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White, L.C., Pothos, E. M. and Busemeyer, J. R. (2015). Insights from quantum
cognitive models for organizational decision making. Journal of Applied Research in Memory
and Cognition, 4(3), pp. 229-238. doi: 10.1016/j.jarmac.2014.11.002
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JournalofAppliedResearchinMemoryandCognition4(2015)229–238
ContentslistsavailableatScienceDirect
Journal
of
Applied
Research
in
Memory
and
Cognition
j ou rn a l h o m e p a 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
Insights
from
quantum
cognitive
models
for
organizational
decision
making
Lee
C.
White
a,∗,
Emmanuel
M.
Pothos
b,
Jerome
R.
Busemeyer
c aDepartmentofPsychology,SwanseaUniversity,SingletonPark,SwanseaSA28PP,UKbDepartmentofPsychology,CityUniversityLondon,LondonEC1V0HB,UK
cDepartmentofPsychologicalandBrainSciences,IndianaUniversity,BloomingtonIN47405,USA
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:
Received15October2013 Accepted15November2014 Availableonline24November2014
Keywords:
Classicalprobabilitytheory Quantumprobabilitytheory Decisionmaking
Conjunctioneffect Interferenceeffects
a
b
s
t
r
a
c
t
Organizationaldecisionmakingisoftenexploredwiththeoriesfromtheheuristicsandbiasesresearch program,whichhavedemonstratedgreatvalueasdescriptionsofhowpeopleinorganizationsmake decisions.Nevertheless,rationalanalysisandclassicalprobabilitytheoryarestillseenbymanyasthe bestaccountsofhowdecisionsshouldbemadeandclassicalprobabilitytheoryisthepreferred frame-workforcognitivemodelingformanyresearchers.Thefocusofthisworkisquantumprobabilitytheory, analternativeprobabilisticframework.Resultsindecisionmaking,whichappearparadoxicalfroma perspectiveofclassicalprobabilitytheory,maymakeperfectsenseifoneadoptsquantumprobability theory.Wereviewsomecognitivemodelsofdecisionmakingbasedonquantumprobabilitytheory.Each ofthesemodelsisbasedonachallengetoprescriptionfromclassicalprobabilitytheory.Thetransition fromlabelingaparticularbehaviorasirrational,byclassicalprobabilitystandards,to(potentially) ratio-nal(or,atanyrate,notfallacious),raisesinterestingpossibilities,includingthatofcharacterizingcertain heuristicsinformal,probabilisticterms.
©2014SocietyforAppliedResearchinMemoryandCognition.PublishedbyElsevierInc.Thisisan openaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/
licenses/by-nc-nd/4.0/).
1. Introduction
Inpsychology,theclassicalrationalmodelofdecisionmaking
assumesthatdecisionmakerscomprehensivelydefineaproblem,
understandallpossiblealternativesandtheirconsequences,and
selecttheverybestactionafterevaluatingalltheavailableoptions
(e.g.,Anderson,1991;March,1997;Simon, 1979).Moreover,all
probabilisticcomputationsareassumedtobecarriedoutinaway whichconformstotheprescriptionfromclassicalprobability(CP) theory.ThelinkbetweenrationalityandCPtheorycanbejustified inimportantaprioriways,suchastheDutchBookargument(e.g.,
Howson&Urbach,1993),whichshowsthatCPreasoningis consis-tent/coherent,inacertainformalsense(Oaksford&Chater,2009; Tenenbaum,Kemp,Griffiths,&Goodman,2011).
Yetmanyresearchershavequestionedtherelevanceofthe
clas-sicalrationalmodelandCPtheoryinmodelinghumandecision
making,especially inthecase ofapplieddecision making
situa-tions(seealso,e.g.,Wakker,2010,forargumentsrelatingtorisk
∗Correspondingauthor.Tel.:+4407812341048;fax:+4401792295679.
E-mailaddresses:[email protected](L.C.White), [email protected](E.M.Pothos),[email protected] (J.R.Busemeyer).
and lossaversion). Thefocus ofthepresent articleis
organiza-tionaldecisionmaking.Insuchcases,decisionmakersareoften
assumedtohavelimitedcognitiveresourcesandarefacedwith
environmentswhichareuncertain,complex,andgobeyondthe
assumptionsandmanipulationsoflaboratory-baseddecisiontasks. Asaresult,ithasbeenarguedthatdecisionmakersoperatewithin thelimitsof‘boundedrationality’,frequently‘satisficing’bymaking goodenoughdecisions(Simon,1955)andadaptingtotheir envi-ronmentbyusingheuristicsandintuition,whichcanbothenhance (e.g.,Gigerenzer&Todd,1999;Gigerenzer,1991;Klein,1998)and biasdecisionmaking(e.g.,Kahneman&Tversky,1996;Kahneman, Slovic,&Tversky,1982).Moreover,workingincomplicated,often emotionallycharged,organizationalsystems,decisionmakershave torespondtotheneedsofmultiplestakeholders,whocan politi-callyinfluencethedecisionmakingprocess(e.g.,Cyert&March, 1963;March&Simon,1958;Pfeffer,1981)andbothinfluenceand
areinfluencedbythecontextandthesituated,embodiedaspects
ofcognition,inwhichthedecisionisbeingmade(e.g.,Niedenthal, Barsalou,Winkielman,Karuth-Gruber,&Ric,2005;Weick,1995; Wheeler,2005).
Alltheseareconsiderationswhichunderminethedescriptive
adequacyofCPtheorydecisionmakingmodelsandtherational
analysisapproach,insituationsofapplieddecisionmaking.Bethat asitmay,formanyresearchers,rationalanalysisstillprovidesthe
http://dx.doi.org/10.1016/j.jarmac.2014.11.002
prescriptionforhowdecisionmakersshouldreason,onthebasis
oftheavailableinformation. Wethink this normativeaspectof
prescriptionfromCPmodelsinagivensituationisparticularly sig-nificant,especiallyinthecaseofapplieddecisionmaking,where, clearly,thereisanextraonustoensurethatdecisionsareas ‘cor-rect’aspossible.Relatedly,becauseofthispoint,itisthecasethat
manyresearchersstillfindappealingcognitivemodelingonthe
basisofCPprinciples(e.g.,Oaksford&Chater,2009),despitethe
evidencethat,inmanypracticalsituations,modelingapproaches
basedone.g.,heuristicsandbiasesmayhaveahigherdescriptive value(Gigerenzer&Todd,1999;Gigerenzer,1991;Kahneman& Tversky,1996;Kahnemanetal.,1982).
Itisthesepointswhichmotivatetheapproachinthepresent
article,basedonquantumprobability(QP)theory.QPtheoryisa
formalframeworkforhowtoassignprobabilitiestoevents,and
soitispossibletodevelopsomenormativeargumentsforQP the-ory,analogoustothoseforCPtheory(Pothos&Busemeyer,2014). Equally,someprocessesinQPtheoryappeartohavenatural
inter-pretationsin terms of existing, well-known heuristics,such as
therepresentativenessoravailabilityheuristics(cf.Busemeyer& Bruza,2012;Pothos&Busemeyer,2013).Itisthenpossiblethat
QPtheorycanprovide aperspective onorganizationaldecision
making,whichisclosetodescriptiveassumptionsfromrelevant
heuristicsandbiasesand,equally,consistentwiththegeneral,a
prioriarguments,whichmotivateCPaccountsandcorresponding
normativeconsiderations.Ourspecificobjectiveistoprovidesome preliminarydiscussionofwhethersuchanexciting(though,also, ambitious)objectivemightbeachievableornot.
