DTIC ADA459037: The Soft Constraints Hypothesis: A Rational Analysis Approach to Resource Allocation for Interactive Behavior

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PsychologicalReview Copyright2006bytheAmericanPsychologicalAssociation
2006,Vol.113,No.3,461–482 0033-295X/06/$12.00 DOI:10.1037/0033-295X.113.3.461
The Soft Constraints Hypothesis: A Rational Analysis Approach to
Resource Allocation for Interactive Behavior
Wayne D. Gray and Chris R. Sims Wai-Tat Fu
RensselaerPolytechnicInstitute UniversityofIllinois,Urbana-Champaign
Michael J. Schoelles
RensselaerPolytechnicInstitute
Soft constraints hypothesis (SCH) is a rational analysis approach that holds that the mixture of
perceptual-motorandcognitiveresourcesallocatedforinteractivebehaviorisadjustedbasedontemporal
cost-benefit tradeoffs. Alternative approaches maintain that cognitive resources are in some sense
protectedorconservedinthatgreateramountsofperceptual-motoreffortwillbeexpendedtoconserve
lesseramountsofcognitiveeffort.Onealternative,theminimummemoryhypothesis(MMH),holdsthat
people favor strategies that minimize the use of memory. SCH is compared with MMH across 3
experimentsandwithpredictionsofanIdealPerformerModelthatusesACT-R’smemorysystemina
reinforcementlearningapproachthatmaximizesexpectedutilitybyminimizingtime.Modelanddata
support the SCH view of resource allocation; at the under 1000-ms level of analysis, mixtures of
cognitiveandperceptual-motorresourcesareadjustedbasedontheircost-benefittradeoffsforinteractive
behavior.
Keywords:reinforcementlearning,rationalanalysis,embodiedcognition,resourceallocation,interactive
behavior
The night before the birthday party you open the box and perceptual, and motor operations (e.g., Gray & Boehm-Davis,
separate the assembly instructions from the parts for the child’s 2000). Although all three types of operations are required for
newtoy.Doyoumemorizealloftheinstructions,putthemaside, any interactive behavior, as in the example of the assembly
andthenassemblethetoyfrommemory?Or,doyoureadthefirst instructions for the new toy, frequent accesses of knowledge
line, put the instructions down, do the first step, pick up the in-the-world (Norman, 1989, 1993) will be characterized as
instructions, read the next line, put the instructions down, do the more interaction-intensive, whereas greater reliance on knowl-
next step, and so on until the toy is complete? Whatever you do, edge in-the-head will be characterized as more memory
youaremakingtradeoffsbetweenstrategiesthatminimizetheuse intensive.
ofmemorybymakingrepeatedinteractionswiththetaskenviron- Few people would be surprised by the observation that some-
ment versus strategies that minimize interactions by increasing timestheytakenotesandsometimestheymemorizethings,orthat
theirdemandsonthememorysystem. theysometimeslookattheirnotesandsometimessimplyremem-
Atasecond-by-secondlevelofanalysis,interactivebehavior ber what they have written. However, although such interactions
canbeanalyzedasacomplexmixtureofelementarycognitive, are commonplace, until recently the interleaving of cognition,
perception,andactionhasbeenlittlenotedandlessstudiedbythe
cognitivecommunity.
Wayne D. Gray, Chris R. Sims, and Michael J. Schoelles, Cognitive
An important spur to the status quo came when researchers
Science Department, Rensselaer Polytechnic Institute, and Wai-Tat Fu,
(Card, Moran, & Newell, 1980, 1983; Larkin, 1989; Larkin &
HumanFactorsDivisionandBeckmanInstitute,UniversityofIllinoisat
Simon, 1987; Norman, 1982, 1989) began trying to apply cogni-
Urbana-Champaign.
TheworkonthisprojectwassupportedbyagrantfromtheOfficeof tive theory to real world problems. These attempts at cognitive
NavalResearchONR#N000140310046,aswellastheAirForceOfficeof engineering (Norman, 1982, 1986), although productive (Gray,
ScientificResearchAFOSR#F49620-03-1-0143.WethankRobertSorkin John, & Atwood, 1993), revealed the limits of cognitive theory
forhisenthusiasticsupportforthisworkandhismanyconversationsabout (Gray, Schoelles, & Myers, 2004) and spurred many cognitive
optimalityanalysisandtheidealobserveranalysis.WewishtothankHans researchers to study how cognition, perception, and the motor
Neth,MariaAngelicaVelazquez,andBrittneyOppermannfortheirclose
system worked together when moderately complex laboratory
readingofanearlierversionofthispaper.Theauthorsespeciallywishto
(Freed,Matessa,Remington,&Vera,2003;Gray&Boehm-Davis,
thank John Anderson and Erik Reichle for their pointed and persistent
2000;Howes,Lewis,Vera,&Richardson,2005;Kieras&Meyer,
proddingonearlierversionsofthearticle.
1997;Ritter,VanRooy,St.Amant,&Simpson,inpress;Taatgen
CorrespondenceconcerningthisarticleshouldbeaddressedtoWayne
D.Gray,RensselaerPolytechnicInstitute,CarnegieBuilding,1108thSt., &Lee,2003)orcomplexreal-worldtaskswereperformed(Byrne
Troy,NY12180.E-mail:[e-mail] &Kirlik,2005;Salvucci,inpress).
461
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462 GRAY,SIMS,FU,ANDSCHOELLES
Initially, researchers were content to demonstrate that the task ior. As we will show in the model results section, the Ideal
environment in which interactive behavior takes places could PerformerModelprovidesaclosefittothehumandata.Thelast
influencethehigher-levelstrategiesthatpeopleadoptfordecision section summarizes the results and concludes that the human
making (Lohse & Johnson, 1996), problem solving (O’Hara & controlsystemisnotbiasedtoconservecognitiveresourcesatthe
Payne, 1998, 1999), or game playing (Kirsh & Maglio, 1994). expense of other resources, but rather that the selection of inter-
Recently,attentionhasturnedtostudiesthathaveshownsystem- activebehaviorsisdrivenbycost-benefitconsiderations.Whenthe
aticeffectsofthedesignofthetaskenvironmentonthemethods expectedutility(i.e.,thecost-benefittradeoff)ofalternativeinter-
that people adopt for routine tasks such as simple mental arith- active behaviors can be quantified in terms of time, those that
metic (Neth & Payne, 2001; Stevenson & Carlson, 2003). Al- minimizemillisecondsareselectedoverthosethatminimizecog-
though each of these studies implies a general sensitivity of the nitiveresources.
humancontrolsystemtoperceptual-motorcosts,whatislackingis
a functional mechanism that adjusts the mixture of low-level Soft Constraints, Minimum Memory, and the Ideal
cognitive,perceptual,andmotorresourcestoproducetheobserved
Performer
higher-levelchangesinbehavior.
