbedrawnwithactionandpracticalreasoning.Atanearlystageonemightnothavetherequisiteknowledgetotakeadvantageofanopportunity;laterononeacquirestheknowledge,buttheopportunityhaspassed.Thiswouldnothappenintheidealworldofflawlessmemoryandunrestrictedreasoningabilities,butwillbecommonplaceintheboundedandimperfectworldthatweinhabit(especiallyasuntrainedjurors).Forinstance,consideracaseinwhichthedefendantischargedwithassault,andpleadsself-defence.Accordingtothelawitiscrucialtoestablishwhetherthedefendantusedforcethatwasreasonableinthecircumstances.Butjurorsareoftennotgivenadefinitionofself-defenceuntiltheendoftrial.Thiscanbeproblematic,becausecriticalevidenceaboutthesuspectactinginself-defencemighthavebeenpresentedbeforethejurorhasanappropriateunderstandingofthelegalnotion.

Despitethesepotentialshortcomings,theonlinegenerationandadaptationofasmallrangeofhypotheseswilloftenbeagoodadaptivesolutiontotheproblemsthatweface.Peopledonotusefull-scale(static)BNrepresenta-tionstheyaremorelikelytoadopt


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small-scalenetworksthatundergo(p.205) discretechangesasnewevidenceisencounteredandhypothesesarerefined,abandonedoraugmented.Thesmall-scalenatureofthesenetworkscanfacilitaterapidandflexibleadjustment.Moreover,thequalitativenatureofthenetworkssparesthenumerousprobabilityestimationsandcomputationsthatafullBNwouldrequire.

CurrentmodelsofevidentialreasoningWehavespeculatedabouttheformthatahumanmodelofevidentialreasoningmighttake.Thusfaronlygeneralprincipleshavebeenarticulated;desideratathatwewouldexpectanyplausibletheoryofhumanreasoningtosatisfy,withoutspecifyingthecognitiveprocessesthatimplementtheseprinciples.Howdoesthisnetworkmodelfitwithotherpsychologicaltheoriesofevidentialreasoning?Therearethreedominantmodels,eachwithprosandcons.

Belief-adjustmentmodelThebelief-adjustmentmodelisageneralpurposemodelforhowpeopleupdatetheirbeliefsinthefaceofnewevidence(HogarthandEinhorn,1992).Appliedtothelegalcontext,themodelassumesthatpeoplestartwithaninitialdegreeofbeliefintheguiltofasuspect,basedonbackgroundinformation.Thispriorinformationcanincludebothspecificdetailsaboutthecase(e.g.natureofthecharge;genderandraceofthedefendantetc.)andgeneralassumptionsorknowledge(e.g.thepresumptionofinnocence).21

Whenanewitemofevidenceisreceived,itisencodedaspositiveornegativeinrelationtotheguilthypothesis,weightedaccordingtoitsjudgedstrength,andthenadditivelycombinedwiththepriorbelief.Thisproducesanadjusteddegreeofbeliefinthesuspectsguilt,whichthenservesasthenewpriorwhenthenextpieceofevidenceisreceived.Thisprocessisiterateduntilallitemsofevidenceareintegrated,andafinaldegreeofbeliefisreached.

Thebelief-adjustmentmodelhassomeattractivefeatures.Itspecifiesasimpleprocessingmodelthatavoidsheavycomputationalorstoragedemands.Atanyonestage,thedecisionmakeronlyneedstoconsidertheirprioropinionandtheimpactofthenewitemofevidence.Ithasbeenappliedtoawidevarietyofcognitivetasks,andcanaccountforarichpatternofempiricalresults.Inparticular,itcanexplainbothprimacyeffectswherepeopleoverweightitemsofevidencethatarepresentedearlyinasequence,andrecency(p.206) effectswherepeopleover-weightitemsofevidencethatarepresentedlaterinthesequence.Inthecaseoflegaljudgments,wheretheevidenceisencodedaspositiveornegativerelativetoatargethypothesis,itpredictsthatlateritemsofevidenceareover-weightedrelativetoearlieritems(KerstholtandJackson,1999).