Manyofthedecisionmakingphenomenathathavebeen
stud-iedas partof the QP research program concern situations for
whichthenormative(fromCPtheory)prescriptiongoesagainsta
verystrongintuitionforanalternativedecision.Intuitionhasbeen definedas“affectively-chargedjudgmentsthatarisethroughrapid, non-conscious, and holistic associations” (Dane & Pratt, 2007: 40).Intuitionisseen asimportantintheuseofheuristics(e.g.,
Kahneman&Tversky,1982;Klein,1998,2003),producesdecisions thatcanattimesappearirrational,atleastwithoutdetailed anal-ysis(e.g.,Klein,1998),andasaprocessisitselfdifficulttoexplain rationally(Dane&Pratt,2007).BothCPtheoryandQPtheoryare,in part,intendedastheoriesforhowintuitionsregardingtherelative likelihoodofdifferentpossibilitiesdevelop.While theworkjust
citedindicatesadivergencebetweenpredictionsfromCPmodels
andcurrentunderstandingaboutintuition,aconsiderationofQP
theorycanleadtoalternativeconclusions.
QPtheorywasdevisedtoexplainparadoxicalfindingsin
quan-tumphysicsthatcouldnotbeunderstoodusingclassicaltheories.It isbasedonaxiomsfundamentallydifferentfromthoseofCPtheory
andsocorrespondingprobabilisticinferenceinvolves
character-istics(suchassuperposition,incompatibility,andentanglement), withnoanalogsinclassicaltheory.Ithashelpedphysicists under-stand,forexample,howdifferenteventswithinasysteminterfere
withoneanotherandhowthemeasurementofasysteminfluences
thestateofthesystem.Suchphenomenaarealsoobservedin deci-sionmakingresearch,forexample,inrelationtoordereffects(e.g.,
Hogarth&Einhorn,1992)andtheconstructiverolethatmakinga choicecanhaveonunderlyingpreferences(e.g.,Payne,Bettman,& Johnson,1993;Sharot,Velasquez,&Dolan,2010).So,proponents oftheapplicationofQPtheoryincognitionhavearguedthatthese specialcharacteristicsofQPalignwellwithhumandecision mak-ingunderuncertainty,atleastundersomecircumstances.Infact,
humandecisionmakingbehavior,whichmayappearparadoxical
orirrationalfromaclassicalperspective,oftenhasasimpleand nat-uralexplanationintermsofQPprinciples.Ofrelevanceisalsothe factthat,inQPtheory,theincompatibilityofcertainpossibilities meansthattheirprobabilisticcomputationneedstobesequential,
sothat,forexample,evenconjunctionsneedtobeassessedina
sequentialway.SuchrequirementsmakeQPtheorycomputation
closertoprocessassumptionsandso,perhaps,moresuitablefor
modelingthesituationsofapplieddecision makingthatweare
interestedin. Ingeneral,it hasbeensuggested that
incorporat-ingprocessassumptionsintocognitivemodelsisanappropriate
directionfortheirdevelopment(Jones&Love,2011;cf.Newell, 1990).
The structure of ourcontribution in this Special Issue is as
follows:first,wewillbrieflysummarizeQPtheoryandconsider
themotivationforexploringitsapplication incognitive
model-ing.Itisnotourintentiontoprovideacomprehensiveoverview
ofQPtheoryresearch,forreviewssee,forexample,Busemeyerand Bruza(2012),Khrennikov(2010),Pothosand Busemeyer(2013)
andWang,Busemeyer,Atmanspacher,andPothos(2013).Second,
we will consider some of the key insights about human
deci-sionmaking,fromexistingQPcognitivemodels,asdevelopedin
thecontextofparticularempiricalapplications(mostlybasedon
Busemeyer&Bruza,2012;Pothos&Busemeyer,2009;Trueblood & Busemeyer, 2011; Wang & Busemeyer, 2013). The selection
ofempirical applicationswillbemotivatedfromcorresponding
conclusionsthathumanbehaviordeviatesfromtheprescription
ofCPtheory.Ofcourse,thereare oftentypically powerful
non-CPtheoryaccountsfor suchfindings(e.g.,Gigerenzer &Selten, 2001;Marewski&Schooler,2011;Tversky&Kahneman,1983).
TheemphasisonCPtheoryrelatestotheemphasisonnormative
considerationsinthispaper.Asdiscussed,wethinkthatthisisa valuableapproach,especiallyinsituationsofappliedsignificance,
wheredecisionmakersmaybeparticularlykeentoachieve
deci-sionsconsidered‘correct’insomeformalsense(sincedeviations fromnormativeprescriptionmayleadtoe.g.,materialloss).For
eachoftheseinsights/applications,wediscussthenew
perspec-tivethatQPprovidesonorganizationaldecisionmakingandthe
possibleimplicationsandbenefits.Thatis,ourdiscussionwillbe
morefocusedonthenormativeperspective(conflictswithCP
the-oryandcorrespondingQPtheoryinsights),lesssobythedescriptive
orboundedrationalityperspective,providedbymodelsbasedon
heuristics and biases (though, obviously, both perspectives are
valuable).
Inevitably,someoftherecommendationsinthispaper,in
rela-tiontoQPtheory,willinvolvespeculation.Our worksofarhas
focusedonestablishingtheformalvalidityofQPcognitive
mod-els,againstempiricalresultsofhighprominenceinthedecision makingliterature.Therehasbeenlittlesystematic investigation orempiricalresearchintotheapplicabilityofQPmodelsin orga-nizationalsettings(forexceptionsseetheworkofLawlessandhis colleaguesdiscussinghowprinciplesofQPcanbeappliedto model-ingsocialdynamics,suchascooperationandcompetition,inteams andorganizations;Lawless&Sofge,2012;Lawless&Grayson,2003; Lawless,Bergman,Louc¸ã,Kriegel,&Feltovich,2007;Lawlessetal., 2011;seealsoYukalov&Sornette,2012,whoapplytheir quan-tumdecisiontheory(Yukalov&Sornette,2008),atheorydeveloped forindividualpersonaldecisionmaking,todecisionmakersunder theinfluenceofothersocialagents).Wehopethatthispapercan servetoinspirefurtherworktowardanapplieddirectionfortheQP cognitionprogram,inrelationtoorganizationaldecisionmaking. Theideasweoutlinebelowprovideanalternativeperspectivefor rationalityandoptimalityinprobabilisticinferenceandmotivate adiscussionofimplications(andpossibleaids)inorganizational
decisionmaking.
2. Anoutlineofquantumprobabilitytheory
QPtheoryisatheoryforhowtoassignprobabilitiestoevents.It isbestknowninitsapplicationtophysics,inthecontextof
L.C.Whiteetal./JournalofAppliedResearchinMemoryandCognition4(2015)229–238 231
inquantummechanics(whatwecallQPtheory)havenoessential
physicalcontentandcan,inprinciple,beappliedinanysituation, wherethereisaneedtoformalizeuncertainty.Wellknown applica-tionsofquantumtheoryoutsidephysicsareininformationtheory (e.g.,Nielsen&Chuang,2010)andinformationretrieval(e.g.,Van Rijsbergen,2004;Widdows,2004).
The application of QP theory in psychology has been
gain-ing momentumin recent years and spansa range of cognitive
researchthemes,suchasconceptualcombination(e.g.,Aerts,2009; Aerts&Gabora,2005),similarity(Pothos,Busemeyer,&Trueblood, 2013),memory(e.g.,Bruza,Kitto,Nelson,&McEvoy,2009),and perception(Atmanspacher&Filk,2010).Indecisionmaking
the-ory, note that, within the QP theory community, a number of
differentmodelingapproaches havebeenadopted(e.g.,Aerts & Aerts,1995;Basieva&Khrennikov,2014;Bordley&Kadane,1999; Bordley, 1998; Busemeyer, Pothos, Franco, & Trueblood, 2011; Khrennikov&Haven,2009;Lambert-Mogiliansky,Zamir,&Zwirn, 2009;Pothos&Busemeyer,2009;Trueblood&Busemeyer,2011; Wang&Busemeyer,2013;Yukalov&Sornette,2008,2009).Wedo notreviewtheseapproachesindetail(foroverviewsorganizedin singlevolumesseeBusemeyer&Bruza,2012;Khrennikov,2010, andthespecialissueofTopicsinCognitiveScience,Wangetal.,
2013).Instead,wefocusonexamplesofmodelswhichwethink
providesimpleillustrationsofthemainprinciplesunderlyingQP
cognitiveaccountsofdecisionmakinggenerallyandthe
implica-tionsthesehavefororganizationaldecisionmaking.
