The response dynamics of preferential choice case study

That is, we address the question of whether, given choice ofthe more pleasant option in a pair, increased pleasantness of the foregone option is associated withincreased ‘‘pull’’ reveale

The response dynamics of preferential choice

Gregory J Koopa,b,⇑, Joseph G Johnsona

to the maxim of risk seeking in losses and risk aversion in gainsmay be the product of at least one ‘‘online’’ preference reversal,and can thus begin to discriminate amongst the candidate models.Finally, we incorporate attentional data collected via eye-tracking(Experiment 3) to develop a formal computational model of jointinformation sampling and preference accumulation In sum, wevalidate response dynamics for use in preferential choice tasksand demonstrate the unique conclusions afforded by responsedynamics over and above traditional methods

Ó 2013 Elsevier Inc All rights reserved

0010-0285/$ - see front matter Ó 2013 Elsevier Inc All rights reserved.

⇑Corresponding author Address: Department of Psychology, 430 Huntington Hall, Syracuse, NY 13244, United States E-mail address: gjkoop@syr.edu (G.J Koop).

Contents lists available atScienceDirectCognitive Psychology

j o u r n 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 / c o g p s y c h

1 Introduction

A hallmark of recent theoretical work in cognitive psychology (and judgment and decision making

in particular) is an increased emphasis on the underlying mental processes that result in behavior.That is, rather than simply trying to predict or describe the overt choices people make, researchersare increasingly interested in forming specific models about the latent cognitive and emotional pro-cesses that produce those decisions Broadly, we might classify these as computational or processmodels, which consist specifically of production rule systems (Payne, Bettman, & Johnson, 1992,1993), heuristic ‘‘toolboxes’’ (Gigerenzer, Todd, & The ABC Research Group, 1999), neural networkmodels (Glöckner & Betsch, 2008; Simon, Krawczyk, & Holyoak, 2004; Usher & McClelland, 2001),sampling models (Busemeyer & Townsend, 1993; Diederich, 1997; Roe, Busemeyer, & Townsend,2001; Stewart, Chater, & Brown, 2006), and more To many, including the present authors, this is awelcome and exciting evolution of theorizing in our field

With an increase in the explanatory scope of these process models comes the need for ment in the methodological tools and analytic techniques by which we evaluate them (Johnson,Schulte-Mecklenbeck, & Willemsen, 2008) Traditional algebraic models, such as Savage’s (1954)instantiation of expected utility, were assumed to be paramorphic representations, not necessarilydescribing the exact underlying mental process of how individuals make choices, but rather whatchoices people make Therefore, researchers were content—and it was theoretically sufficient—to onlyexamine choice outcomes and the maintenance (or not) of principles such as transitivity and indepen-dence (e.g.,Rieskamp, Busemeyer, & Mellers, 2006) However, contemporary emphasis on processmodeling requires more sophisticated means of model evaluation

advance-In the past few decades, process-tracing techniques such as mouse- and eye-tracking have becomepopular for drawing inferences about the information acquisition process in decision making (Franco-Watkins & Johnson, 2011; Payne, 1976; Payne et al., 1993; Wedel & Pieters, 2008; Wedell & Senter,1997; and many more) This large body of work seeks to verify the patterns of information acquisitionthat decision makers employ, and compare these to the predictions of various process models Thisrepresents a boon in the ability to critically assess and compare different theoretical processing ac-counts Granted, there are some strong assumptions that need to be made when using this paradigm,and some limitations in the resulting inferences (Bröder & Schiffer, 2003, and the references therein;Franco-Watkins & Johnson, 2011) Still, this paradigm has proven valuable in acknowledging theimportance of bringing multiple dependent variables to bear on scientific inquiry in decision research

