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Citation:

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

This is the published version of the paper.

This version of the publication may differ from the final published

version.

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http://openaccess.city.ac.uk/4742/

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http://dx.doi.org/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,UK

bDepartmentofPsychology,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

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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

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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.

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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

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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

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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

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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

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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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