Gray and Boehm-Davis (2000) noted that the procedural steps The essence of soft constraints is a hypothesis about the func-
that implement low-level goals are selected as if milliseconds tional basis for selecting one low-level interactive routine over
matter.Althoughotherresearcherstendtoagreethattheselected another. Interactive routines are envisioned as dependency net-
routines conserve milliseconds, they do not agree that temporal worksoflow-levelcognitive,perceptual,andmotoroperatorsthat
costs are the causal basis of selection as opposed to a correlated come together at a time span of about 1/3 to 3 seconds in the
measure.Inaseriesofstudies,Carlsonandassociates(Carlson& service of low-level interactive behavior (Gray & Boehm-Davis,
Sohn,2000;Cary&Carlson,1999;Sohn&Carlson,1998,2003; 2000).1Interactivebehaviorproceedsbyselectingoneinteractive
Stevenson & Carlson, 2003) have shown that people adapt their routineafteranotherorbyselectingastablesequenceofinterac-
interactivebehaviortothetoolstheyhaveavailable.Indeed,ifleft tiveroutines(i.e.,amethod)toaccomplishaunittask(Cardetal.,
to their own devices, people spontaneously adopt methods for 1983).AdoptingBallard’s(Ballard,Hayhoe,Pook,&Rao,1997)
doing simple arithmetic that shave 200 ms off of alternative analysis of embodiment, we see these interactive routines as the
routines. However, rather than basing selection on time per se, basicelementsofembodiedcognition.
Cary and Carlson (1999, p. 1067) concluded that, “Participants
without memory aids tended to choose solution paths that mini-
The Soft Constraints Hypothesis
mizedworkingmemorydemands.”
Similarly, when the cost of accessing needed information was Therationalanalysisperspective(Anderson,1990,1991;Oaks-
increasedbymillisecondsfromaneyemovementtoaheadmove- ford & Chater, 1998) has shown that it is important to step back
ment,Ballard,Hayhoe,andPelz(1995;Pelz,1996)notedasmall from the study of mechanisms to ask about the environments in
decrease in gaze frequency to an external display. However, like whichthesemechanismsareapplied(Gray,Neth,&Schoelles,in
Carlsonandassociates,ratherthanconcludingthattheselectionof press). If we assume that the mechanisms responsible for goal-
interactivebehaviorsminimizeseffortdefinedbytime,theycon- directedhumanbehaviorareadaptedtothestructureoftheirtask
cluded that, “Observers prefer to acquire information just as it is environment, then finding an appropriate description of the envi-
needed,ratherthanholdinganiteminmemory”(Hayhoe,2000,p. ronmentmayyieldimportantconstraintsonthenatureandbehav-
50).Aselaboratedlater,thisminimummemoryhypothesisappears ior of functional mechanisms. Anderson and Schooler’s classic
related to views that cognitive limitations (in this case, working work on the structure of the environment for human memory
memory) bias the control system to offload work onto the (Anderson&Schooler,1991)isaprimeexampleofthisapproach,
perceptual-motor system (Wilson, 2002). The minimum memory as is the more recent work on the statistical properties of the
hypothesis is thus one candidate explanation for the functional perceptualenvironment(Geisler&Diehl,2003;Purves,Lotto,&
mechanism that adjusts the mixture of low-level cognitive, per- Nundy,2002).
ceptual,andmotorresources. Interactive behavior is usually in the service of higher-level
Throughout this paper the implications of the soft constraints goals. Anything that increases its performance helps us achieve
hypothesisforresourceallocationwillbecontrastedwiththoseof thesegoalsfaster.Inthenonlaboratoryworld,besidesdecreasing
theminimummemoryhypothesis.Thenextsectionintroducesthe costsintermsoftime(andpresumably,resources),efficientinter-
softconstraintshypothesisasanalternativefunctionalmechanism active behavior may make the difference between the success or
totheminimummemoryhypothesis.Thedistinctionbetweensoft
constraints and minimum memory hypotheses is elaborated, and
the concept of an ideal performer analysis as a tool to study the 1InGrayandBoehm-Davis(2000)weusedtheterm“basicactivity”to
describethesecombinationsoflowleveloperators.Ourcurrentuseofthe
implicationsofconstraintsoncognitionisintroduced.TheExper-
phrase“interactiveroutine”is,inpart,ahomagetoHayhoe’s(2000)and
iments section is an overview of three experiments that provide
Ullman’s(1984)useoftheterm“visualroutines.”However,inlargerpart,
increasinglypersuasiveevidenceinfavorofsoftconstraints.Our
“interactiveroutine”betterreflectsthenotionthatcertaincombinationsof
IdealPerformerModel,basedonouridealperformeranalysis,is
low-levelcognitive,perceptual,andactionoperationscanberegardedas
presented next. This model serves as an explicit test of the suffi- building blocks of interactive behavior as well as the notion that at this
ciencyofthesoftconstraintshypothesisasanexplanationforthe levelofdescriptionallbehavioriscomposedofcognitive,perceptual,and
functionalmechanismunderlyingthecontrolofinteractivebehav- motoroperations.
APPLYINGRATIONALANALYSISTOINTERACTIVEBEHAVIOR 463
failure of higher-level tasks. Hence, in situations as diverse as memory strategies (Ballard et al., 1997). An attraction of the
playing computer games, tuning a radio while driving in busy minimummemoryhypothesisisthatitoffersasimpleheuristicfor
traffic, searching for information amid the near-infinite space governing behavior, and unlike the soft constraints hypothesis,
definedbytheWorldWideWeb,andassemblingachild’stoy,the does not require an accounting of costs sensitive at the level of
time required for interactive behavior may be a cost, whereas hundredsofmilliseconds.