In the current work, we are not disparaging the contribution of process-tracing techniques to ourunderstanding of decision processes However, the process-tracing paradigm is focused on patterns ofinformation acquisition, but not necessarily the direct impact this information has en route to making

a decision That is, even though this approach is able to monitor the dynamics of information tion, it does not dynamically assess how this information influences preferences or ‘‘online’’ behavioralintentions In fact, it cannot do so: the only indication of preference in these tasks remains discrete, inthe form of a single button press or mouse click to indicate selection of a preferred option at the con-clusion of each trial At best, then, process-tracing paradigms can only draw inferences about howaggregate measures (such as number of acquisitions or time per acquisition) relate to the ultimatelychosen option, or the strategy assumed to produce that option In response to this general shortcom-ing, we simply propose to dynamically monitor the response selection action as well Just as process-tracing has been used as a proxy for dynamic attention in decision tasks, we propose that response-tracing can be used as a dynamic indicator of preference We begin with some theoretical contextand a brief survey of this paradigm’s success in cognitive science before presenting a validation, exten-sion, and application of this approach to preferential choice

collec-1.1 Embodied cognition

Our basic premise rests on the assumption that cognitive processes can be revealed in the motorsystem responsible for producing relevant actions This proposition can be cast as an element ofembodied cognition, which is already theoretically popular in behavioral research (for overviews,

seeClark, 1999; Wilson, 2002) For example, recent work on the hot topics of ‘‘embodied’’ and ated’’ cognition—even now ‘‘embodied economics’’ (Oullier & Basso, 2010)—suggests that our cogni-tive, conceptual frameworks are driven by metaphorical relations (at least) to our perceptual andmotoric structures.

‘‘situ-Indeed, the recent trend in social sciences has been away from classical theories and towardsembodiment theories (Gallagher, 2005) Whereas classical theories separate the body from mentaloperations, theories of embodiment maintain the importance of the body and its movements forcognitive processes The theoretical perspective of embodied cognition can take several forms (seeGoldman & de Vignemont, 2009; andWilson, 2002, for two possible classifications) One strong inter-pretation assumes that the neural machinery of thought and action are singular and inseparable,whereas a milder assumption, adopted here, is that cognitive operations produce systematic and reli-able physical manifestations In general this approach appreciates the close interaction between cog-nition and the motor system, and questions the reductionistic tendency to study either in isolation(seeRaab, Johnson, & Heekeren, 2009, for a collection of papers in the context of decision making).Embodiment theories have been spreading within and beyond cognitive sciences—they have been ap-plied to the fields of learning, development, and education and have found their way into specializeddomains such as sports, robotics and virtual environments

Contemporary decision models, in contrast, still explicitly (Glimcher, 2009, p 506) or implicitly sume that the motor component of the decision is the final consequence of cognition; at best, they aresilent on this relationship This is problematic as it ignores a number of empirical phenomena such ascognitive tuning (or motor congruence) that suggest the potential for motoric inputs to cognitive pro-cessing (Friedman & Förster, 2002; Förster & Strack, 1997; Raab & Green, 2005; Strack, Martin, & Step-per, 1988) For instance,Strack, Martin, and Stepper (1988)showed how inducing facial muscles toperform the action required of smiling or frowning affected the assessment of a stimulus’ valenceaccordingly (e.g., cartoons rated as funnier when facial muscles were in a position related to smiling).Förster and Strack (1997)andRaab and Green (2005)found similar effects for gross motor movementssuch as the flexion or extension of the arm on categorization and association tasks Proprioceptive andmotor information may also be directly relevant for decision making in other ways, such as by con-straining the set of available options, or altering the perception of available options or their attributes(seeJohnson, 2009, for elaboration within the context of a computational model) Some of the process-tracing work in decision research is also beginning to acknowledge these connections, such as workthat shows the influence of visual attention (measured via eye-tracking) on preference (Shimojo, Sim-ion, Shimojo, & Scheier, 2008) and problem solving (Thomas & Lleras, 2007) Just as the existing workhas identified a robust connection from the motor system to cognitive processes, the current workintroduces evidence for the reciprocal connection of cognitive processes to the motor system It does

as-so by capitalizing on a recent development in other fields that have employed continuous responsetracking paradigms