TheAchillesheelofthebelief-adjustmentmodel,whenappliedtolegalcontexts,isthatittreatsallpiecesofevidenceasindependent.Itignorestheinterrelationsbetweenitemsthatmakelegalcasessocompelling.Thisisasubstantialshortcoming,eveninrelativelysimplesituations.Forexample,itcannotcaptureinstancesofexplainingaway,andthuscannotdistinguishrebuttalfromaffirmativeevidence.ConsideragaintheWitnessforthe


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Prosecutionstory.ThepolicehadevidencethattherewasbloodonVolescuffs,andthismatchedthevictimsblood.ThedefencerebuttedthispieceofevidencebyshowingthatVolehimselfhadthesamebloodtypeasthevictim,andclaimingthathehadcuthimselfslicingham.ThisrebuttalwasinturnsupportedbythefactthatVolehadafreshscaronhiswrist.Accordingtothebelief-adjustmentmodel,thebloodonthecuffsconstitutespositiveevidenceofguilt,andtheclaimthatVolecuthishand,andthescaronhiswrist,constitutenegativeevidence.Butthefactthatthisnegativeevidenceimpactsontheguilthypothesisonlybyunderminingthepositiveevidencecannotberepresented.

Theinabilitytorepresentinterrelationsbetweenitemsofevidencecanrapidlyleadtocounter-intuitiveconsequences.Forexample,supposethatfurtherforensictestsrevealthatthebloodonVolescuffsdoesnotmatchthevictims.ThisfindingrulesoutthispieceofincriminatingevidenceagainstVole,butitalsorenderstheclaimthathecuthishandslicingham,andthescaronhiswrist,irrelevanttowhetherornotheisguilty.Theseitemsofrebuttalevidencearenolongerneeded(theblooddoesnotmatch);theynolongercountaspositiveevidence.Thebelief-adjustmentmodelcannotcapturethesechanges.Ithasnomechanism,orrepresentationalstructure,thatallowsittore-evaluateearlieritemsofevidence.

Itmightbearguedthatwhiletheneglectofinterrelationsunderminesthemodelasanormativeaccount,thisfeaturemightfitwithactualhumanreasoning.However,thereisawealthofempiricaldata(seebelow),pluseverycrimewritersintuitions,suggestingthatpeoplecanaccommodatethesepatterns.

StorymodelIndirectcontrasttothebelief-adjustmentmodel,thestorymodel(PenningtonandHastie,1986,1992)placesstrongemphasisontheinterrelationsbetween(p.207) itemsofevidence.Thismodelmaintainsthatpeopleconstructstoriesinordertomakesenseoftheevidencepresentedincourt,andthesenarrativesarekeydeterminantsofthefinalverdictsreached.AccordingtoPenningtonandHastiethesestoriesinvolvecomplexnetworksofcausalrelationsbetweenbothphysicaleventsandpsychologicalstates(e.g.intentions,desiresandmotives).Thesecausalnetworksdrawonevidencepresentedinthecase,aswellaspriorassumptionsandcommon-senseknowledge.Theyareusedtoconstructaplausiblenarrativefortheunfoldingofthecrime.

Thestorymodelhasgarneredbroadempiricalsupport,butremainsvaguelyspecifiedwithrespecttotheunderlyingcognitiveprocessesandmechanisms.Forexample,nopreciseaccountisgivenforhowpeopleconstructorupdatetheircausalmodels,orhowtheydrawinferencesfromthem.Moreover,PenningtonandHastiearguethatthestorymodelonlyappliestoglobaljudgements(thosemadeoncealltheevidenceisprocessed).Inthecaseofonlinejudgements,peoplearesupposedtoreverttoasimplerbelief-adjustmentmodel.

Thequalitativenetworkperspectivearguedforinthispapersharesmanyoftheinsightsofthestorymodel.Inparticular,thatevidentialreasoninginvolvestheconstructionof


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causalnetworksthatorganiseandmakesenseoftheavailableevidence.Incontrasttothestorymodel,however,ourperspectiveemphasisestheroleofprobabilisticlinksbetweenevidenceandhypotheses.Thestorymodelexplicitlyrulesoutanyroleforprobabilisticevaluations.22OuraccountusesaformalBayesianframeworktorepresenttheserelations,andcaptureimportantpatternsofinference.Thestorymodelissilentonthesedetails.Inaddition,ouraccountappliesequallytoonlinejudgements,astheevidencecomesin,andtoglobaljudgements,oncealltheevidenceispresented.