achievingthegoalsofthebehaviormaybeabenefit. The minimum memory hypothesis seems to embrace a limited
Simply stated, the soft constraints hypothesis maintains that at capacityviewofmemoryinwhichcapacityisdefinedeitherbythe
the 1/3 to 3 sec level of analysis, the control system selects number of slots available in a short-term or working memory
sequences of interactive routines that tend to minimize perfor- buffer (Miller, 1956) or a limit on the amount of activation
mancecostsmeasuredintimewhileachievingexpectedbenefits. availabletothatbuffer(Just&Carpenter,1992;Just,Carpenter,&
Cost-benefit considerations provide a soft constraint on selection Keller, 1996). (For more detailed and more recent discussions of
as they may be overridden by factors such as training or by limited capacity see, e.g., Cowan, 1997, 1999; Engle, Tuholski,
deliberatelyadoptedtop-downstrategies. Laughlin, & Conway, 1999.) If there is only “so much” memory
Negotiatingcost-benefittradeoffsintheselectionofinteractive availableforuse,thenitisreasonablethatthispreciousresourceis
routinesdoesnotguaranteeoptimalperformanceinatask;thatis, conservedwheneverpossibleeithertoavoidoverloadingthesys-
locallyoptimalinteractiveroutinesmaynotleadtogloballyopti-
tem or to have reserves available if needed for more important
mal performance. Rather, the soft constraints hypothesis predicts
tasks.
optimalperformanceonlyintaskswheremaximizingtheexpected
Allmemorytheoriesofwhichweareawareholdthatencoding
gains and minimizing the expected costs of interactive routines
itemsintomemoryrequirestimeandthatonceitemsentermemory
(i.e.,over1/3to3sec)iscongruentwithanoptimalstrategyatthe
theymaybeforgotten.Thesoftconstraintshypothesisimpliesthat
global task level. In environments that violate this property, the
on the memory side of the tradeoff between interaction-intensive
softconstrainthypothesispredictspersistentlysuboptimalperfor-
and memory-intensive strategies, the only factors that matter are
mance(Fu&Gray,2004,inpress).Thisfocusonlocaloptimiza-
thetimerequiredtoencode,thetimerequiredtoretrieveanitem
tionisconsistentwiththerationalanalysispositionthat“Specify-
from memory, and the probability that an encoded item can be
ing the computational constraints essentially amounts to defining
retrieved (i.e., is not forgotten) when needed. An item that is
the locality over which the optimization is defined” (Anderson,
forgotten represents time wasted in the original encoding, time
1990,p.247).Theextenttowhichhumangoalscanbeachieved
wasted in the attempted retrieval, and additional time required to
by optimizing at the level of interactive routines is the extent to
recodeandreretrievetheitem.Hence,thesoftconstraintsviewon
whichthesoftconstraintshypothesisrepresentsarationaladapta-
useofmemoryasaresourceisthatonlymillisecondsmatter;there
tiontotheenvironment.
is no particular premium on conserving memory and no inherent
Insummary,thesoftconstraintshypothesisappliestherational
biasfavoringperceptual-motoreffort.
analysis (Anderson, 1990, 1991) approach to the allocation of
Inasearchoftheliteraturewehavefoundnoteststhatdirectly
cognitive,perceptual,andmotorresourcesforinteractivebehavior.
pitanyformoftheminimummemoryhypothesisagainstanyform
These resources are encapsulated in interactive routines that are
of the soft constraints hypothesis. However, at least two studies
describedatthe1/3to3seclevelofanalysis.Totheextentthatthe
have indirectly examined tradeoffs between memory utilization
elementsgoingintothecalculationofexpectedutilityarevariable,
andperceptual-motoreffort,onebyBallard(Ballardetal.,1995)
unstable,oroverriddenbydeliberatelyadoptedpolicy,thencost-
andonebyGrayandFu(2004).
benefit calculations provide a soft, not hard, constraint on the
Ballard,Hayhoe,andPelz(1995)usedaBlocksWorldtask(for
selection of interactive behavior. However, the soft constraints
our version of the Blocks World task see Figure 1) to study
hypothesisassumesthattheselectionofinteractiveroutinesmin-
patterns of information access. The participant’s task was to re-
imizes performance costs measured in the currency of time. The
produce the pattern of blocks presented in the Target Window in
objective of minimizing time is a soft constraint, and it is the
deviationsfromthispolicythatmustbeexplained.Inthispaperwe theWorkspaceWindowusingblocksobtainedfromtheResource
seektostrengthenthesoftconstraintshypothesisbyshowingthat Window. In Ballard’s study (and unlike ours) all windows were
its predictions are supported by empirical data and that an Ideal freelyvisibleatalltimes.Informationaccessrequiredonlyaneye
Performer Model, which enforces a strict temporal cost-benefit movement.
accounting,fitstheempiricalresults. Ballard and colleagues report that participants preferred an
interaction-intensive strategy in which they would look at the
TargetWindowfirsttoencodeablock’scolor,getablockofthat
Soft Constraints Versus the Minimum Memory Hypothesis
color from the Resource Window, look again at the Target Win-
In contrast to the soft constraints hypothesis, alternative views dowtoencodetheblock’slocation,thenmovetotheWorkspace
of embodied cognition suggest that cognitive resources are con- Window to place the block. They report that the interaction-
servedbybiasesthatfavortheuseofperceptual-motorresources intensivestrategyoflookingtwicetook3stoexecute,whereasthe
(Wilson, 2002). The minimum memory hypothesis provides a morememory-intensivestrategyofencodingcolorandlocationat
specificinstanceofthisviewofembodimentwhichsuggeststhat the same glance took 1.5 s to execute. They comment that “It is
the control system is biased toward reducing memory costs even surprising that participants choose minimal memory strategies in
when the costs of information access (as measured by time) for view of their temporal cost” (Ballard, Hayhoe, & Pelz, 1995, p.
perceptual-motor strategies are much greater than the costs for 732).
464 GRAY,SIMS,FU,ANDSCHOELLES
Target Window Workspace Window
Resource Window
Stop-Trial
ERASE
Figure1. TheBlocksWorldtask.ThefigureshowsarandomarrangementofeightcoloredblocksintheTarget
Window(topleft),eightcoloredblocksplusaneraserintheResourceWindow(bottomleft),andoneblock
(correctlyplaced)intheWorkspaceWindow(upperright).Intheactualtaskallwindowsarecoveredbygray
boxes,andatanytimeonlyonewindowcanbeuncovered.(Notethatthewindowlabelsdonotappearinthe
actualtask.)