1.2 Mental operations revealed in response dynamics

Most recently, continuous online response tracking has been used in cognitive science as evidencefor the ‘‘continuity of mind’’ (Spivey, 2008) This work, here referred to as the study of response dynam-ics, simply involves spatial separation of response options for simple tasks to allow for continuousrecording of the motor trajectory required to produce a response Substantial evidence suggests thistrajectory reveals approach tendencies for the associated response options (seeDale, Kehoe, & Spivey,2007; Spivey, Grosjean, & Knoblich, 2005;Duran, Dale, & McNamara, 2010, for methodological de-tails) Such recordings have been successfully applied to gross motor movements, such as lifting thearm to point a response device at a large screen (Koop & Johnson, 2011;Duran et al., 2010), as well

as the fine motor movements associated with using a computer mouse (Spivey et al., 2005, among ers) Essentially, the major innovation is to monitor the online formation of a response, rather thansimply the discrete or ballistic production of a response that is typically collected in experimental set-tings (a single button press, or mouse click) The validity of this research paradigm is supported bywork that correlates the neural activity across the cognitive and motor brain regions for several tasks(Cisek & Kalaska, 2005; Freeman, Ambady, Midgley, & Holcomb, 2011), including perceptual decision

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making (seeSchall, 2004, for a review) Response dynamics research has revealed new insights aboutbehaviors such as categorization (Dale et al., 2007), evaluation of information (McKinstry, Dale, & Spi-vey, 2008), speech perception (Spivey et al., 2005), deceptive intentions (Duran et al., 2010), stereotyp-ing (Freeman & Ambady, 2009), and learning (Dale, Roche, Snyder, & McCall, 2008; Koop & Johnson,2011) Additional related work has been conducted within the ‘‘rapid reach’’ paradigm (seeSong &Nakayama, 2009, for an overview).

A concrete example may help to illustrate the basic paradigm.Spivey et al (2005)asked pants to simply click with a computer mouse the image of an object (e.g., ‘‘candle’’) that was identifiedthrough headphones The correct object was paired either with a phonologically similar distractor(e.g., ‘‘candy’’), or with a dissimilar control object (e.g., ‘‘jacket’’) Their results showed that the curva-ture of the response trajectories was affected by the similarity of the paired object—the similar distrac-tor produced an increase in curvature, suggesting a competitive ‘‘pull’’ during the response movementcaused by an implicit desire to select the phonologically similar distractor

partici-The current work presents one of the first true extensions of this body of research to decisionsinvolving preferential choice (see alsoDshemuchadse, Scherbaum, & Goschke, 2013, for an application

to intertemporal choice) Previous research using this paradigm has largely focused on tasks such asidentification and categorization where objectively correct responses could be determined a priori

In contrast, the current work will seek to validate the method to situations where preferences aremore subjective, and extend it to a traditional risky decision making task among gambles Our worktherefore makes contributions not only from a methodological perspective to the response dynamicsparadigm, but also theoretically to the study of human decision making behavior Anecdotal support(e.g., your finger’s movements when selecting a cut of meat in the grocer’s display case) and informalapplications (e.g., the online tracking of focus groups’ perceptions during presidential debates) to pref-erential choice may abound Here, however, we hope to establish the scientific use of this paradigm fordecisions in a controlled experimental design We present three experiments using this paradigm thatestablish its validity, ability to address theoretical predictions, and efficacy for formal computationalmodeling We also provide enough detail for researchers to consult as a primer in applying thesemethods and metrics in their own research

2 Experiment 1

Because this is the first extension of the response dynamics method to preferential choice, our firsttask is to demonstrate the validity of the method within this domain In order to do so, we utilized anextremely well-studied set of stimuli, the International Affective Picture System (IAPS;Lang, Bradley,

& Cuthbert, 2008) The IAPS consists of over 1000 photographs that have been well normed (byapproximately 100 participants for each picture) on three dimensions of emotion: affective valence(or pleasantness), arousal, and dominance We focused on the dimensions of pleasantness and arousalunder the assumption that preference would be roughly analogous to ratings of pleasantness, givenequal levels of arousal Thus we were able to directly test the claim that measures of response dynam-ics can accurately represent the development of preference