Coherence-basedmodelsCoherence-basedmodels(Simon,SnowandRead,2004;SimonandHolyoak,2002;Thagard,2000)alsoaccentuatethecomplexinterrelationsbetweenitemsofevidence.Thesemodelsderivefromearlierpsychologicaltheoriesofcognitiveconsistency(Heider,1946),andarebasedontheideathatthemindstrivesforcoherentrepresentationsoftheworld.Evidenceandhypotheses(p.208) arerepresentedasnodesinalarge-scaleconnectionistnetwork.Therelationsbetweennodesarerepresentedasbidirectionallinksthatareeitherexcitatory(wheretheactivationofonenodeincreasestheactivationofthelinkednode)orinhibitory(wheretheactivationofonenodedecreasestheactivationofthelinkednode).Someofthesenodesareinstantiatedastruestatements(e.g.observationalreports),whileothersaresetatrandomorprespecifiedvalues.

Judgments(e.g.isthedefendantguiltyonthebasisofthegivenevidence?)aresupposedtoemergefromaninteractiveprocessthatmaximisestheoverallcoherenceofthenetworkviaconstraintsatisfaction(Thagard,2000).Thisprocesscanleadtosubstantialre-evaluationofhypothesesandevidence.Inparticular,eventheevaluationofassumedfactscanshifttoachievegreatercoherencewiththeemergingverdict(Simonetal.,2004).

Coherence-basedmodels,likeBNs,representmultipleinterrelationsbetweenitemsinaprobabilisticfashion,andrepresentationiscloselytiedtoinference.Thenatureoftherepresentationissomewhatdifferent.WhereasBNsaimtorepresenteventsandprocessesintheworld,coherence-basedmodelsrepresenttheflowofinferenceintheminditself.AnotherimportantdifferenceisthatBNsusedirectedlinks(oftencorrespondingtocausaldirection)whereascoherence-basedmodelshavebidirectionallinks.Thisisacriticaldifference,andmeansthatthelattermodelsareunabletorepresentbasicformsofinferencesuchasexplaining-away.ReturningtotheexampleofthebloodonVolescuffs.Therearetwomainexplanationsforthispieceofevidence:thebloodcamefromthevictim,andthusraisestheprobabilityofguilt,oritcamefromVolehimself,andthuslowerstheprobabilityofguilt.However,tocapturethisinference,acoherence-basedmodelmustassumethatthetwoexplanationsareexclusive(oratleastnegativelycorrelated).Butthisisaninappropriaterepresentationoftheirtruerelationintheworld.WhetherornotVolecuthimselfslicinghamisunrelatedto(independentof)whetherornotheisguiltyofmurder.Thetwoexplanationsonlybecomedependentgiventheevidenceofbloodonthecuffsthattheybothseektoexplain.Asnotedearlier,thispatternofinferenceisnaturallycapturedinaBNrepresentation.Animportantquestionforfutureempiricalresearchistheextenttowhichhumanreasonersengageinexplaining


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awayinferences,withoutassumingthatalternativeexplanationsarealwaysexclusiveornegativelycorrelated.

(p.209) RecentstudiesontheroleofnetworkmodelsinevidentialreasoningMostoftheempiricalstudiesconductedsofarprovidesupportforeitherthestoryorcoherencemodels.However,thekeyfindings,thatpeoplearesensitivetobothcausalityandcoherence,canalsobeexplainedonthenetworkmodelproposedinthischapter.Onemajorfactorthatdiscriminatesbetweenthenetworkmodelandtheothertwomodelsistheroleofprobability.Boththestorymodelandthecoherencemodelexplicitlyrejecttheideathatpeoplethinkaboutevidenceinaprobabilisticfashion.ThisconclusionislargelybasedonthefactthatpeopledonotseemtofollowtheprescriptsofBayesrulewhenevaluatingevidence(PenningtonandHastie,1986,1992).Inparticular,peopleseemtobemoreconservativethanBayesianupdatingrequires.Webelievethatalthoughsuchfindingsmilitateagainstthenotionthatpeoplecarryoutpreciseprobabilitycomputations,theydonotunderminethepossibilitythatpeoplearesensitivetothequalitativestructureofprobabilisticreasoning.Forexample,judgingthatonepieceofevidenceisrelevant(orirrelevant)toaspecifichypothesisdoesnotrequireprecisenumericalestimates.Wecanallagreethatthepresenceofthesuspectatthecrimesceneincreasesthelikelihoodofguilt,especiallyifthesuspecthasnootherreasontobethere,evenifwecannotassignexactprobabilitiestotheseevents.Comparativejudgementslikethesewilloftensufficetobuildupaqualitativenetworkthatlinksrelevantpiecesofevidence.Thissuggestsaslightlydifferentlineofresearchtoassesstheextenttowhichpeoplecanengageinprobabilisticreasoning:howcloselydoestheirreasoningapproximatethequalitativeprescriptsofBayesiannetworks?Inthefinalsectionofthischapterwewillreviewsomerecentstudiesthataddressthisquestion.