TheuseofQPtheoryinpsychologyhasenabledtheintroduction ofseveralnoveltheoreticalconcepts.Onenewconceptisthat,in
QPtheory,certainquestionsareconsideredincompatible,
mean-ingthatcertaintyforonerequires(ontic)uncertaintyfortheother. Theideaofincompatibilityisrelatedtotheexistenceofuncertainty relations;thatis,therequirementthatthecombineduncertainty forparticularpairsofquestionscanneverbereducedbelowa
min-imumlevel.Anothernewconceptisthataperson’sknowledgecan
becharacterizedasasuperpositionstate,withrespecttoparticular
questions,whichmeansthatprecisevaluesforthecorresponding
questionsdonotexist, untila measurementismade.Finally,in
QPtheorycognitivestatescanbeentangled,sothatcorresponding measurementsmayresultinsuper-correlations,notpossibleinCP theory.
AlotofthestrangenessofQPtheoryarisesbecauseeventsare representedassubspacesinamultidimensionalvectorspace,called aHilbertspace.1Bycontrast,eventsinCPtheoryaresubsetsofa
samplespace.Greatlyoversimplifying,thedifferencebetweenQP
andCPtheoryisonebetweenageometricrepresentationof
prob-abilitiesvs.aset-theoreticrepresentationone.Theimplicationof thisdifferenceisthatthestructureofeventsinCPtheoryisthatofa Booleanalgebra,butinQPtheoryitisonlyapartialBooleanalgebra, meaningthat,inthelatter,operationslikeconjunctionor disjunc-tionarenotdefinedforallpossiblepairsofpossibilities(Hughes, 1989).
Weaimtopresentourexamplesbelow,asmuchaspossible,
withlittlemathematicaldetail.So,weherediscussonlythevery basicaspectsofhowprobabilitiesareassignedtoeventsinQP the-ory(e.g.,Isham,1989).Considerthementalstateofaparticipant,
e.g.,when contemplating which of two optionstochoose.This
mentalstateisrepresentedasavectorinaHilbertspace.Then, dif-ferenteventsorchoicesfortherelevantsituationarerepresented
assubspacesin theHilbertspace.Such subspacescanhaveany
dimensionality.AfundamentalassumptioninQPtheoryisthatthe probabilitythatthestateisconsistentwithaparticulareventisthe squaredlengthoftheprojectionontothecorrespondingsubspace.
1Hilbertspacesarevectorspacesdefinedonacomplexfieldendowedwithan innerproduct,andhavingcertainconvergencepropertiesaswell.
Note,thismeansthatmutuallyexclusiveeventshavetobeatright
angleswitheachother.Incompatibleeventsarerepresentedas
subspacesatobliqueangles,relativetoeachother,suchthatthe
smaller theangle, the higher the classical correlation between
thesepossibilities.Finally,ifapersonobservesthataneventistrue, thenanewcognitivestateisformedbyprojectingthecurrentstate
ontothesubspaceoftheobservedevent.Thisisthe“infamous”
statereductionor“collapse”thatoccursinquantumtheory.We
donotwishtodiscussthemathematicsofQPtheoryanyfurtherat thispoint,butratherfleshoutsomeoftheunderlyingprinciples,
asthisbecomesrelevantintheexamplesbelow.
3. Strategicdecisionmakingandincompatibility
Strategicdecisionsarecharacterizedasbeingnovel,
ambigu-ous, complex, open-ended (Mintzberg, Raisinghani, & Theoret, 1976),andinfluencedbyadiverserangeofinteractingsocial, emo-tionalandpoliticalfactors(e.g.,Cyert&March,1963;Eisenhardt& Zbaracki,1992;March&Simon,1958;Pfeffer,1981;Tetlock,1985). Forexample,ifadecisionmakerisrequiredtolookatwhichnew
productiontechnologytheyshouldinvestin,heorshewillneed
toconsiderobjective informationaboutthecompetingsystems,
alongsidethedifferentviewsheldbystakeholdersaboutthecost oftheinvestment,thequalityofthenewtechnologyandthetimeit willtaketogetproductionupandrunning.Thesevarious consider-ationsrepresentdistinctrationaleswhich,dependingonthepower andsocialinfluenceofthestakeholders,candivergeoroverlap(e.g.,
Janis,1972;Langley,1995).Thistypeoflooselystructuredcontext issaidtofostertheuseofintuitionindecisionmaking(e.g.,Klein, 1998;Shapiro&Spence,1997).Duringthecourseofthedecision makingprocess,thevariousinputsmayinteractwithoneanother, sothat,forexample,ifthedecisionmakeriscertainthatqualityisan importantfactor,thenperhapstheirfeelingsabouttheimportance ofcostortimetoproductionbecomelesscertain.
Fromacognitivemodelingpointofview,theideathatthe inter-actionof differentcognitiveevents(e.g.,a thoughtora feeling)
mightinfluenceadecisionmaker’sintuitionandfinaljudgmentis
quiteplausibleandcanbeillustratedbytheconjunctionfallacy,
one of the most famous phenomena studied in the
heuristics-and-biasesprogram.TverskyandKahneman(1983)presentedto
participantsa shortvignetteabouta hypotheticalperson,Linda, whowasdescribedverymuchasafeminist,butnotabankteller.
Then,participantswereaskedtorankorderasetofstatements
aboutLinda.Thecriticalstatementswere(1)thatLindaisabank teller(BT)and(2)thatLindaisabanktellerandafeminist(BT&F).
Participantsrankedthelatterasmoreprobablethantheformer,
hence indicating that they considered Prob(BT&F)>Prob(BT), a
result that is called theconjunction fallacy. Since Tversky and
Kahneman’s(1983)seminalstudy,theconjunctionfallacyhasbeen frequentlyreplicatedwithmanyotherkindsofstimuliand exper-imentalsituations(thoughseee.g.,Hertwig&Gigerenzer,1999).
TverskyandKahneman(1983)arguedthattheconjunction fal-lacyarisesbecauseLindaisverysimilartothetypicalfeminist,so thatsheislikelytobeconsideredaprobablebanktelleranda femi-nist.Itwassuggestedthatthisrepresentativenessheuristiciswhat guidesdecisionmakingandthat,indeed,CPtheoryhasnothingto dowithcognition(atleastinsuchcases).Theconjunctionfallacyis veryhardtoreconcilewithaCPprescription,becauseCPtheoryis basedonsettheoryandasinglesamplespaceforallevents;amore
specificeventcanneverbemoreprobablethananinclusive,more
generalone.Putdifferently,thehypotheticalLindaswhoarebothF
andBTcanneverbemorenumerousthantheoneswhoarejustBT.
fromformalprobabilitytheory.IfCPtheoryisconsidereda norma-tivestandard,anddecisionmakerscommittheconjunctionfallacy, doesthatmeanthatitisincorrecttouseaheuristicinthissituation andinsteadisitmoredesirabletopursuecorrectives?The applica-tionofQPtheoryintheproblemcanhelpinformthiskeyquestion.