2.1 Methods

2.1.1 General paradigm

The general paradigm simply involves participants making choices on a screen as depicted inFig 1.Participants began each trial by clicking on a box at the bottom-center of the screen Once they did so,this box disappeared and the picture stimuli (described in Stimuli) appeared in boxes at the upper-leftand upper-right of the screen In this way, it was possible to achieve a considerable distance betweenthe initiation and termination of the response, as well as sufficient distance between the two responseoptions Clicking in the box of their preferred picture recorded their choice, removed the picture re-sponse boxes from the display, and began the next trial Immediate, complete, and unadulterated pref-erence for one option would suggest that the response trajectory proceeds in a straight line from thepoint of initiation to the point of response Deviation from this direct path is interpreted as an

attraction to the competing (non-chosen) response option (e.g.,Spivey & Dale, 2006) In our case, thiswould suggest that even if a participant selects Picture A, the degree of curvature in the associatedresponse trajectory serves as an indication of implicit and concurrent attraction towards Picture B dur-ing the formation of the response—an online measure of relative preference.

2.1.3 Stimuli

All stimuli were drawn from the IAPS based off of their previous ratings of average pleasantnessand arousal on nine-point scales (Lang et al., 2008) We selected 140 pictures that ranged from veryunpleasant (pleasantness = 1.66) to very pleasant (pleasantness = 8.34), and paired pictures based

on their similarity in pleasantness ratings to create 70 trials Arousal rating was held constant ence < 0.45) within trial pairs These 70 trials were further divided into 7 trial classes (10 pairs perclass), representing seven levels of our independent variable, Difference Specifically, we manipulatedthe similarity in pleasantness ratings between the pictures, ranging from similar (Difference  0) todissimilar (Difference  6) The experiment was conducted in a professional setting, which resulted

(differ-in 10 picture pairs be(differ-ing removed at the behest of the employer due to their graphic content Theremoved trials were more likely to have come from more dissimilar classes because these classesrequired more strongly negative pictures to achieve such large differences in pleasantness This leftslightly unequal numbers of trials in each trial class (seeTable 1) Thus, we were left with a total of

60 picture pairs that varied in pleasantness ratings but were each roughly matched for arousal

Fig 1 The general response dynamics paradigm Participants are initially presented with a ‘‘Start’’ button and two empty response boxes, which are then populated with response options once the ‘‘Start’’ button has been clicked.

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2.1.4 Procedure

After providing informed consent, participants were led to individual testing booths and providedwith instruction slides on the nature of the task Participants were told that they were going to beshown two pictures, and they simply had to click on the picture they preferred To insure that the re-sponse trajectories reflected the natural accumulation of preference rather than demand characteris-tics, participants were not told their mouse movements would be recorded, and were given no specialinstructions or motivations regarding mouse movements Prior to beginning the main task, partici-pants completed a practice trial without stimuli to ensure familiarity with the response process Next,each participant completed five practice trials with increasingly unpleasant stimuli The purpose ofthese trials was to acclimatize participants to the range of pleasantness they would see in the taskand were not included in analyses Following these five acclimatization trials, participants completedthe main block of 60 trials The main block was randomized for each participant both for left/right pic-ture presentation, as well as for trial order Immediately following the experiment, participants weregiven their payment vouchers, debriefed, and thanked for their participation

2.2 Results

2.2.1 Aggregate-level data analysis

Our goal for this study is to establish that the response dynamics methodology is valid for a typicalpreference task Therefore, we will focus on those analyses that we feel are best suited to achievingthis end, but are by no means exhaustive We refer the reader to previous work for additional detailsabout the rationale and procedural steps for many of the analyses we perform (in particular,Dale et al.,2007; Spivey et al., 2005; andDuran et al., 2010)

The choice data show that participants were globally more likely to choose the picture in each pairthat was rated as more pleasant (Table 1)1, and a repeated-measures ANOVA revealed an effect of Dif-ference on individual choice proportions, F(5, 485) = 184.67, p < 01 These outcome data represent an ini-tial validation of our assumption that the pleasantness ratings in IAPS are an appropriate normed analog

to preference Furthermore, the data suggest that the presentation format and procedure did not have anidiosyncratic effect on choice behavior, and we can dive more deeply into the response trajectories with-out concern

Rather than merely interpreting discrete choices, response dynamics allows us to observe theprocess underlying these choices In order to aggregate the response trajectories, we first recodedall x-coordinates to remove the counterbalance for left/right presentation order Because we recordedmouse position at a constant rate of 100 Hz, each trial necessarily produced a different number ofmeasurements based on individual response times For ease of direct comparison, we next time-normalized the complete trajectory for each trial of each participant into a series of 101 ordered(x, y) pairs These were calculated by including the initial and terminal x,y-coordinates, followed bylinear interpolation of the positional data stream at 99 equally-spaced time intervals (Spivey et al.,

2005, established this precedent for all subsequent work)

Table 1

Trial classes and choice proportions for Experiment 1.