ModelsofalibievidenceAlibievidenceisoftencriticalincriminalcases.Ithasgreatpotentialtoexonerateasuspectifthesuspectwasnotatthecrimesceneatthetimeofthecrime,itisveryunlikelythattheyareguilty.However,alibievidenceisoftentreatedwithsuspicion(Gooderson,1977),especiallyifitisprofferedbyafriendorrelativeoftheaccused.Thisisbecausethealibitestimonyisreadilyexplainedawaybythepossibilitythatthealibiproviderislyingtoprotectthesuspect.

Despitetheubiquityofalibisincourtcases,alibievidencehasnotbeensubjectedtomuchformalorempiricalstudy.Thefewpsychologicalstudiesonalibis(CulhaneandHosch,2004;OlsonandWells,2004)havereached(p.210) sensibleconclusions;forexample,thatpeoplearemoreconvincedbyanalibiwhenitisprovidedbyanimpartialstrangerratherthanbyapartialfriendorrelative;andmoreconvincedbyphysicalcorroboration(e.g.atime-stampedreceipt)thanbypersonalcorroboration(e.g.theverbalstatementofacashier).However,thisleavesopenawholeraftofquestionsabouthowpeopleevaluateandassessalibis.

Ofparticularinterestforthecurrentchapterishowalibievidenceisassessedinthelightofotherpiecesofevidence.Asdiscussedabove,onesubtletyofalibievidenceisthatit


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canprovideinformationover-and-abovetheissueofwhetherthesuspectwasactuallyatthecrimescene.Wedevelopedabasicalibimodel23thatrepresentsthenetworkofrelationsintypicalalibisituations.Themodelimpliesthatwhenasuspectsalibiisrefutedbyanotherpieceofevidence(e.g.CCTVfootageshowingthatthesuspectwasatthecrimescene)thiscanincriminatethesuspectalongtwoseparateroutes:(a)evidencethatthesuspectwasatthecrimesceneraisestheprobabilityofguilt;(b)knowingthatthesuspectliedintheirstatementalsoraisestheprobabilityofguilt.Furthermore,wedistinguishedtwosituations:(1)whenthealibiproviderdoesnotknowwhetherornotthesuspectisguilty(e.g.whenthealibiproviderisanimpartialstranger);(2)whenthealibiproviderdoesknowwhetherornotthesuspectisguilty(e.g.whenthesuspectisthealibiprovider).Wearguethatthediscreditofanalibistatementincriminatesthesuspectalongbothroutesincase2butonlyalongroute(a)incase1.

ThisiscapturedbythetwomodelsinFigure7.4.Model1representsthecaseinwhichthealibiproviderdoesnotknowwhetherthesuspectisguilty,Model2representsthecasewherethealibiproviderdoesknow.ThekeydifferenceisthelinkfromguilttodeceptioninModel2butnotModel1.

Howwelldothesetwoalibimodelscapturepeoplesactualreasoningwhenconfrontedwithalibievidence?Weconductedanexperimentalstudytoexplorethisquestion(seeLagnado,2010).Allparticipants24inthestudyweregiventhebackgroundstorytoanassaultcase(basedonthedetailsofarealcase).Thegistofthecasewasthatayoungmanwasaccusedofassaultingawomanshortlyaftersheleftanightclub.Thesuspectmatchedthedescriptiongivenbythevictim,andheadmittedtobeingatthenightclubonthenightinquestion.Participantsgaveinitialestimatesfortheprobabilitythatthesuspectwasguilty,whichservedasbaselinesfortheirsubsequentjudgements.Theywerethenpresentedwithalibievidenceinoneofthreeversions.In(p.211) condition(i)thesuspectprovidedthealibistatement.Heclaimedthathecaughtanightbusfromtheclubandwasathomeatthetimeofthecrime.Incondition(ii)thesuspectsmotherprovidedanequivalentalibistatement,andincondition(iii)thenightbusdriverprovidedit.Thecontentofthealibistatementwaskeptasconstantaspossibleacrossthethreeconditions,sothattheessentialdifferencebetweenconditionswasthenatureofthealibiprovider(suspect,motherorstranger).Theconditionswereconstructedsothattheyvariedastowhetherthealibiproviderwasmotivatedtolietoprotectthesuspect(conditionsiii)andwhetherthealibiproviderknewifthesuspectwasguilty(conditioni).SeeTable7.1forasummary.