Therelationshipbetweenvariablesindecisionmakingandthe
sequenceinwhichtheyareconsidered,liesattheheartof incom-patibility, one ofthe key conceptsof QP.Bohr (1928), anearly pioneerofquantumtheory,introducedtheconcept.Interestingly,
thereissomeevidencethatBohrmayhavebeeninfluencedbythe
workofJames(1890a,b),whohadconsideredtheseissuesfrom
a psychologicalperspective (Holton,1970).In quantum theory,
twoobservablesormeasurementswhicharenon-commuting(e.g.,
positionandmomentum)aresaidtobeincompatible.When
mea-surementsareincompatibletheyaresubjecttoordereffectssothat
measuringinoneordermayproduceresultsdifferentto
measur-inginadifferentorder,AB=/ BA.Thisisdifferentfromclassical
observables,whichhavetoobeythelawofcommutativityin
con-junctions(e.g.,AB=BA).Asobservablesinquantumtheoryareboth propertiesofandoperationsonthestateofthesystem,theycan alsobeconsideredactions(Wangetal.,2013).Thismeansthatthe effectofagivenactionsequenceonaninitialstatewilldependon theorderinwhichthoseactionsoccur.
Busemeyeretal.(2011)haveshownhowaQPmodelcanprovide anaturalaccountfortheconjunctionfallacy.Thekeyassumption wasthatthepossibilitiesthatLindaisanFand,separately,aBT,
areincompatible,sothat theycannot beassessed concurrently.
Therefore,theconjunctionBT&Fdoesnotexistand,instead,one needstoevaluatethesequentialconjunctionBT& thenForF& thenBT(Busemeyeretal.,2011,arguedthatthelatterismore cog-nitivelyplausible).HowdoestheQPmodelwork?Forincompatible questions,establishingtheanswerforonechangestheperception foransweringtheother.InQPtheory,probabilisticassessmentcan
bestronglyorderandcontextdependent.Thus,forexample,from
theperspectiveoftheinitialstoryaboutLinda,sheisextremely
unlikely tobea BT. But,onceparticipantshave acceptedthe F
propertyforLinda,thenitiseasiertorecognizethatfeministscan haveallsortsofprofessions.Fromthisfeministperspective,itis easiertoacceptthepossibilitythatLindamightbeaBT(inboth cases,‘easier’isrelativetohoweasyitistoacceptthepossibility thatLindamightbeaBT,fromthebaselineperspectiveofjustthe story).
Translating this example into an applied context, strategic
decisions that concern significant organizational change might
illustratehow‘committing’theconjunctionfallacycanmakesense. Insuchsituations,decisionmakerscanbeemotionallyattachedto existingstrategies(e.g.,Finkelstein,Whitehead&Campbell,2008) anditisarguedthat,inordertochange,decisionmakersneedto loosentheiremotionalcommitment(Eisenhardt&Martin,2000; Hodgkinson&Healey,2011;Teece,Pisano,&Shuen,1997). Resis-tancetochangecanbeaproductoftheperceivedthreatthatthe changesposetosocialidentities(e.g.,Gioia,Schultz,&Corley,2000; Haslam,Eggins,&Reynolds,2003;Hogg&Terry,2000).Theability
ofanorganizationtomanagehowitsemployeesaffectivelyreact
toorganizationalchangesthatimpactontheirsocialidentity(e.g.,
Hodgkinson&Healey,2011)andrespondtothecollective emo-tionsoftheorganization(e.g.,Huy,1999,2002)canbecriticalin thesuccessofchangeinitiatives.Havingpeoplemakedecisionsthat runcontrarytotheirexistingperceptionsoftheirorganizationis difficult;largechangesinidentityareperceivedasunattainable
andsmallchanges areperceived asirrelevant(Reger,Gustafon,
Demarie,&Mullane1994).Onewaythroughthisisbyexploiting theprinciplesofQP,asdemonstratedintheexplanationofthe con-junctionfallacy,thattheconjunctionoftwoeventscanincrease
theprobabilityofmakingadecisioninagivendirection,because
acceptingamoreprobableeventcanfacilitatetheacceptanceof
alessprobableone(assumingthetwoeventsarelinked,insome
way).
ConsideranewCEOofamanufacturingcompany.Strategically,
shethinksthatsheneedstochangethepositioningofthecompany, tobeingmoretechnologicallyadvanced.Doingsowillbothincrease
theefficiencyofproduction andalsoconveytherightimageof
theorganizationtocustomersandshareholdersthatisneededto
succeedinthefuture.Theboardneedstodecideinfavorofthis changeinstrategicdirection,but,historically,investmentinnew
technologyhasnotbeenapriorityfor thiscompanyandsothe
probabilityofthemdecidingtopursueitislow.Arethereany
con-ditionsunderwhichtheboardmightdecidetosupporttheCEO’s
favoredstrategy?
ConsidernextanalternativeapproachtheCEOcouldadopt.She
suggeststhatstrategicallytheorganizationneedstore-position
itself as a more environmentally friendly firm, atthe forefront
ofensuringhighenvironmentalstandards,whichareincreasingly
favoredbycustomersandsubjecttogovernmentguidelinesand
regulations.Thisargumentmightbeeasiertomake,asitresonates
withtheimportanceofmaintainingarevenuestream.Havingmade
this argument and convinced the board,it might then become
easiertopersuadethemtoinvestinnewtechnologytoimprove
efficiency,therebymakingtheirproductionprocessesmore
envi-ronmentally friendly. Depending on the information presented
and,critically,thesequence in which itis presented,the
prob-abilityoftheboardselectingtheCEO’spreferredapproachmay
beincreased,inawayanalogoustohowtheconjunctionfallacy
emerges. In other words, this is a case whereby the
probabil-ityofa singlechange(being technologicallyadvanced)islower
thantheprobabilityofa(quantum)conjunction(being
environ-mentallyfriendlyandthenbeingtechnologicallyadvanced;note,
thequantum modelpredictionsregardingtheemergenceofthe
conjunctionfallacyareorder-dependent,inrelationtothe consid-erationofthepremises;Busemeyeretal.,2011).Havingaccepted thechangeinrelationtobeingenvironmentallyfriendly,itbecomes
moreplausibletoacceptthefurtherchangeofbeing
technolog-icallyadvanced–thefirstchangehasafacilitatoryeffectonthe
secondone,becausethetwoshareacausalconnection. Forthis
to be the case, the two changes have to be ‘incompatible’ (in
thequantum sense)and, moreover,onechange(which wecan
callthefacilitatory change) hastomakethetarget changeone
moreplausible.Finally,clearly,facilitationcanoccuronly ifthe changesarecarriedoutinacertainorder,fromfacilitatoryto tar-get.
This example from organizational decision making
demon-strateshow anexplanationinformaltermscanbeprovidedby
QPtheoryforadecisionwhich,sofar,couldonlybeexplainedin heuristicterms.Ofcourse,therearealternativeexplanations,for
why,intheaboveexample,theprobabilityoftheboard
accept-ingthe proposalis influenced bytheconjunction of those two
particularoptions.Forexample,resistancemaybediminishedby
linkingoneaspectofthechangethatdoesaccordwithpeoples’
socialidentity(beingenvironmentalfriendly)withanotheraspect
that doesnot (being technologically advanced).This and other
perspectivescanhelpelaboratetherelevantcognitiveprocesses.