Next, we explored whether the degree of curvature was indeed indicative of increased tion’’ from the foregone option In the context of the current task, it stands to reason that selectionsamong pairs of similar stimuli should produce more competition and less direct response paths,whereas choices made among dissimilar stimuli should contain more unequivocally preferred optionsand thus more direct paths To assess this claim, we examined those trials in which participants chosethe more positive option In highly dissimilar trials (Difference P 4), most participants never selectedthe more unpleasant option This is understandable given the nature of the stimuli, but unfortunatelycauses a substantial loss of power in within-subjects analyses Most likely, the majority of instanceswhere participants selected the less pleasant option could be considered ‘‘error’’ trials For example,choice of the less pleasant option on one trial in the Difference  6 trial class entailed choosing a pic-ture entitled ‘‘Starving Child’’ over one entitled ‘‘Wedding.’’ Thus, we choose to focus only on those tri-als where participants selected the more pleasant option, and can therefore quantify the competitivepull of non-chosen, less pleasant options That is, we address the question of whether, given choice ofthe more pleasant option in a pair, increased pleasantness of the foregone option is associated withincreased ‘‘pull’’ revealed by curvature in the response trajectory.

‘‘competi-The resulting aggregate trajectories suggest an effect of Difference via the predicted ordinal tionships in curvature between trajectories (Fig 2) Choices of the more pleasant option were mostdirect in the Difference  6 trial class, where the more pleasant option is most easily identifiable Witheach successive increase in pleasantness similarity, curvature in the response trajectory also in-creased This trend culminated in the Difference  1 trial class, which appears to be subject to themost competitive pull from the non-chosen, less pleasant option As predicted, this pattern indeed

rela-−400 −300 −200 −100 0

X−coordinate

Difference = 1Difference = 2Difference = 3Difference = 4Difference = 5Difference = 6

Fig 2 Response trajectories for selections of the more positive option by difference class Plots are time-normalized to 101 time steps, plotted as offset (in pixels) from trial initiation point Placement of response box is approximate Solid lines (moving from dark to light) represent the Difference  1, Difference  2, and Difference  3 trial classes respectively Dashed lines (again

G.J Koop, J.G Johnson / Cognitive Psychology 67 (2013) 151–185

suggests increasing preference for the non-chosen option, and an increasingly powerful competitivepull therefrom, as pictures become more similarly pleasant.

2.2.2 Individual-level data analysis

The plots shown inFig 2necessarily aggregate across participants for clarity and power, but it isimportant to consider metrics calculated on the level of the individual participant as well Responsedynamics provides a number of methods for quantifying such differences visible in the aggregate tra-jectory plots One benefit of such metrics is that they are done on each individual trajectory, and thenaveraged across trials within each condition for each participant, which is important given the dangersinherent in working solely with aggregate data (e.g.,Estes, 1956; Estes & Maddox, 2005) For example,

we calculated measures of absolute deviation (Euclidean distance) from a hypothetical direct responsepath at each of the 101 time-normalized bins mentioned in Section2.2.1 Maximum absolute deviation(MAD) is simply the maximum value in this set, whereas average absolute deviation (AAD) is the math-ematical average across the entire time-normalized trajectory (similar to the ‘‘area under the curve;’’seeFreeman & Ambady, 2010) MAD is better at highlighting differences occurring in the ‘‘heart’’ ofeach trial, whereas AAD is less susceptible to spurious outliers but constrained by endpoints held incommon by each trial We calculated MAD and AAD for each trial, for each participant, and then cal-culated each participant’s average of these metrics across all trials within each condition where themore pleasant option was selected As expected based on the aggregate response trajectories shown

in Fig 2, the analysis of individual data shows the six trajectories differ in both MAD,F(5, 470) = 34.60, p < 001, and AAD, F(5, 470) = 25.60, p < 001 Furthermore, the linear contrast foreach metric was also significant (Fig 3a and b; p < 001) These individual analyses confirm that thetrend visible in the aggregate trajectories was not merely an artifact of averaging