Although this dramatic bias toward perceptual-motor access InastudyinvolvingprogrammingasimulatedVCR,Grayand
costsseemstosupporttheminimummemoryhypothesis,thestudy Fu(2004)showedaprogressiveincreaseinerrorsandintrials-to-
that Ballard and colleagues report contains a potential confound. criterionasthecostofinformationaccessincreased.Wemanipu-
Participantsusedtheinteraction-intensive(i.e.,mostlyperceptual- lated the cost of accessing the information required to program
motor)strategyatthebeginningofthetaskandusedthememory- shows.Forallgroups,showinformationwaslocatedinawindow
intensive strategy “only at the end of the construction” (Ballard, 5in.belowtheVCRwindow.FortheFree-Accessgroup,theshow
Hayhoe,&Pelz,1995,p.732)ofthe8-blocktrial.Thedifferential informationwasclearlyvisibleatalltimes.FortheGray-Boxand
useofthetwostrategiesatdifferentphasesofconstructionraises Memory-Test groups, field labels (such as Channel, Start Time,
the question of whether the cost of encoding required by the EndTime,andDay-of-Week)wereclearlyvisible,butthevalues
memory-intensive strategy was paid at the end of the trial, as ofthesefields(suchas32,11:30,12:30,andSat)werecoveredby
Ballard seems to assume, or whether it was amortized over the gray boxes. To access, for example, the current value of the
entiretrial.Ifmemoryforthepatternofblockswasstrengthened Channelfield,participantswererequiredtomovethemousetoand
throughoutthetrial(e.g.,Chun&Nakayama,2000;Ehret,2002), clickonthegraybox.Priortoprogrammingashow,theMemory-
by the time the last few blocks were placed, their color and Testgroupwasrequiredtomemorizetheshowinformation(thus
position information could be retrieved from memory with little theterm,Memory-Test).
additional encoding. Hence, if encoding time is amortized over For each group, Gray and Fu estimated the costs of accessing
both early and late block placements, then end of trial events do informationin-the-headversusin-the-world.Theretrievallatency
notprovidecleanestimatesofthetimecostsforencodingblocks for well-learned information was estimated as between 100 and
inmemory. 300 ms (Memory-Test group); whereas the latency for less well-
APPLYINGRATIONALANALYSISTOINTERACTIVEBEHAVIOR 465
learned information (the Free-Access and Gray-Box groups) was timerequiredtoretrieveitemsfrommemory,andtheprobability
estimatedasbetween500and1,000ms.Contrariwise,thecostof ofretrievinganencodeditemovertime.
shiftingvisualattentionandtheeyestofreelyaccessibleinforma-
tion in-the-world was estimated as 500 ms (Free-Access group),
Ideal Performer Analysis
whereas the cost of moving the mouse, visual attention, and
clicking on a gray box was estimated as 1,000–1,500 ms (Gray- Both the minimum memory hypothesis and soft constraints
BoxandMemory-Testgroups). hypothesispresenttheoriesforthefunctionalmechanismunderly-
By informal standards it would seem that the Free-Access and ing the selection of low-level, interactive routines. Although be-
Gray-Box groups (i.e., the two groups that were not forced to havioraldatawillbeextremelyimportantinestablishingtheplau-
memorizeshowinformation)hadeasyaccesstoperfectknowledge sibilityofthesoftconstraintsaccountofresourceallocationover
in-the-world; such access could easily compensate for their less thatoftheminimummemoryhypothesis,itisnotcleartousthat
thanperfectknowledgein-the-head.Hence,itwassomewhatsur- behavioral data by themselves can be decisive. The minimum
prisingthattheMemory-Testgroupmadefewererrorsandreached memoryhypothesisdoesnotdenythateffortisanimportantfactor
criterion in fewer trials than either of these groups. Indeed, for in deciding the mix of resources brought to bear on interactive
these two groups, performance was inversely correlated with the behavior.Itmerelyassertsthat,allelseequal,thecontrolsystem
costofexternalinformationaccess.TheFree-Accessgroup,which isbiasedtoexpendperceptual-motorresourcestoconservemem-
couldobtainshowinformationatanytimebyshiftingtheirpoint- ory resources. Unfortunately, it is difficult for an empirical ap-
of-gazeby5in.,performedbetterthantheGray-Boxgroup,which proachtodeterminewhen“allelse”isequal.
had to move their mouse cursor 5 in. and click the mouse to Astringenttestofthetwohypothesesrequiresbehavioraldata
uncoveraninformationfield. plusamodelingapproachthatcombinestwokeycomponents.In
These findings were interpreted as suggesting a race between predictinghumanperformance,Simontoldusthatitisvitaltonail
thetimecostsformemoryretrievalversusthetimecostsrequired downthe“sideconditions”suchas“visualacuity,strength,short-
either to move, click, and perceive, or to saccade and perceive. termmemory,reactiontimes,andspeedandlimitsofcomputation
Rather than obtaining perfect information from in-the-world as and reasoning” (Simon, 1992). Hence, the first component is a
they needed it, both the Free-Access and Gray-Box groups pre- detailed and accurate estimate of the constraints or “side condi-
ferred to rely on knowledge in-the-head. Unfortunately, this tions” that bounded rationality places on human performance
knowledge was obtained in the course of programming a show (Simon, 1996). In the Blocks World task, these side conditions
and,asthedatasuggest,wasnotaswelllearnedasthatobtained includethetimespentencodinganitem;thetimespentretrieving
bytheMemory-Testgroup.Surprisingly,thisincreasedrelianceon an item from memory; and the probability that retrieval will be
imperfect knowledge in-the-head over perfect knowledge in-the- successful given the amount of initial encoding and the retention
worldwasobtainedeventhoughitproducedmoreerrorsandkept interval.Thesecondcomponentisacomputationalormathemat-
participants in the experiment longer. This surprise is consistent ical approach that is formally guaranteed to optimize temporal
with our earlier observation that soft constraints work locally to costs as opposed to any other metric. To conjoin these two key
select least-effort interactive routines. However, locally optimal components (as well as several other necessary components) we
interactiveroutinesmaynotleadtogloballyoptimalperformance combine elements of the ideal observer analysis approach from
(Fu&Gray,2004,inpress). signal-detectiontheorists(Geisler,2003;Macmillan&Creelman,
Unfortunately, neither Ballard’s study nor ours directly com- 2004)withrationalanalysis(Anderson,1990,1991)topresentan
paredminimalmemorywiththesoftconstraintshypothesis.Nei- IdealPerformerModel.