But,the conjunction fallacy hasbeen labeleda fallacy because
itdoesnot makesensein termsof a normativeperspective on
decision making,based onCP theory.But,it is fullyconsistent
with QPtheory, an alternative formal probabilistic framework,
whichraisesthequestionofwhethertheconjunctionfallacyshould really beconsidereda fallacy at all.The applicationof QP
the-ory sohelpselucidate thekey questionof normative guidance
thatweareinterestedinanditalsodemonstrateshowthenovel
theoreticalconcepts in QPtheory (inthis case incompatibility)
can help increase our understanding of human decision
L.C.Whiteetal./JournalofAppliedResearchinMemoryandCognition4(2015)229–238 233
4. Uncertainty,organizationalchangeandviolationsofthe lawoftotalprobability
Organizationalinertia,thetendencyofbusinesses, especially thoseatthematurity phaseofthelifecycle,tocontinue operat-inginthesameway,isanissuefacingmanyorganizationsasthey makedecisionsaboutstrategy.Inertiatypicallyprecedesdeclinefor manybusinesses,especiallyincumbentbusinessesfacingtheentry ofnewplayersintheirmarkets,unlessattemptsaremadeto over-cometheirrigidity(Christensen&Rosenbloom,1995;Tushman &Anderson,1986).Suchbusinessesdemonstrateanapathyand reluctancetowardchange,preferringtostickwiththeirestablished approaches(Miller&Friesen,1980;Tushman&Romanelli,1985) anddefendingpreviousdecisions,inspiteofevidencethat demon-stratestheirfailure(Staw,1976;Staw&Ross,1987).Thedifficulty oforganizationalchangeinthissituationisoftenduetothestrength ofemotionalattachmenttopreviousstrategiesandthethreatthat thechangesposetoself-esteem(e.g.,Eisenhardt&Martin,2000; Finkelsteinetal.,2008;Hodgkinson&Healey,2011;Teeceetal., 1997;Tushman&Anderson,1986).AsLewin(1951)argued,if peo-plearehappywiththestatusquo,regardlessofwhatinternalor externaltriggersfororganizationalchangeexist,thereisno impe-tusforthemtochange.
From the perspective of modeling cognitive processes in
decision making, this situation reflects what we will call the
‘total probability trap’. The law of total probability is a
funda-mental principle in the mathematical structure of CP theory
andisillustratedbythesure-thingprincipledescribedbySavage (1954). Savage demonstrated his principle using as an
exam-ple, a familiar scenario in organizational decision making, a
deliberationregarding a strategic investment.A business
exec-utive is contemplating investing in a property and he believes
the outcome of the next American presidential election to be
critical to the decision. After asking whether he would invest
if a Democrat or Republican won the election and concluding
thathewouldinvestregardlessofwhowon,theexecutive
con-cludesthatheshouldinvest,eventhoughheisuncertainaboutthe outcomeoftheelection.Note,accordingtothesurethingprinciple,
Prob(invest)=Prob(invest|republicn)·Prob(republican)+Prob(invest| democrate)·Prob(democrate), so that Prob(invest) is bound by
Prob(invest|republican)andProb(invest|democrate).So,iftheagent
thinkshe shouldbe behaving rationally (areasonable
assump-tion!), then he may feel compelled to invest in the unknown
case,in awayconsistentwiththelawof totalprobability.This
requirement clearly constrains possible behavior, but, as the
followingexampleshows,people’sdecisionmakingisnotalways
constrainedbythelawoftotalprobability.
ShafirandTversky(1992)providedaningenioustestofwhether
humandecisionmakingisconsistentwiththelawoftotal
proba-bility.Theyhadparticipantsplayaprisoner’sdilemmagame.Asis standardinsuchgames,thereweretwopossibleactions,defect(D)
andcooperate(C)andtwoplayers,which,inShafirandTversky’s
experimentweretheparticipantintheexperimentanda
hypo-theticalopponent.Thecombinationoftheactionoftheparticipant
andthehypotheticalopponentdeterminedthepayofftoboth.The
payoffsweresetupinsuchaway,thatnomatterwhatthe
hypo-theticalopponentdid,itwasadvantageousfortheparticipantto D.ShafirandTversky’s(1992)experimentinvolvedsomeso-called bonustrials,inwhichtheparticipantwastoldoftheopponent’s action.Predictablyenough,whenatypicalparticipantwastoldthat
theopponentchosetoD,shewouldDaswell;likewise,whenshe
wastoldtheopponentchosetoC,byfarthemostcommonaction
wastoD.Thesurprisingfindingwasthat,whentheopponent’s
actionwasunknown,manyparticipantsreversedtheiractionand
chosetoC.Thus,ShafirandTversky(1992)showedthatProb(D,
unknown)=/ Prob(D∧knownD)+Prob(D∧knownC),soviolatingthe
lawoftotalprobability.Sincethispioneeringstudy,severalother analogousresultshavebeenreported(e.g.,Busemeyer,Wang,& Mogiliansky-Lambert,2009;Croson,1999).
The intuition about the psychologicalprocess in Shafir and
Tversky’s(1992)experimentisthatthereareperhapsgoodreasons
fordefectingundereachofthe‘known’conditions.Forexample,
whenaparticipantknowstheopponentcooperates,itmakessense
tochoosetoD,soastomakemoremoney. Whenaparticipant
knowstheopponentdefects,aDactionmakessense,asretribution.
But,thesetworeasonstoDfailtocometomindintheunknown
condition.Itisasif,whenthereisuncertainty,theseindividually goodreasonstoDinterferewitheachother,thatis,canceleach otherout.
RegardingShafirandTversky’s(1992)experimentalsituation,
theclassical prescriptionis straightforward.If you doaction A, givenXandyoudoactionA,given∼X,thenyoushoulddoaction
A, regardlessofwhetheryou knowaboutX ornot. Pothosand
Busemeyer(2009)showedhowaquantummodelforShafirand Tversky’s(1992)experimentalsituationreproducestheobserved violationsofthelawoftotalprobability(relatedapplicationsare inTrueblood&Busemeyer,2011;Wang&Busemeyer,2013).What thismeansisthat,althoughaccordingtoCPtheoryitiswrongto violatethelawoftotalprobability,accordingtoQPtheory,given thatapersonchoosesactionA,givenXand,separately,given∼X, thenit canbecorrect (inthesenseofprobabilistic prescription fromQPtheory)toreversehis/herdecisionanddo∼A,ina situa-tionwherethereisuncertaintyaboutX.Note,itisnotthecasethat apersonshouldreverseactioninthesituationofunknown informa-tion,ratherthat,accordingtoQPtheory(andcontrarytoCPtheory), consistencyofactionwiththeindividualknownconditionsisnot required.
Soaswithourdiscussionoftheconjunctionfallacy,weaskare theresituationsinorganizationaldecisionmakingwherebreaking thelawoftotalprobabilitymightmakesense?Take,forexample, alarge,matureorganizationwhichhasanewlyhired,enthusiastic marketingmanager,whothinksthatthereisaneedtore-energize
andpromoteabrandwithanewmarketingcampaigninorderto
increasesalesrevenue.Anewcampaigncarriesrisk,untilithas beentriedandtested.Whyshoulddecisionmakerssanctionatrial?
Ifourmarketingmanagerarguesthattheexistingmarketing
cam-paign(A)doesnotgeneratethelevelofsalesthattheproductshould beachieving(∼X),decisionmakers inanorganizationsuffering frominertiamaystillrejectthemarketingmanager’sproposal.For
example,theymaybeemotionallycommittedtotheexisting
cam-paign,theymayfeelthattheyhavemadeasignificantinvestment, and,finally,thatthecurrentapproachisatleastgeneratingsome
revenue.Thus,theymayelecttocontinuewiththeexisting
cam-paign(A).Iftheexistingcampaign(A)isgeneratinganacceptable levelofsales(X),thentheywillelecttocontinueanyway. Psycho-logicallytheymaybesufferingfromthesunkcostfallacy(Arkes& Blumer,1985)andmayalsofearreputationalrisktothemselves,if thenewcampaignfails.Andofcoursetheremayalsobeothersocial, emotionalandpoliticalforcesatwork(Hodgkinson&Healey,2011; Teeceetal.,1997;Tushman&Anderson,1986)thatarehelpingto maintainthestatusquo.Atthispoint,withthisexample,allwe havedoneispointoutthatanundesirableaction,A,islikelytobe
adoptedunderbothcircumstancesXandcircumstances∼X.
Clas-sically,bythelawoftotalprobability,thenormativeprescription
requiresustoadoptA,evenwhenknowledgeaboutXislacking.