2.3 Discussion

The results of Experiment 1 represent an important validation of the response dynamics paradigmwithin the domain of preferential choice To provide this validation, we utilized extremely well-normed stimuli and instructed participants to simply select the image that they preferred in a pair.The analyses performed above suggest that response dynamics can be effectively utilized to more fullyelucidate the preferential choice process We contend that the curvature in participants’ response tra-jectories was the product of the similarity in preference between the choice options, as operational-ized by normed pleasantness ratings The ordinal relationships in similarity between the six trialclasses were manifested in the aggregate response trajectories Selections of the more pleasant options

on the most dissimilar trials (Difference  6) were subject to the least competitive pull, and with each

0102030405060708090100

(a) Maximum Absolute Deviaon (b) Average Absolute Deviaon

Fig 3 Absolute deviation from a direct path in pixels for Experiment 1 Maximum absolute deviation (MAD; a) and average absolute deviation (AAD; b) were computed for each trial class in Experiment 1 Similarity in pleasantness was highest in the

successive increase in similarity, competitive pull (i.e., curvature) increased as well These datasupport the fundamental response dynamics assumption previously validated in other domains(e.g.,Spivey et al., 2005): curvature produced in the motor response is the product of competitionbetween response options.

The general paradigm has been well established in cognitive science, but the key validation vided uniquely by this study is the use of response dynamics in the domain of preferential choice,where responses are based on subjective evaluation rather than objective criteria Although this initialvalidation is an important step, we are more enthusiastic about the possibilities for using the responsedynamics method to evaluate competing models of preferential choice Response dynamics has thepotential to offer a substantial increase in the resolution with which researchers can test process mod-els To demonstrate this new avenue for model testing, we will now use response dynamics to testqualitative (Experiment 2) and quantitative (Experiment 3) predictions for select models of risky deci-sion making

pro-3 Experiment 2

Given the validation provided by Experiment 1, we can now proceed to apply the method to a ditional risky decision-making task of gamble selection—almost certainly the most common task indecision research over the past few decades Because gambles afford a high degree of experimentalcontrol, it has often been sufficient to design stimuli that discriminate amongst models on the basis

tra-of discrete choice patterns alone Response dynamics, however, enables examination tra-of process dictions beyond discrete choices, and can thus provide a novel look at this most classic of decision-making tasks In Experiment 2, we develop unique response predictions for a representative subset

pre-of process models, including ‘‘one-reason’’ (Brandstätter, Gigerenzer, & Hertwig, 2006; Gigerenzer

et al., 1999), default-interventionist dual-systems (Greene, Morelli, Lowenberg, & Cohen, 2008; wenstein, Weber, Hsee, & Welch, 2001; or seeEvans, 2008), and evidence accumulation (e.g.,Buse-meyer & Townsend, 1993; Diederich, 1997; Usher & McClelland, 2001) models

Loe-3.1 Qualitative model predictions

We begin with the assumption that the response trajectories as shown inFig 2can be a suitableproxy for online measurement of preference towards a given option during deliberation, as supported

by the validation study in Experiment 1 Therefore, in order to evaluate processing claims proposed bypopular contemporary models, we can derive predictions for how these paths should look according toeach model class First, for each model we derive stylized predictions regarding preference develop-ment (Fig 4) Second, where relevant for some models, we also derive predictions regarding the veloc-ity of the response movement (Fig 5) Predictions such as these provide additional means by which toevaluate sufficiently specified models, and further illustrate the unique capacity of the responsedynamics paradigm