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Figure7.4 .Twoalibimodels:(1)whenalibiproviderdoesnotknowwhethersuspectcommittedthecrime(e.g.strangerprovidesalibi);(2)whenalibiproviderdoesknowwhethersuspectcommittedthecrime(e.g.suspectprovidesalibi).

Onceparticipantsreceivedthealibiinformationtheyagainestimatedtheprobabilitythatthesuspectwasguilty.Next,participantsinallconditionswerepresentedwithapieceofevidencethatunderminedthealibi.ThisconsistedinastatementtotheeffectthatCCTVfootageandfacerecognitionanalysisrevealedthatthesuspecthadfollowedthevictimveryneartothecrimesceneataboutthetimeofthecrime.Afterreadingthisstatement,participantsmadetheirfinalestimatesastotheguiltofthesuspect.Inadditiontothethreealibi(p.212) conditions,acontrolconditionwasrunonanothergroupofparticipants.ThiscontrolgroupwaspresentedwiththebackgroundinformationandthentheCCTVevidence,butwithnoalibievidenceinbetween.Thisprovidedacriticalcomparison,becauseitservedasameasureofhowmuchtheCCTVevidencealonewasjudgedtoraisetheprobabilityofthesuspectsguilt.

Table7.1.Threeconditionsinthealibistudy.Alibiprovider

Motivatedtolie?

Knowsthatsuspectisguilty?

Alibimodel

Modelprediction

Suspect Yes Yes 2 P(H|E&A)P(H|E)

Mother Yes No 1 P(H|E&A)=P(H|E)

Stranger No No 1 P(H|E&A)=P(H|E)

TheresultsforthisexperimentareshowninFigure7.5.Thebarslabelledalibirepresentthedifferencesbetweenthebaselineprobabilityratings(basedonthebackgroundinformation)andtheratingsafterthealibiswerepresented.Effectivelythesebarsshowtheimpactsofthethreealibis.Itisnotablethatonlythestrangersalibilowersthejudgedprobabilityofguilt.Inalltheotherconditionsthealibihaslittleeffect.Thisfitswithourexpectationsthatalibisfrompartialwitnessesaretreatedwithgreatsuspicionthereisanobviousalternativeexplanationfortheirstatement(e.g.theymightbelyingtoprotectthesuspect).WhathappenedwhenthealibisweresubsequentlyunderminedbytheCCTVevidence?ThisisshownbythebarslabelledCCTV,whichcorrespondtothe


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differencebetweenbaselineratingsandthosegivenaftertheCCTVevidenceispresented.Inallthreecasesthejudgedprobability(p.213) ofguiltrises,reflectingtheincriminatingeffectoftheCCTVevidence.However,thelevelforthesuspectissignificantlyhigherthanfortheotheralibiproviders.And,mostimportantly,itishigherthanthejudgedprobabilityofguiltbasedonCCTVevidenceintheabsenceofanalibi.(Innumbers,P(H|E&A)P(H|E).)

Figure7.5 .Baselinesubtractedratingsforthreealibiconditionsandcontrol(standarderror).

Thispatternwaspredictedbyouralibimodel.ThesuspectisincriminatedbytheCCTVevidencealongtworoutes:itshows(a)thathewasatthecrimescene,and(b)thathewaslyinginhisalibistatement.Thispatternisnotpredictedbyanadditivemodelofevidenceintegration.TheCCTVevidencebyitselfislessincriminatingthanthecombinationofCCTVevidenceandalibistatement,despitethefactthatthealibistatementbyitselfslightlylowersthejudgedprobabilityofguilt.ThissuggeststhatModel2bestcapturespeoplesreasoningaboutthesuspectsalibi.Incontrast,Model1bestcapturespeoplesreasoningaboutthemotherandstranger.Inthecaseofthebusdriver,wesupposethatthepreferredexplanationforhisfalsealibiwaserrorratherthandeception.ThiswouldaccountforwhytheCCTVevidencedoesnotraisethelevelofguiltashighaswiththeotheralibiproviders.Thispossibilityissupportedbysomeotherstudiesonalibievidence(OlsonandWells,2004),whichshowthatwhenastrangerprovidesanalibiforthesuspect,thequestionofcorrectidentificationisraised(whichismuchlesslikelyforafriendorrelativeofthesuspect).