Someheuristicapproaches,suchasthefailureof
consequen-tialreasoning principlein Shafirand Tversky’s(1992) research,
provideadescriptiveaccountofviolationsofthelawoftotal
prob-ability.However,suchaccountsdonotallowustooverturnthe
thereisarequirementfordecisionmakingtoconformtoa nor-mativestandard,thatis,insituationsinwhichreasoninghastobe consideredcorrect.But,ifQPtheorycanbeappliedinthe situa-tionofinterest,thendecisionmakerscan,correctly,reversetheir action,whenthereisuncertaintyaboutthecritical information. TheQPtheoryformulationresonateswithLewin’s(1951)classic3 stepmetaphorforchange.Thefirststep,unfreezing,involvesthe reductionofforcesthataremaintainingstabilityandintroducing
moreuncertaintysothatchangescanbemade.
Inthecaseofourmarketingmanager,thismeansthatheshould
notrefertotherevenuesassociatedwiththeexistingcampaign
andwhetherornottheyareacceptable.Hemightdiscuss alterna-tivereasons,but,heshouldmaintainuncertaintyaboutthecritical information.Withanabsenceofthecontextualinformationthatis responsibleformakingpeoplereachidenticaldecisions,thisallows forthepossibilitythatreversedecisionswillbemadeanda viola-tionofthelawoftotalprobability.Notethat,thestandardintuition
isthat decisions shouldbemadeonthebasis of availability of
allnecessaryinformation;uncertaintygeneratedbyanabsenceof informationwouldnotbeconsideredoptimalordesirable.Thisis
nottosaythatpeoplecanmanageuncertaintyinanoptimalway.
Indeed,peoplearegenerallyuncertainty averse(Ellsberg, 1961; Epstein,1999;Fox&Tversky,1995)anduncertaintyisregardedas anaversivestatethatpeoplearemotivatedtoreduce(e.g.,Hirsch, Mar,&Peterson,2012;Hogg,2000;Weary&Edwards,1996).
Withtheabovethoughtsinmind,onewaytounderstandthe
QPformulationinmorepsychologicaltermsisthatperhaps
con-textualinformationanchorsorforcesthedecisionmakingprocess intoinevitabledirections.However,feelings ofuncertaintyhave
beenshown toprolong positive moodsand stimulate curiosity
(Bar-Anan,Wilson,&Gilbert,2009;Kurtz,Wilson,&Gilbert,2007; Wilson,Centerbar,Kermer,&Gilbert,2005).Theabsenceof infor-mation,then,allowsforadditionalperspectivesindecisionmaking andflexibilityinthinking.
5. Organizationaldecisionmakingandordereffects
Thecomplexityofreal-life,organizationaldecisionsmeansthat decisionmakersfrequentlyhavetoconsidervariouspiecesof infor-mationprocessedinaparticularsequence.Differentfactors,such associalinfluence,politicsororganizationalproceduresmay deter-minethesequencingofinformationinthedecisionmakingprocess.
Forexample, organizationsoftenhave tomake decisionsabout
theirpersonnelaspartoftheirselectionandperformanceappraisal
procedures.Thesetypesofdecisionshavebeenshowntobe
sus-ceptibletotheeffectsofinterferencebetweendifferentvariablesin thedecisionmakingprocess(Highhouse,1996,2008;Thorsteinson, Breier,Atwell,Hamilton,&Privette,2008).Inassessmentcenters,
whichrepresentacommonwayofselectingnewemployees,
con-trasteffectshavebeendemonstrated,whenthereisadifferencein
performancelevelsbetweencandidates,suchthatonecandidate’s
performancecanberatedaspoororstrongdependingonthe
per-formanceofothercandidatesinthesameexercise,evenwhenthe
targetcandidate’sperformanceisnodifferentineithersituation (e.g.,Gaugler&Rudolph,1992).Similarly,inperformanceappraisal,
theproceduresbywhich organizationsevaluateemployeescan
besubjecttoordereffectsgeneratedbycontrastingvariationsin performancebetweendifferentemployees(e.g.,Palmer,Maurer,& Feldman,2002).
Thecognitiveprocessesunderlyingsuchdecisionmakingcan
beviewedasheuristicprocessestakingplaceunderconditionsof uncertainty(Reb,Greguras,Luan,&Daniels,2014).Inparticular,the orderinwhichinformationisprocessedanddecisionsaremadecan influencetheoutcome.AstudybyMoore(2002),usingGalluppolls, providesagoodillustrationoftheseideas.Moore(2002)considered
thesametwoquestions,askedintwodifferentorders,withina
Galluppoll.For example,participantswereaskedthequestions
“DoyougenerallythinkBillClintonishonestandtrustworthy?”
and“DoyougenerallythinkAlGoreishonestandtrustworthy”
ineitheroftwoorders.WhentheClintonquestionwasfirst,50%
answeredyes,whensecond57%.WhentheGorequestionwasfirst
andsecond,thecorrespondingpercentageswere68%and60%.The
resultspartlysuggestaprocessofassimilation,wherebythesecond
questionproducesananswerwhichindicatesadegreeof
consis-tencywiththefirst(Moore,2002).Psychologically,suchresultsare intuitive.Whenaquestionisaskedfirst,thepersonmustrelyon
knowledgeshecanretrievefrommemoryrelatedtothequestion.
But,ifthisquestionisprecededbyanotherone,thentheperson willincorporatesomeofherthoughtsretrievedfromtheprevious questionintoheranswerforthesecondone(e.g.,Schwarz,2007). AccordingtoCPtheory,suchordereffectsarefallacious.
Con-sider two events, saying ‘yes’to theClinton question(Clinton)
andsaying‘yes’totheGore question(Gore).Then,theclassical descriptionofthesituationisthattheprobabilityofsayingyes
to Clinton and yes to Gore is the probability of saying yes to
Clinton,followedbytheprobabilityofsayingyestoGore,giventhe Clintonanswer.Inotherwords,wehaveProb(Gore|Clinton)·Prob (Clinton)=Prob(Gore&Clinton)=Prob(Clinton|Gore)·Prob(Gore). So,classically,it isanerrorif,acrossasampleofobservers,the answerstotheClinton,Gorequestionsproducedifferent
probabil-ities(aclassicalmodelcanbeaugmentedwithorderparameters
tonumericallyaccommodatesuchresults,butthenthemodeling
frameworkbecomesmerelydescriptive).
AQPmodelforquestionordereffects(e.g.,Wang&Busemeyer, 2013;forasimplifiedexpositionseePothos&Busemeyer,2013)
would assume that the possibilities that Clinton is honest and
Gore is honest areincompatible, but alsocorrelated with each
other.Then,theanswertothetwoquestionsisaquantum
con-junction, so that, depending on order, we would have either
Prob(Clinton&thenGore)orProb(Gore&thenClinton).Letus con-siderthesecondorder.ItisassumedthatevaluatingtheClinton questioninisolationrequiresthatClintonisnotconsidered par-ticularlyhonest.However,havingacceptedGoreashonestcreates
analternativeperspective,fromwhichClintonappearsmore
hon-est(becauseoftherelationbetweenthetwocandidates).Itisas
ifthehigherhonestyofGoresomewhattransferstoajudgment
aboutClintonaswell.ThistransferispossiblebecauseGoreand Clintonwould,ingeneral,beperceivedfairlysimilar,sincethey rantogether.
ApplyingtheseQPideastothesituationofpersonneldecision makingsuggeststhat,ifyouareevaluatingtheperformanceofAl
andBill,theratingforeachmightdependonwhomyouevaluate
first.IfyoufirstconsiderAl,youarelikelytoincorporatesomeofthe thoughtsretrievedaboutAlintoyourevaluationofBill.According totheQPmodelforordereffects,suchinfluencesarelikelytobe
generated,whenthereissomekindofconnectionbetweenAland
Bill,forexample,perhapstheyworkonthesameteamoronsimilar tasks.Notethat,whenadecisionsimplyinvolvestherankordering oftworelatedoptions,thensuchordereffectscouldbelessofan issue.IfyouhadtochoosebetweenjustAlGoreandBillClinton
basedonhowtrustworthyyoufelttheywere(cf.Moore,2002),
thenwhicheverorderyouconsidered,AlGore wouldhavebeen
L.C.Whiteetal./JournalofAppliedResearchinMemoryandCognition4(2015)229–238 235
second.Clearly,whetherGorereceivesthetopratingnowdepends onhisassessmentorder,relativetoClinton.