3.1.1 ‘‘One-reason’’ decision making

Starting withSimon’s (1956)work in the 1950s, research has repeatedly shown that decision agents

do not (and often cannot) optimally utilize all available information while making a choice (e.g.,Payne

et al., 1993; Tversky, 1972) Fortunately, making decisions on the basis of incomplete information is not

as detrimental as one might think Heuristic models that ignore pieces of information en route to ing a decision can often perform nearly as well as optimization models for both inference (Gigerenzer &Goldstein, 1996; Gigerenzer et al., 1999) and preference (e.g.,Payne et al., 1993) tasks The priority heu-ristic (Brandstätter, Gigerenzer, & Hertwig, 2008; Brandstätter et al., 2006) is a recent example of a lex-icographic model that attempts to describe decision making on gamble-based decision tasks Thepriority heuristic provides the order in which individuals attend to outcome and probability informa-tion The model predicts that individuals will first survey all information during a ‘‘reading’’ stage be-fore moving on to a ‘‘choice’’ stage where the decision process is terminated as soon as a single attribute(or ‘‘reason’’) wholly determines preference for an option (Brandstätter et al., 2008) It is important to

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note however, that ‘‘even if all [attributes] are screened, [the priority heuristic] bases its choice on onlyone reason’’ (Brandstätter et al., 2006, p 414).

Therefore, a strong claim of this model (and lexicographic models more generally) is that uals should remain indifferent between choice options until a single reason entirely determines pref-erence This strong version of one-reason decision making predicts a response pattern that does notmove away from the y-axis until the critical information is encountered, at which point there would

individ-be immediate and direct movement towards the selected option (Fig 4, line ‘‘A’’) While it is also sible that during the initial reading stage there could be a slight ‘‘drift’’ due to hand movements cou-pling with eye-movements for extracting information, the resulting variability in the initial verticalmovement should then average out across trials Another possibility is a complete absence of move-ment (resting at the origin) until the moment when the critical information in acquired, at which pointthe response would begin and thus produce a direct path (AAD  0)

pos-3.1.2 Default-interventionist dual-systems models

As within many other areas of psychology, the field of judgment and decision making has seen asharp rise in the popularity of dual-systems models over the last two decades These models generallyclaim that decisions are the product of an interaction between a fast, intuitive, and emotion-driven

‘‘System 1,’’ and a slower, controlled, more deliberate ‘‘System 2’’ (Kahneman, 2011; Stanovich & West,

Fig 4 Predicted stylized aggregate response trajectories (cf Fig 2 ) for three classes of decision-making process-models.

Fig 5 Predicted stylized velocity profiles for three classes of decision-making process-models, showing change in pixels (pixels/s) as a function of time (see also Fig 8 ).

2000) A subset of these models, known as ‘‘default-interventionist’’ models (DI;Evans, 2008), makesspecific temporal predictions about the nature of this interaction Specifically, DI models predict thatthe faster System 1 often dominates, unless System 2 overrides that prepotent response (Greene,Nystrom, Engell, Darley, & Cohen, 2004; Greene, Sommerville, Nystrom, Darley, & Cohen, 2001; Greene

et al., 2008; Kahneman, 2011; Kahneman & Frederick, 2002; Loewenstein, Rick, & Cohen, 2008).Although this critical temporal prediction is held in common by many dual-systems models, find-ing methods with sufficient temporal resolution to test this assumption has been problematic (Hueb-ner, Dwyer, & Hauser, 2008; but seeStarns, Ratcliff, & McKoon, 2012for such a test using the driftdiffusion model) Response dynamics again allows us to develop qualitative predictions about the nat-ure of the response process based on these temporal claims We see two possibilities for a DI concep-tualization of dual-systems models in decision making If the option preferred by System 1 iscompatible with that of System 2, then there would be a consistent sustained movement towards thatselection (trajectory:Fig 4, line ‘‘B’’; velocity:Fig 5, line ‘‘B’’) Alternatively, if the two systems prefercompeting options, the response trajectory would show initial movement towards the option pre-ferred by System 1, followed by a reversal towards the option preferred by System 2 after it overridesthe initial preference (Fig 4, line ‘‘C’’) The velocity profile of this competing response would followthat of the compatible response until override is exerted, at which point movement towards the Sys-tem 1 preferred option decelerates Once the override is complete, the response is free to move quicklytowards the final choice (Fig 5, line ‘‘C’’)