Thisexperimentsuppliesinitialsupportforthealibimodelsproposedearlier.Moregenerally,itconfirmstheclaimthatpeoplesreasoningcanbesensitivetotheinterrelationsbetweenhypothesesanditemsofevidenceaspredictedbythequalitativeaspectsofBayesiannetworkmodels.

TheimpactofdiscreditedevidenceRecalloneofthemajortwistsintheplotoftheWitnessfortheProsecution.Voleswife,


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Romaine,fabricatedthelettersthatunderminedherowntestimonyagainstVole.Shereasonedthatthejurywouldnotbelieveherifshesimplyprovidedanalibiforherhusband(andourstudiessuggestthatshewasrightaboutthis).Instead,RomainethoughtthatabetterwaytopersuadethejuryofVolesinnocencewastoundercutasubstantialpillaroftheprosecutionscase,namely,herowntestimonyagainstVole.Amoregeneralpsychologicalmaximcanbeextractedfromthislineofreasoningthatonceastoryismountedinfavourofoneside(inthiscasetheprosecution),thediscreditingofoneelementofthatstorycanservetocollapsethewholestory,eveniftherestillexistsincriminatingevidenceunaccountedfor.

Exactlythispatternofreasoninghasbeenexploredinarecentsetofstudies(LagnadoandHarvey,2008).Wewereinterestedinhowthediscrediting(p.214) ofonepieceofevidencemightaffectotheritemsofevidence.Accordingtoapurelynormativeaccount,thediscreditshouldonlyaffectrelateditems,i.e.thosethatbearsomecausalorevidentialrelationtothediscrediteditem.Forexample,considerasituationinwhichasuspectisaccusedofhouseburglary,andawitnesstestifiesthatthesuspectwasloiteringintheareaafewdaysbeforethecrime(statementA).Thissamewitnessalsotestifiesthatshesawthesuspectnearthecrimesceneonthenightofthecrime(statementB).WhathappensifitissubsequentlydiscoveredthatthewitnesshasfabricatedstatementB.Forexample,perhapsthereisstrongevidencethatshewasoutoftownonthenightinquestion,butfabricatedherstatementbecauseshedislikesthesuspect?ClearlyoneshoulddisregardstatementBitnolongerprovidesvalidevidenceagainstthesuspect.ButwhataboutstatementA?Shouldthisalsobedisregarded?

Inthesituationwheretheitemsarerelated(e.g.bothareproducedbythesameindividual),itseemsappropriatetoextendthediscreditofstatementBtostatementA.Afterall,ifthewitnessislyingononeoccasion,shouldntwedoubtherotherstatementstoo?Especiallynowthatweknowthatshehasreasontofabricateevidenceagainstthesuspect.Attheoppositeextreme,italsoseemsclearthatweshouldnotextendthisdiscredittopiecesofevidencethatareentirelyunrelated,forexample,forensicevidencesuchasamatchbetweenthesuspectsshoesandfootprintsfoundatthecrimescene.Thereis,however,alargegreyareainbetween,wheretheextenttowhichadiscreditshouldbegeneralisedisunclear,andwilldependheavilyontheprecisedetailsofthecase.Forexample,shouldwealsocallintoquestionthetestimonyofotherneighbours?Whatiftheyarefriendsofthediscreditedwitness?

Weconductedasetofstudiestoinvestigatesuchquestions.Participants25werepresentedwithvariouscrimescenarios,andjudgedtheprobabilitythatasuspectwasguiltyonthebasisofseveralpiecesofevidence.Inthefirststudypeoplealwaysreceivedtwoitemsofexoneratingevidenceinarow,followedbyinformationthatdiscreditedtheseconditem.Forexample,atstageonetheyweretoldaboutafootprintmatch,atstagetwotheyweretoldaboutthewitnesstestimony,andatthefinalstagetheywereinformedthatthewitnesshadfabricatedtheirstatement.Participantsgaveprobabilityofguiltjudgementsateachstage.Thekeyquestionwaswhetherthejudgedprobabilityatthefinalstage,afterthediscreditingoftheseconditemofevidence,simplyreturnedto


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theestimategivenatstageone(afterthefirstitemofevidence).Ifitdidreturn,thiswouldsuggestthatthediscreditinginformation(p.215) hadonlyaffectedtheseconditemofevidence.Ifitdidnot,thiswouldsuggestthatthediscreditwasbeingextendedinsomeway.