Noresearch,tothebestofourknowledge,applyingQPideas
topersonnelevaluationhasbeencarriedout,althoughthereare
a numberof empirical studiesthatsuggest that QPmight bea
fruitfulavenue formodeling thecognitiveprocesses underlying
performanceappraisal.Ordereffectsinevaluationareanobvious
directionforfurtherwork,butthere areotherpromising
direc-tionsaswell.Forexample,inresearchonthedecisionmakingof selection,theso-calleddecoyeffectinvolvestheintroductionofa thirdoption,whichisdominatedbyonlyoneofanexistingpairof equaloptions.Thiscanleadtodecisionmakersfavoringthe dom-inatingoption(e.g.,Highhouse,1996;Huber,Payne,&Puto,1982; Slaughter,Bagger,&Li,2006),suggestinginterferenceeffectssuch asthosetypicalofQPmodels.Dilutioneffects,wherebynew,
appar-ently irrelevant information, produces less extreme judgments
(Nisbett,Zukier,&Lemley,1981),mayalsoinfluenceperformance appraisal(e.g.,Rebetal.,2014)andbeagoodavenueofexploration withQPmodeling.Furthermore,thesetypesofeffectsareobviously
notrestrictedtopersonneldecision making,butcanequallybe
appliedtoothertypesoforganizationaldecisions,suchasthe
eval-uationofdifferentmarketingcampaignsforthesameproductor
instrategicdecisionmakingwhenconsidering,forexample,two
separate,butrelated,markets(e.g.,KoreaandTaiwan).Ourmain
pointisthat,typically,QPbasedmodelscanplausibly
accommo-dateeffects,suchastheonesdescribedaboveandsoofferinsight intotheunderlyingcognitiveprocesses.Forexample,inthecase ofquestionordereffects,thecontextcreatedbythefirstjudgment orpieceofinformationthatisprocessedaltersthecognitivestate
andsointerfereswiththesubsequentjudgment;theadvantageof
usingaQPmodelisthatitallowsamoredetailedspecificationof
theunderlyingrepresentationsandprocesses.
6. Intuition,superpositionandtheconstructivenatureof humanjudgment
It has been argued that whilst intuition can be fostered
throughexperience,thedevelopmentofexpertise,andcomplex,
domainrelevantschemas,intuitivejudgmentsthemselvescannot
beforced.Insteadtheyhappeninstantaneouslyandinvoluntarily
asaresponsetointernalorexternalstimuli(Dane&Pratt,2007; Hodgkinson,Langan-Fox,&Sadler-Smith,2008).Giventhat intu-itionis,byitsverynature,hardtoexplainrationally(Dane&Pratt, 2007),itmightbeagoodcandidateforaQPbasedapproach.Inthis section,weconsideraspecificquestioninrelationtointuition:does thetransitionfromuncertaintyaboutwhichresponseis appropri-ate,tothecertaintyassociatedwithmakingtheresponse,impact
ontheunderlyingrepresentations?
Acommonassumptionformanyformalmodelsusedindecision
theory,especially those based onCP theory,is that the
cogni-tivesystemchangesfrommomenttomoment,butatanyspecific
momentisconsideredtobeinadefinitestatewithrespecttoa
decisiontobemade.UsingQPtheorythesituationisdifferent.QP allowsthecognitivesystemtobeinanindefiniteorsuperposition
stateateachmomentbeforethedecisionismade.Thismeansthat thecognitivesystemhasthepotentialforanyofthepossible
deci-sionsateachmomentintime,butwhichoneisselectedcannot
bedetermineduntilthesystemismeasured(e.g.,theindividual
providesaresponse).Thisleadstoasecondimportantdifference
betweenCPandQPtheory.Accordingtomodelsbasedonbaseline
CPtheory,themeasurementtakenofasystematagivenmoment
reflectsthestateofthesystemimmediatelypriortothe
measure-ment.However,inQPtheory,takingameasurementofasystem
createsratherthanrecordsapropertyofthesystem(Peres,1998),
whichmeansthatthesubsequentstateofthecognitivesystemis
constructedfromtheinteractionbetweenthesuperpositionstate
andthemeasurementtaken(Bohr,1958).
White, Pothos, &Busemeyer(2013) and White, Pothos, and Busemeyer(2014)haveprovidedanempiricaldemonstrationof
theinfluencethatmeasurementcanhaveonthecognitivesystem,
usingasimpletwo-stepaffectiveratingstask.Inthefirststep,a
positive (ornegative) imagewasshown andinthesecondstep
animagemadeupof acombination ofthefirstpositive
(nega-tive)imageandanegative(positive)imagewasshown.Inawithin subjects,counterbalanceddesignparticipantsratedthesame
sec-ondmixedimagestwice;afterratingthefirst(single)imageand
afteronlyviewingthefirstimagewithoutratingit.Thisenableda
withinsubjectscomparisonofratingsofthesecondmixedimage,
whenparticipantshadseenidenticalfirstimages,presentedinan identicalorder,withtheonlydifferencebeingthepresenceofan intermediateratingforthefirstimageornot.Doesthis interme-diateratingaffectthesecondone?BaselineprescriptionfromCP theorytellsusthatitshouldnot(seealsoHogarth&Einhorn,1992, forthesameprediction,onthebasisofanalternative,standard
framework).However,Whiteetal.(2013,2014)reportedthatthe
intermediaterating ledtomorenegativeratingsfor thesecond
imageinthepositive,negativeorderandviceversa(i.e.,whenthe imageswerepresentedinanegative,positiveorder,an intermedi-ateratingledtomorepositiveratingsforthesecondimage).
Psychologically, such results are not surprising. Several
researchers haveargued that makinga choicecan have a
con-structiveinfluence,inrelationtotheunderlyingpreferencestates.
Simplyput,theactofchoosinganoptioncansometimesincrease
preferenceforthatoption(e.g.,Ariely&Norton,2008;Sharotetal., 2010;cf.Festinger,1957).Theintuitionisthat,insomecases, inter-nalvaluesdonotexist.Forexample,theprocessofarticulatinga preferenceelaboratestherelevantinternalstatessothat,afterthe preference,theseinternalstatesarenolongerthesame.
Of course,many classical systemsexist, such thatmaking a
choicecanaltertherelevantinternalstates.Ifwerestrictourselves
toCPmodels,thenabaselineassumptionisthatalluncertainty
is epistemic,but internal valuesexist (itis justthat wedo not
know whatthese valuesare).Therefore, theprocess of making
a (non-invasive) measurement ontherelevant states is simply
oneofreadingofftheinternallyexistingvalues.Onecancertainly
endowCPapproacheswithmechanismswhichallowjudgmentsto
beconstructive,butsuchmechanismsareadditionalcomponents.
Bycontrast,accordingtoaQPapproach,whenthementalstateis asuperpositionstate,thenaspecificvalueforthecorresponding choiceorquestiondoesnotexist.Itisonlythroughanactof mea-surement(e.g.,anexpressionofapreferenceordecision),thata
valuecomestobe.