therstudyattemptedtoruleoutattemptstoconservememoryorto In our case, the Ideal Performer Model will use a machine
demonstrate a bias favoring perceptual-motor effort. In the work learningapproach,reinforcementlearning(Sutton&Barto,1998),
presented here, we attempt to show that differences of several to optimize the tradeoff between time costs of the human
hundredsofmillisecondsareenoughtoshifttheallocationofthe perceptual-motorsystemandthetimecostsofthehumanmemory
resources used for interactive behavior from more interaction systemacrossthesixconditionsofourthirdBlocksWorldexper-
intensivetomorememoryintensive. iment.Asdiscussedinalatersection,thetimeofeachinteractive
Tosummarize,althoughtradeoffsbetweeninteraction-intensive routineisderivedfromempiricalortheoreticalaccountsofhuman
andmemory-intensivestrategieshavebeendocumented,itisless cognition. Obtaining the optimal sequence of these interactive
clear what the nature of these tradeoffs are. Gray and Fu argued routinesforeachoftheexperimentalconditionsislefttoatypeof
(2004) that, when alternative means of performing a task exist, reinforcement learning that is formally guaranteed (Watkins &
costs-benefittradeoffsactassoftconstraintsinchoosingonesetof Dayan,1992)toconvergeonthesequenceofmodelcomponents
interactiveroutines(i.e.,onepatternofcognitive,perceptual,and thatminimizestimeforeachofoursixconditions.Followingother
actionoperations)overanother.Hence,incontrasttotheminimum usesofreinforcementlearning(e.g.,Berthier,1996),wemakeno
memoryhypothesis,softconstraintspositsthatthecontrolsystem claim that the process followed by the algorithm mimics any
isindifferenttothesourceoftheresourcesitusesandissensitive processfollowedbyhumancognition.Wedoclaim,however,that
onlytotheirexpectedutilityasmeasuredintime.Likewise,while the outcome of this approach approximates what would be ex-
the minimum memory hypothesis implies a bias to conserve a pected if human cognition calculated costs as if milliseconds
limitedresource,softconstraintsimpliesthattheoperativefactor mattered.Hence,agoodfitofthemodeltothedatawillbetaken
is not a limit in the number of slots or amount of activation as support for the soft constraints hypothesis and as evidence
available,butratherthetimeneededtoencodeitemsinmemory, againsttheminimummemoryhypothesis.
466 GRAY,SIMS,FU,ANDSCHOELLES
The Experiments Experiment1. Threelevelsofaccesscostwerevaried.Inthelow-cost
condition(e1-low)theTargetWindowopenedandstayedopenwhenthe
ThreeexperimentswereconductedusingtheBlocksWorldtask controlkeyonthekeyboardwaspressedandremainedopenforaslongas
shown in Figure 1. As in Ballard’s studies (e.g., Ballard et al., thecontrolkeywashelddownoruntilthemousecursorenteredanother
1995,1997)therearethreewindows:aTargetWindowcontaining window. In the medium-cost condition (e1-med) the Target window
a pattern of colored blocks, a Workspace Window where the openedassoonasthecursorentered(samemethodandcostastoopenthe
participant must reproduce the pattern, and a Resource or parts ResourceandWorkspacewindows).Inthehigh-costcondition(e1-high),
a1-slockoutwasimposedbetweenthetimethecursorenteredtheTarget
Windowcontainingblocksthatmaybepickedup,carriedto,and
windowandbeforethewindowopened.
placedintheWorkspaceWindow.
Experiment2. ToopentheTargetWindow,allparticipantsinExperiment
Unlike Ballard’s studies, a gray window covered each of the
2movedthecursortoabuttonlocatedatthecenteroftheTargetwindowand
threetaskwindows.TheResourceandWorkspaceWindowswere
clicked.Inthisexperiment,thecostofaccessinginformationwasmanipulated
uncoveredassoonastheparticipantmovedthecursorintooneof bychangingthesizeofthebuttonintheTargetWindow.Fore2-lowthebutton
thegraywindows;however,themethodandcostofuncoveringthe wasasbigasthewindow,260(cid:1)260pixels.Fore2-medthebuttonwas60(cid:1)
Target Window varied across the three studies. Experiment 1 60pixels.Fore2-highthebuttonwas8(cid:1)8pixels.
combinedanintuitiveestimateoflowversusmediumperceptual- Changing the button size manipulated perceptual-motor effort along
motorcostwithatimeconsuming(butpresumablylowperceptual- with time by changing the mean Fitts Index of Difficulty (MacKenzie,
motor effort) manipulation for medium versus high cost. Experi- 1992) for moving to the button from either the Resource or Workspace
windowfrom1.7(e2-low)to2.8(e2-med)to6.2(e2-high).TheFittsIndex
ment2manipulatedtheperceptual-motoreffortalongwithtimeby
ofDifficulty(ID)isacontinuousscaledefinedas,
varyingtheFittsIndexofDifficulty(MacKenzie,1992)(discussed
(cid:1) (cid:2)
inthefollowingsection).Astheresultsfrombothofthesestudies D
suggestedthatthetradeoffsweobservedweresensitivetotimeper ID(cid:1)log2 W(cid:2)1 ,
se, and not perceptual-motor effort, Experiment 3 increased the
rangeofaccesscostsstudiedbyvaryinglockouttimeofthetarget whereDisthedistancetothetargetandWisthewidthofthetarget.Fitts’
lawpredictsmovementtime(MT)as,MT(cid:1)a(cid:2)b(cid:1)ID,whereaisthe
window across six between-subjects conditions from 0 to 3,200
interceptandbistheslope(theseparametersarenotusedincomputingthe
milliseconds. As the three studies were very similar, we present
ID). Fitts’ law is an approximation that has held up for over 50 years.
anddiscussthemtogether.
Hence,althoughthereasonsforwhythisequationusuallyworksandan
Method explanationofdeviationsfromitcontinuetoberesearched(Meyer,Smith,
Kornblum, Abrams, & Wright, 1990), the Index of Difficulty can be
Participants considered a standard and generally accepted measure of the type of
informationaccesscostsvariedinthisstudy.
Acrosseachofthethreestudiesaminimumof16andamaximumof18 Experiment3. Forthethirdstudy,thebuttonsinsidetheTargetWin-
participantswereassignedtoeachcondition.Foreachstudyundergradu- dowwereremovedandtheBlocksWorlddisplaywasrestoredtothelook
atesparticipatedinthestudyforcoursecreditandwererandomlyassigned it had in Experiment 1 (see Figure 1). Six between-subjects conditions
toexperimentalconditions. variedlockouttimefrom0to200to400to800to1,600to3,200ms.Due
to software errors, data from four participants were lost, one each from
Equipment and Software lockoutConditions0,200,1,600,and3,200.