Thereweretwomainexperimentalconditions:thetwoitemsofevidencewereeitherrelated(e.g.twostatementsfromthesamewitness)orunrelated(e.g.afootprintmatchandawitnessstatement).AreasonablepredictionandindeedthatsanctionedbyanormativetheorybasedonBNswouldbethatthediscreditshouldonlybeextendedtorelateditemsofevidence.Forexample,thediscreditofawitnesstestimonyshouldaffectotherstatementsfromthesamewitness,butshouldnotaffectfootprintmatchevidence.ThiscanbeillustratedbyconstructingtwoBNmodelsoneforthecaseofunrelatedevidence,theotherforrelatedevidence(seeFig.7.6).

Theresultsforthisfirststudydidnotcompletelyfitwiththenormativepredictions(reinforcingtheimportanceofempiricalstudies!).Inthosecaseswherethetwoitemswererelated(e.g.twostatementsfromthesamewitness)thefinaljudgementwassignificantlylowerthanthatgivenatstageone.Thusthediscreditingoftheseconditemwasextendedtothefirst(related)item.Thiswasasexpectedbyanormativemodel.Ifthewitnesshasliedinonestatement,thereisincreasedreasontosupposethathehadliedinanotherstatement.However,thisextensionofthediscreditinginformationalsotookplacewhenthetwoitemsofevidencewereunrelated.Forexample,thediscreditingofawitnesstestimonywasextendedtoanunrelateditemoffootprintevidence.Thisisclearlynotsanctionedbythenormativetheory.

Atfirstblushthesefindingscanbemostsimplyexplainedbythebeliefadjustmentmodel.Onthismodellateritemsofevidenceareover-weightedrelativetoearlieritems.Itcanthereforeexplaintheresultsbyassumingthatthefinaldiscreditinginformationisover-weighted(hencethefinalstagejudgement(p.216) islowerthanthefirststagejudgement).Thisbeliefadjustmentmodelalsoassumesinsensitivitytotheinterrelationsbetweenitemsofevidence,andthusexplainswhythiseffectoccursirrespectiveofwhethertheitemsarecausallyrelated.

Figure7.6 .Twomainconditionsinthediscreditedevidencestudy.

Totestoutthissimpleexplanation,asecondstudyvariedtheorderinwhichtheitemsofevidencewerepresented.Inparticular,participantsreceivedinformationinoneoftwoorders:(i)latediscredit,asinstudy1,inwhichthediscreditinginformationwas


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presentedatthefinalstage,and(ii)earlydiscredit,inwhichthediscreditinginformationwaspresentedafterthefirststage,andthenanotheritemofevidencewaspresentedafterwards.Forexample,awitnessstatementwaspresentedfirst,andatthesecondstageitwasdiscredited.Atthefinalstageanotherpieceofincriminatingevidencewaspresented(eitherrelatedorunrelatedtotheinitialitem).

TheresultsaredisplayedinFigure7.7.ThelatediscreditconditionreplicatesthefindingfromStudy1thediscreditingisextendedirrespectiveoftherelationsbetweentheitemsofevidence(andagainstthepredictionsofanormativemodel).Incontrast,theearlydiscreditconditionfallsinlinewiththenormativepredictions.Thediscreditofoneitemisonlyextendedtotheotheritemwhentheyarerelated,notwhentheyareunrelated.

Thisisapuzzlingpatternofresultswhyshouldpeoplemakenormativelyappropriatejudgementswhentheyreceiveinformationinoneorder,butnotwhentheyreceiveitinadifferentorder?Weadvancedanexplanationforthispatternthatdrawsoncoherence-basedmodelsofdecisionmaking.Coherencemodels(e.g.Simonetal.,2004)presumethatthemindstrivesforthemostcoherentrepresentationoftheevidenceandhypothesesinthedecisionproblem.Inparticular,elementsthatcoherewitheachotherwilltendtobe(p.217) acceptedorrejectedtogether.Appliedtoourexperiments,weassumethatpeopletendtogroupitemsofevidencetogetheraccordingtowhethertheyincriminateorexoneratethesuspect.Thisbasicdivisionisstronglyencouragedbythelegalcontext,andthedistinctionbetweenprosecutionanddefenceevidence.Duringthedecision-makingprocessthesetwogroupings(evidencefororagainsttheaccused)willcompetewitheachothertobeaccepted,whereasthewithin-groupelementswillmutuallycohere,irrespectiveoftheexactcausalrelationsbetweenthem.