Obviouslynotalljudgmentsinvolveaconstructiveprocess,as formanycasesthereisapreviouslylearntresponse,whichissimply retrievedatthepointofmeasurement.However,forthosetypesof
looselystructured,ambiguoussituations,whichaffordmore
com-plex, creative judgments,and which are more likely to feature
intuition(e.g.,Klein, 1998;Shapiro&Spence,1997),QPmaybe
amorenaturalmethodforunderstandingthecognitiveprocesses
involvedinthetransitionfromambiguitytocertainty.Priortothe decision,inQPterms,theindividualisinanuncertainor super-positionstate,withrespecttothedecisionbeingmade.QPtheory canprovideatheoryfortheprocessesandrelatedrepresentations, asthis(superposition)uncertaintyisresolvedand,more specifi-cally,provideconcretepredictionsregardingthewayconstructive influencescanarise.
7. Concludingcomments
Research ondecisionmaking inorganizationshasgenerated
Gigerenzer,1991;Gigerenzer&Todd,1999),biases(e.g.,Kahneman etal.,1982;Kahneman&Tversky,1996),andsocio-political influ-ences(e.g.,Cyert&March,1963;March&Simon,1958;Weick,
1995).Thereisgeneralagreementthattheseapproachesprovide
anaccurate,ecologicallyvalid,descriptionofdecisionmakingin organizationalandotherreal-lifesettings.Nevertheless,manystill
arguethatmodelsbasedonrationalanalysisandCPtheoryoffer
thebestprescriptionforhowdecisionsshouldbemade.Asaresult,
descriptiveaccountsof decision makingbasedon, for example,
heuristics,whencomparedagainstrecommendationsbasedonCP
theory,canappearirrationalorinaccurate.Inotherwords, conjunc-tionsbetweenlessandmoreprobableevents,uncertainty,orother interferenceeffectsinorganizationaldecisionmakingcanleadto resultswhicharehardtoreconcilewiththe‘correct’predictions fromCPtheory.
ComparedwithrationalanalysisandmodelsthatuseCPtheory,
QPmodelshavebeenmorefrequentlyshowntobeconsistentwith
descriptivemodelsandtheoriesoforganizationaldecisionmaking. AsitispossibletobuildnormativeargumentsforQPtheory, simi-lartothoseforCPtheory(Pothos&Busemeyer,2014),wesuggest that,insomecases,QPtheorycanbeusedtojustifydecisionsthat wouldotherwisebeconsideredfallaciousandre-castthemasbeing formallycorrect(inQPterms).
Westatedearlierinthispaperthatourworksofarhasbeen
focusedonevaluatingthevalidityofQPcognitivemodels,against
well-known empirical results. Indeed,much ofthe workin QP
theoryhasfocusedontheorydevelopmentandlessattentionhas
beengiventoempiricaldemonstrations.Equally,whereempirical
evidencehasbeengathered,ithasfocusedonlaboratory
experi-ments;verylittleappliedworkhasbeencarriedout(foranotable exceptionseeWang,Solloway,Shiffrin,&Busemeyer,2014).The
objectiveof this paperis toexplorewhetherthe theoreticalor
research-orientedsuccessofQPmodelscantranslateto
implica-tionsforreal-lifeorganizationaldecisionmaking.Whathavewe
learnedaboutreallifedecisionmakingfromtheQPcognition
pro-gram?Ourapproachhasbeentoprovideasummaryofourcurrent
workwithQPcognitivemodelsandsomotivatearangeofintuitive applicationsinorganizationaldecisionmaking.Inotherwords,we havesoughttogeneralizethelab-based,experimentalsituations,
againstwhich currentQPmodelshavebeendeveloped,to
anal-ogousreal-lifesituations. We thinkthat thegeneralizations we
makearereasonable,nevertheless,atthispoint,inevitablythey
involvea fairamountofspeculationtoo.Withoutdirect
experi-mentaltesting,itwouldbeimpossibletosettlethecaseoneway oranother.
Howmightwegoabouttestingsomeofourideasinanapplied
setting?Asreviewedinthispaper,QPmodelscanbetestedusing
methodologiescommontomostjudgmentanddecisionmaking
research.However,QPmodelsalsoincorporateprocess
assump-tions.Thus,experimentsthatinvolvesequencingofinformation
and varyingrequirements ontiming ofdecisions couldlead to
strongtestsofQPmodels.Forexample,thein-trayexercise,a
man-agementsimulationusedinassessmentandmanagementtraining,
involvespresentingparticipantswithemailsandmemos
concern-ingorganizationalissuesandaskingthemtomakedecisionsabout thoseissues.Stimulicanbeaboutdifferenttypesofissues(e.g., strategic,operational,personnel).Stimuliaredeliveredeitherall together,where theability toplanand prioritize is partofthe
assessment or sequentially, over the courseof the exercise,so
thatadaptabilitycan beassessed. So, forexample, theexercise
couldenabletestsofhowapriordecisionmightinfluencea
sub-sequentdecision,aswellashowtheactofmakingadecisionitself
mightinfluencelaterjudgment.Anotherpotentialareafor
test-ingsomeoftheprocessassumptionsinQPmodelsisthedecision
makingofselectorsworkingonanassessment centerwho,asa
requirementoftheassessmentcenterprocedures,willexperience
differentsequencesintheevaluationofcandidates.Business
sim-ulations,atoolusedinmanagementdevelopmentorcasestudies,
amainstayofbusinessschooleducation,maybeusefulwaysof
testingourideasregardingtheconjunctionfallacyandlawoftotal probability.Forexample,abusinessopportunitywithavarietyof characteristicsmightbeevaluated,withaviewtoinclude charac-teristicswhichmightleadtoaconjunctionfallacyorensurethe absenceofcertaininformation,soastoproduceaviolationinthe lawoftotalprobability.Suchexperimentaltestspresentuswithan excitingdirectionforfutureresearch.
Asourceofoptimismregardingthismoreapplieddirectionof
theQPresearchprogramisthattheapplicationofQPtheorydoes
notassumerepresentationalresources,which,inanapplied
set-ting,canbe consideredunrealistic. InCPtheory,it is generally possibletoconstructacompletejointprobabilitydistribution,for arbitrarysetsofpossibilities(Griffiths,2003,callsthistheprinciple ofunicity).Buthowrealisticisthisrequirement?Forexample,in thecaseofLinda,classically,weneedacompletejointprobability distribution,notjustforthepropertiesofbeingabanktelleranda feminist,butforanyarbitrarycombinationofproperties,including oneswhicharerarelyencounteredtogether.Itisunclearwherethe
informationforthesejointprobabilitydistributionswouldcome
from.Moreover,there is anissueof computationalcomplexity,
since,forNbinarypossibilities,specificationofthecompletejoint wouldrequire2Nprobabilities(andmanymoreforthe
correspond-ingmarginals).Such complexitymaybebeyondthecapacityof
thehumanmind(cf.Simon,1955).Quantumtheoryavoidssuch
problemsandsoperhapsprovidesamorenaturalframeworkfor
modelinghumandecisionmaking,especiallyinappliedsettings.
Wehopethatsuchaprioriarguments,togetherwiththedirections weoutlinedinthispaper,willhelpmakethecasethatthe
develop-mentofQPcognitivemodelsisapromisingendeavorformodeling
decisionmakinginappliedcontextsoffairlydirectpractical signif-icance.
Conflictofintereststatement
Theauthorsdeclarethattherearenoconflictsofinterest.
Acknowledgements
E.M.P. wassupportedby LeverhulmeTrust grant
RPG-2013-004andJ.R.B.byNSFgrantECCS-1002188.E.M.P.andJ.R.B.were
supportedbyAirForceOfficeofScientificResearch(AFOSR),Air
ForceMaterialCommand,USAF,grantsFA8655-13-1-3044andFA
9550-12-1-0397respectively.TheU.SGovernmentisauthorized
toreproduceand distribute reprintsfor Governmental purpose
notwithstandinganycopyrightnotationthereon.Wearegratefulto
UlrichHoffrageandtwoanonymousreviewersfortheir
construc-tiveandhelpfulcommentsonearlierversionsofthemanuscript.
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