TheexperimentswereconductedonMacintoshcomputersrunningversions Procedure
8.6(Experiments1and2)or9(Experiment3)oftheoperatingsystem.All
experimentsusedamouseforinputanda17-inchmonitorsetat1024(cid:1)768 Toselectablock,participantsmovedthemousecursortotheResource
resolution.BlocksWorldwaswritteninMacintoshCommonLisp(MCL).All Windowandclickedonacoloredblock.Themousecursorthenchanged
window events (e.g., mouseEnter and mouseLeave) and key presses were toasmallversion(16(cid:1)16pixels)ofthecoloredblock.Toplaceablock
recordedandsavedtoalogfilewith16.67msaccuracy. intheworkspace,thecursorwasmovedintothatwindow(whichopened
as soon as the cursor entered it), moved to the desired position, and the
Design mouseclicked.
Whentheparticipantsbelievedthatthemodelpatternhadbeencopiedto
Foreach8-blockpattern,eachofthe(48(cid:1)48pixel)blockswaschosen the Workspace Window, they pressed the “Stop-Trial” button. The pro-
randomlywiththeconstraintthatnocolorbeusedmorethantwice.The gramnotifiedtheparticipantsifthepatternsdifferedandrequiredthemto
blockswereplacedatrandomintheTargetWindow’snonvisible4(cid:1)4 reviseorcompletethepatternbeforetheycouldmoveontothenexttrial.
grid.TheWorkspaceWindowwasthesamesizeastheTargetWindowand Misplaced blocks could be corrected at any time during the trial (i.e.,
containedthesame4(cid:1)4grid(seeFigure1). beforeoraftertheStop-Trialbuttonwaspressed).Wrongcolorplacements
Across all conditions of all experiments the Target, Resource, and couldbecorrectedbyselectingthecorrectcolorblockfromtheResource
Workspacewindowswerecoveredbygrayboxes.Onlyonewindowwas Windowandplacingitontopofthewrongcolorblock.Wronglocation
visibleatanyonetime.Inallthreeexperiments,theResourceorWork- placementscouldbecorrectedbyselectingawhite“erase”blockfromthe
spacewindowsopenedassoonasthemousecursorenteredthewindow. ResourceWindowandplacingthisontopofthewronglocationblock.
Except for the low-access cost condition of Experiment 1 (e1-low, dis- Foreachexperiment,allparticipantsreceivedinstructionbybeingledby
cussedbelow),allwindowsinallconditionsstayedopenforaslongasthe the experimenter through a PowerPoint™ demonstration. Within each
cursorremainedinsideofthemandclosedassoonasthecursorleft.Across experiment, the same slides with the same prerecorded narration were
thethreestudies,theonlydifferenceinprocedurewasinthemethodand provided to each group. After this demonstration, the participants com-
costofopeningtheTargetwindow.Forallexperiments,allmanipulations pletedonepracticetrialwhiletheexperimenterwatchedandansweredany
werebetweensubjects. questionstheparticipantmighthave.Astheparticipanttypicallyhadno
APPLYINGRATIONALANALYSISTOINTERACTIVEBEHAVIOR 467
problemswiththispracticetrial,theexperimentertypicallysaidnothing.After Table2
thepracticetrialtheexperimenterlefttheroomandtheparticipantscompleted MeanResultsforExperiment1OverTrials11–40
theremaining39trialsinExperiment1and47trialsinExperiments2and
3bythemselves.Allexperimentslastedapproximately45minutes. Informationaccesscondition
(keypress) (0-lock) (1000-lock)
Results
Low Medium High
For each experiment, we provide one general measure of the
Numberoftargetwindowaccesses 6.8 6.4 4.1
differences between conditions and then focus on two specific
Durationoffirstlook(ms) 1179 1241 2334
measures.Thegeneralmeasureisacountofthemeannumberof Blockscorrectlyplaced(firstlook) 1.7 1.9 2.9
times during a trial that the Target Window was uncovered. The
twospecificmeasureslookateventssurroundingthefirstuncov-
ering of the Target Window: median duration of the first uncov- Number of Target Window Accesses
ering and mean number of correct placements following the first
uncovering. There are two rationales for focusing on events sur- Eachstudyshowedamaineffectofaccesscostconditiononthe
roundingthefirstuncovering.First,foreachtrial,atthetimeofthe meannumberoftimesthetargetwindowwasaccessed(seethetop
first uncovering of the Target Window, there were eight not-yet- thirdofTable1).ForExperiment1(seeTable2),aseriesofthree
placed blocks. For all subsequent uncoverings, the mean number plannedcomparisonsshowedthataccessesfore1-lowande1-med
of not-yet-placed blocks varied between conditions. Comparing didnotdiffer,butthateachmademoreaccessesthane1-high(low
across conditions is easiest when the number not-yet-placed is vs.high,p(cid:3).0008;medvs.high,p(cid:3).0039).ForExperiment2
equal for each condition. Second, focusing on events prior to the (see Table 3), a series of three planned comparisons revealed
secondandsubsequentuncoveringsavoidsanypotentialconfound e2-low(cid:4)e2-med(p(cid:3).016)ande2-low(cid:4)e2-high(p(cid:5).0001),
with any cumulative memory trace for the block pattern. This but that e2-med did not significantly differ from e2-high. For
ensuresthatthemeasuresofdurationandcorrectplacementscan Experiment 3 (see Table 4), the slope of the linear trend across
beattributedtoeventssurroundingthefirstuncoveringandarenot conditions significantly (p (cid:5) .0001) differed from zero and ac-
influencedbyacumulativememorytracefortheblockpattern. counted for 98% of the variance for condition. The linear trend
Asweareinterestedinthestrategiesthatparticipantsuseafterthey showsthatthechangesacrossthesixconditionsareallinthesame
adapt to the access costs in their condition, the first 10 trials were direction.
eliminated,andforeachparticipantoneachmeasureeitherthemean
or median score (depending on the measure) across Trials 11–40 Duration of First Look
(Experiment1)or11–48(Experiments2and3)wasused.
Each study showed a main effect for condition on the median
For each of the three experiments, an independent analysis of
duration that the Target Window stayed open on its first access
variance(ANOVA)wasperformedoneachdependentvariable.A
(seethemiddlerowsofTable1).ForExperiment1(seeTable2),
summaryofallANOVAsperformedoneachdependentvariableis
plannedcomparisonsshowedsignificantdifferences(p’s(cid:5).001)
providedinTable1.ThemeanormedianscoresforExperiments
betweene1-highandeachoftheothertwoconditions.Therewere
1–3arereportedinTables2-4,respectively.
nodifferencesbetweene1-lowande1-med.ForExperiment2(see
Table3),aseriesofthreeplannedcomparisonsrevealede2-low(cid:5)
e2-med (p (cid:3) .035), e2-low (cid:5) e2-high (p (cid:3) .0012), but that
Table1
e2-meddidnotsignificantlydifferfrome2-high.ForExperiment
AnalysisofVarianceTableforAllDependentMeasuresfor
3(seeTable4),thelineartrendacrossconditionswassignificant
EachoftheThreeExperiments (p(cid:5).0001)andaccountedfor87%ofthevarianceforcondition.