Figure7.7 .Meanprobabilityofguiltratings(standarderror)forStudy2inlatecondition(leftpanel)andearlycondition(rightpanel).

Onthisviewofthedecisionprocess,theover-extensionofthediscreditinginformationinStudy1arisesbecauseitemswithacommondirection(e.g.twopiecesofincriminatingevidence)aregroupedtogether,andasubsequentdiscreditofoneoftheseitemshurtsthewholegroup,bringingpeoplesfinalestimatesofguiltbelowtheirfirststageestimates.ItcanalsoexplainthedifferencebetweenthelateandearlydiscreditingconditionsinStudy2.InthelateconditionparticipantsreceiveitemsA+andB+,26andgrouptheseaspositiveevidenceagainstthesuspect(seeFig.7.8).Thetwoitemscoherebecausetheyarebothincriminating.ThenparticipantsreceiveinformationC,which


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discreditsB.ThisdiscreditisextendedtoitemAbecauseofthepriorgrouping.ThemutualcoherencebetweenAandB,andCssubsequentdiscreditofB,meansthatAandBarebothundermined.Incontrast,intheearlyconditionparticipantsreceiveitemB+first;thisitemisthendiscreditedbyC.WhentheyreceiveA+thisisnotgroupedwithB+becauseB+hasalready(p.218) beendiscredited.ThusA+isonlydiscreditedifCappliestoitdirectly(i.e.ifthereisanappropriatecausalrelation).

Figure7.8 .Theeffectofgroupingondiscrediting.InthelateconditiongroupingofAandBleadstoover-extensionofthediscreditCfromBtoA;intheearlyconditionnogroupingoccurs,sodiscreditCisrestrictedtocausallyrelatedevidence.

Thisgroupinghypothesishassometestablepredictions.Inparticular,itpredictsthatcoherentgroupingswillonlyemergewhenevidentialelementssharethesamedirection(e.g.bothincriminatingorbothexonerating).Thisimpliesthatwhenthetwoitemsofevidencearemixed(e.g.oneitemincriminatingandtheotherexonerating)thediscreditofoneitemwillnotbeextendedtotheother.ThispredictionwastestedinStudy3.Therewerefourconditions:

(1)Twoincriminatingitems(A+,B+),followedbythediscreditofB+(2)Twoexoneratingitems(A,B),followedbythediscreditofB(3)Oneincriminatingandoneexoneratingitem(A+,B),followedbydiscreditofB(4)Oneexoneratingandoneincriminatingitem(A,B+),followedbydiscreditofB+

Inshort,thereweretwonon-mixedconditions(1and2)andtwomixedconditions(3and4).Asinthepreviousstudies,thecausalrelationsbetweenthetwoitemsofevidencewerealsovariedwithineachcondition.Forexample,incondition(3)thetwoitemswereeitherrelated(e.g.itemA+andBwerebothwitnessstatements,A+statingthatthesuspectwasseenatthecrimescene,Bstatingthatthesuspectwasseenelsewhere)orunrelated(e.g.itemA+wasfootprintevidenceplacingthesuspectatthecrimescene,Bawitnessstatementstatingthatthesuspectwasseenelsewhereatthattime).

TheresultsforStudy3areshowninFigure7.9.Thepredictionsofthegroupingmodelweresupportedinallconditions.Inthenon-mixedconditions(bothitemspositiveorbothitemsnegative)thediscreditwasextendedirrespectiveofwhetherthetwoitemsofevidencewererelatedorunrelated.Incontrast,inthemixedconditions(e.g.onepositive


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itemandonenegativeitem)therewasnoextensionofthediscredit,againirrespectiveofwhetherthetwoitemsofevidencewererelatedorunrelated.Thissuggeststhattheflowofinferenceinpeoplesevidentialnetworkswasdictatedbythepositivevsnegativegroupingofevidence,ratherthantheprecisecausalrelationsbetweentheelements.Thisfindingdoesnotshowthatpeopledonotusecausalreasoning;theyclearlyusedexplaining-awayinferenceswhenevidencewasdiscredited.However,theirreasoningdoesnotappeartobeneatlycapturedbyaBayesianmodelofinference.

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