Degreesof Mean-square Significance
Experiment freedom F-value error level(p) Blocks Correctly Placed Following the First Look
Numberoftargetwindowaccesses Thismeasureexaminedthemeannumberofblocksplacedafter
the first look that correctly matched the color and location of a
E-1 (2,45) 7.53 34.50 .0015 block in the Target Window. Across all three studies the differ-
E-2 (2,51) 9.27 10.83 .0004
E-3 (5,104) 11.60 16.99 .0001
Table3
Durationoffirstlook
MeanResultsforExperiment2OverTrials11–48
E-1 (2,45) 9.16 6,756,009 .0005
E-2 (2,51) 6.01 8,055,996 .0045 Informationaccesscondition
E-3 (5,104) 13.18 26,924,234 .0001
Low-ID Med-ID High-ID
Blockscorrectlyplacedfollowingthefirstlook
Indexofdifficulty 1.7 2.8 6.2
E-1 (2,45) 9.84 6.56 .0003 Numberoftargetwindowaccesses 5.1 4.2 3.5
E-2 (2,51) 8.85 3.72 .0005 Durationoffirstlook(ms) 1345 2182 2669
E-3 (5,104) 17.39 5.85 .0001 Blockscorrectlyplaced(firstlook) 2.22 2.69 3.13
468 GRAY,SIMS,FU,ANDSCHOELLES
Table4
MeanResultsforExperiment3OverTrials11–48
Informationaccesscondition(lockoutdurationinms)
0 200 400 800 1600 3200
Numberoftargetwindowaccesses 5.6 4.8 4.5 3.7 3.5 2.9
Durationoffirstlook(ms) 1603 1702 1929 2392 3614 4634
Blockscorrectlyplaced(firstlook) 2.00 2.39 2.49 2.94 3.11 3.58
encesacrossconditionsweresignificant(seebottomthirdofTable (duetothe1,000mslockoutfore1-high),and1,046msbetween
1). For Experiment 1 (see Table 2), a series of three planned e1-lowande1-high.
comparisonsrevealedasignificantdifferencebetweene1-highand If access costs are measured in time, then the Experiment 1
each of the other two conditions (see Table 2, p (cid:3) .0015). For results are very regular. As access time increased, participants
Experiment 2 (see Table 3), planned comparisons revealed e2- openedtheTargetWindowlessoften,butthedurationofthelook
low(cid:5)e2-med(cid:5)e2-high(e2-lowvs.e2-med,p(cid:3).034;e2-lowvs. increased, as did the number of correct and incorrect retrievals
e2-high, p (cid:3) .0001; e2-med vs. e2-high, p (cid:3) .048). For Experi-
from memory. Although the e1-low versus e1-med difference in
ment 3 (see Table 4), the linear trend across conditions was
access time of 46 ms was not enough to produce significant
significant(p(cid:5).0001)andaccountedfor97%ofthevariancefor
differences,itwasenoughtoproducetheexpectedpatternacross
condition.
thethreemeasures.Allthreemeasuresfoundasignificantdiffer-
encebetweene1-highandeachoftheothertwoconditions.
Discussion of the Experimental Data Experiment 2 replicated the results of Experiment 1 using a
manipulation that covaried difficulty of perceptual-motor activity
Eachofthethreestudiesfoundaprogressiveswitchfrommore
withtime.TheExperiment1and2resultssuggestedthat,forthe
interaction-intensivetomorememory-intensivestrategiesasinfor-
Blocks World task, time is the operative factor and it does not
mation access costs increased. The number of times the Target
matter whether time for information access is manipulated by
Window was opened decreased, while the duration that it was
varyingtheFittsIndexofDifficultyorbylockout.Wetestedthis
opened increased. Presumably, the increased duration that the
suggestioninExperiment3byusingsixlevelsoflockouttimeas
TargetWindowwasopenedreflectsincreasedtimespentencoding
ourindependentvariable.TheuseoflockouttimeinExperiment3
itscontents.Thisinterpretationissupportedbytheincreaseinthe
also enabled us to more precisely control access time while also
numberofblocksplacedfollowingthefirstlook.Asaccesscosts
increase, people minimize time per trial by accessing the Target producing a wider range of access costs. Hence, Experiment 3
Windowlessandusingmemorymore. providesourbestempiricaltestofthenotionthataccesscostscan
bemeasuredbyaccesstime.
Acrossthreestudies,theempiricaldatasupporttheviewthatas
Differences Between Methods of Information Access
access costs increased participants switched from more
Acrossthethreestudieswevariedthemethodofaccessingthe interaction-intensive to more memory-intensive strategies. This
TargetWindow.ForExperiment1weweredisappointedtofindno strategic switch was signaled by the decreasing number of open-
significantdifferencesbetweenthee1-lowande1-medconditions ings of the Target Window across conditions as well as by the
onanyofourthreemeasures.Ourintuitivenotionsofeffortseem increasing duration that the Target Window was open. We argue
nottohaveproducedtheexpecteddifference.Couldtheseresults that the increase in the duration that the Target Window is open
be better understood by using access time to characterize the reflectsthegreateramountoftimethatparticipantsspentencoding
differencesbetweenconditionsinaccesscosts? thecontentsoftheTargetWindow.Thisexplanationissupported
Unfortunately, access time for the Experiment 1 conditions is by the increase across conditions in the number of correct block
hard to compare since for e1-low the log file only collected the placementsfollowingtheinitialuncoveringoftheTargetWindow.
time at which the control key was pressed and for e1-med and
e1-high the log file only reported the time at which the cursor
entered the Target Window. However, in prior research (Gray &
Boehm-Davis,2000),wemeasuredkeydowntimeas100ms.For
the Blocks World paradigm, we estimated the time to move the
2Alternative bases exist for estimating time difference in these two
cursor into the Target Window as 146 ms. This estimate is the
conditions. An alternative we tried was based on CPM-GOMS (Gray &
average of the Fitts’ law (MacKenzie, 1992) time to move the
Boehm-Davis, 2000; Gray et al., 1993). As the difference predicted by
cursor to the Target Window from the Workspace and Resource
thosemodelsis51ms,wehaveelectedtoreportandexplainthesimpler
Window.Hence,bytheseestimatesthedifferenceinexpectedtime differencebetweenkeydowntimeandmovementtime(46ms),ratherthan
between e1-low and e1-med is 46 ms2 (i.e., 146 ms for el-med providing the level of detail required to understand the CPM-GOMS
minus100msfore1-low),1,000msbetweene1-medande1-high models.
APPLYINGRATIONALANALYSISTOINTERACTIVEBEHAVIOR 469
Limits of the Experimental Data as to minimize total time. Each of these aspects of the Ideal
PerformerModelisdiscussedinthesectionsthatfollow.
The empirical data demonstrate that as access costs increase
people adjust their strategies to be less interaction intensive and
more memory intensive. However, although we view the steady Hard Constraints: Defining the Task Environment
increaseintradeoffsaspersuasiveevidenceinsupportofthesoft
constraints hypothesis, the empirical data do not rule out weaker Thegoalsofthehumanperformercombinedwiththephysical
formsoftheminimummemoryhypothesis.Forexample,thesoft propertiesofthetaskenvironmentactashardconstraintsonhow
constraints hypothesis argues that as information access costs the task is performed. Given the task environment shown in
increase,theuseofinteraction-intensiveversusmemory-intensive Figure1andthegoaltoreproducethepatternofTargetWindow
strategies is driven by their expected utility (i.e., cost-benefit blocksintheWorkspaceWindow,thenthetaskanalysisbreaksthe
tradeoff)asmeasuredbytime.Theempiricaldatashowashiftin taskintoaseriesofENCODE-kstrategieswherekisthenumber
strategies but, by themselves, do not relate the shift to expected ofblocks(1–8)encodedoneachround.EachENCODE-kstrategy
utility. To make this argument, in the next section, we turn to a consistsoftwounittasks,anEncodeBlocksunittaskandaGet&
machine-learning algorithm, reinforcement learning, that is for- Placeunittask.AsshowninthepseudocodeprovidedasTable5,
mally guaranteed to maximize expected utility (using time as its thefirstunittaskencodessomenumberofblocksfromtheTarget
metric)ifprovidedwithsufficienttrainingandadequateexplora- Window pattern (lines 1–9) and the second gets blocks from the
tion of the problem space (Sutton & Barto, 1998). In fitting the Resource Window and places them into the Workspace Window
model, the six between-subjects conditions of Experiment 3 will (lines10–25).
provide data on multiple measures against which to compare the Thistoplevelofdescriptioniscompletelyobjectiveinthatitis
predictions of the soft constraints hypothesis against the implica- basedonthegoalsofthetaskandthetaskenvironmentavailable
tions of the minimum memory one. As discussed in the next for achieving these goals. For guidance on how to flesh out the
section, conformity to the reinforcement learning solution would interactive routines required by each unit task we turned to an
supportthesoftconstraintshypothesis.Incontrast,deviationsfrom ACT-Rmodelthatperformedthetaskusingthesameexperimen-
the reinforcement learning solution would support the minimum tal software as the human participants in Experiment 3 (Gray,
memoryhypothesis. Schoelles, & Sims, 2005). Although that model lacked a mecha-
nism for optimizing time, it did provide a detailed cognitive task
analysisthatallowsustobreakeachunittaskdownfurther.Each
Ideal Performer Analysis: Ideal Observer Analysis Meets
line with an entry in the cost column of Table 5 represents an
Rational Analysis3
interactive routine. If we further fleshed out the model, each
interactive routine would be composed of an activity network of
Our ideal performer analysis combines elements of an ideal
cognitive, perceptual, and motor operations (as illustrated and
observer analysis (Geisler, 2003; Macmillan & Creelman, 2004)
discussedinGray&Boehm-Davis,2000).
withthoseofrationalanalysis(Anderson,1990,1991).Theideal
FortheEncodeBlocksunittasktheperformermustshiftvisual
observeranalysis(Geisler,2003;Macmillan&Creelman,2004)is
attentiontoandmovethemouseintotheTargetWindow(lines2
used to “determine the optimal performance in a task, given the
and 3). Between conditions, hard constraints built into the task
physical properties of the environment and stimuli” (Geisler,
environmentdeterminehowlongtheperformermustwaituntilthe
2003).Theidealobservermaybedegradedinasystematicfashion
window opens (line 4). Once the Target Window is open, the
by including side conditions, “for example, hypothesized sources
performerencodesoneormoreblocks(lines5–9).Thenumberof
ofinternalnoise(Barlow,1977),inefficienciesincentraldecision
blocksencodedinmemoryisnotconstrainedbythetaskenviron-
processes (Barlow, 1977; Green & Swets, 1966; Pelli, 1990), or
ment,andinourIdealPerformerModelthechoiceofnumberof
known anatomical or physiological factors that would limit per-
blocks to encode corresponds to the selection of a particular
formance (Geisler, 1989)” (Geisler, 2003). In Simon’s term
ENCODE-k strategy. (The issue of selecting ENCODE-k strate-
(1992),theidealperformeranalysisallowsustodetermineoptimal
giesisdiscussedinthenextsection.)Functionally,theprocessof
performance given “side conditions” that represent the known
encoding a block in our model corresponds to creating a new
limitsoftheperformer.
declarativememoryelement(seeAppendixA)andrehearsingthe
Rationalanalysis“involvesthreekindsofassumptions:assump-
elementbyperformingtworetrievalsbeforemovingontothenext
tions about the goals of a certain aspect of human cognition,
block.
assumptions about the structure of the environment relevant to
The second unit task is Get & Place. In this unit task the
achieving these goals, and assumptions about costs. Optimal be-
performer must move visual attention and the mouse cursor into
haviorcanbepredictedbyassumingthatthesystemmaximizesits
the Resource Window (lines 11–12), which then opens. The per-
goalswhileitminimizesitscosts”(Anderson,1990,p.244).
formermustthenrememberthecolorofanencoded,butnot-yet-
Conjoining the ideal observer analysis with rational analysis
placedblock,movetoablockofthatcolor,andclickonthecolor.
yieldsfourcomponentsofouridealperformeranalysis:adescrip-
tion of the task environment; the systematic degradation of the
ideal observer by adding in known human limits; defining se- 3AnannotatedCommonLispfileofthemodelisavailableattheAPA
quencesofinteractiveroutinesthatallowustocharacterizeinter- archivesiteforPsychologicalReviewandispostedonourwebsitehttp://
activebehaviorasmoreinteractionintensiveormemoryintensive; www.rpi.edu/(cid:6)grayw/pubs/papers/GSFS06_PsycRvw/GSFS06_PsycRvw
andtheoptimal(ideal)sequencingoftheseinteractiveroutinesso .htm.