3.1.3 Evidence accumulation models

Evidence accumulation models assume that preferential choice is the product of an accumulation

of momentary evaluations represented by an evolving preference state until sufficient preference ists to surpass a decision criterion (Busemeyer & Townsend, 1993; Diederich, 1997; Roe et al., 2001;Usher & McClelland, 2001) Assuming this to be the case, evidence accumulation models could show agreat deal of vacillation depending on the nature of the information presented, and the order in whichindividuals attend to that information (Fig 4, line ‘‘D’’) For example, if an individual first attends toinformation favoring the left option, these models predict that preference will accrue towards that op-tion and the mouse response should move to the left accordingly If the individual next attends toinformation favoring the right option, the response movement will then drift towards that option.Thus, any momentary change in mouse position reflects the impact of the currently attended informa-tion, and the current mouse position at any point indicates the accrued preference up to that point (aprediction that will be more fully developed in Experiment 3) Likewise, the velocity profiles predicted

ex-by accumulation models could also show a great deal of variability as momentary valences favor oneoption or the other (Fig 5, line ‘‘D’’) However, previous applications of one such accumulation model(Usher & McClelland, 2001) have predicted that as competing options are inhibited, the speed withwhich the response can move towards the ultimately selected alternative increases—thus the generalacceleration near the end of the profile (Wojnowicz, Ferguson, Dale, & Spivey, 2009)

The nature of these predictions highlights the substantial increase in resolution with whichresearchers can test process models using the response dynamics paradigm Accordingly, we havedeveloped qualitative predictions for the form (and velocity) of response trajectories predicted bythree prominent process models of decision making: ‘‘one-reason,’’ default-interventionist dual-systems, and evidence accumulation models Experiment 2 tests these qualitative predictions byapplying response dynamics to a traditional gamble-based decision task

3.2 Method

We imported the response dynamics paradigm into a standard laboratory risky decision-makingtask of gamble selection In short, we utilized the same method as Experiment 1, but populated theresponse boxes with economic gambles rather than pictures (Fig 6)

selected the experiment from an online sign-up site that included a number of experiment options Fortheir participation, students received course credit and a monetary reward based on their performance

in the task

3.2.2 Stimuli

Stimuli in the form of single (nonzero) outcome gambles were created as follows First, we createdone gamble for each success probability of 0.90, 0.80, 0.70, and 0.60 We assigned outcome values tothese success probabilities in an attempt to approximately equate EV; we attached outcome values of

$60, $70, $80, and $90, respectively, to the success probabilities (e.g., win $60 with probability 0.90,else nothing) Next, we subtracted $10 from the outcome values of these four gambles to create fouradditional stimuli (e.g., win $50 with probability 0.90), then subtracted $10 from each of those to cre-ate our final four stimuli (e.g., win $40 with probability 0.90) Finally, by hand we created pairwisecomparisons among these twelve stimuli where one gamble had a higher success probability, butthe other had a higher outcome value This resulted in a total of 43 trials, to which we also added threetrials with a dominant option We then attached negative signs to all of the outcomes in these 46 Gaincondition pairs to create a second set of 46 gambles for the Loss condition Note that some of thesetrials were ultimately excluded from analyses (described later); complete pairings (shown for the Gaincondition) can be found inAppendix A

3.2.3 Procedure

After providing informed consent, participants were informed that they would earn money based

on their responses during the experiment The nature of the experiment required extra time to processthe response data and calculate final payments—thus, participants also filled out payment vouchersthat linked them to their choice data so that they could be paid at the end of the week in which theytook the experiment This process was thoroughly explained to participants by the experimenter andrepeated on instruction slides After filling out the payment voucher, participants read through com-puterized instruction slides that explained the nature of the task Participants were told that theywould be playing a series of gambles for real money and that every gamble they selected would besimulated in order to determine a final payment amount

The two conditions varied in regards to the exact method used to calculate a final payment in order

to avoid the clearly undesirable potential to have students ‘‘owing’’ us money in the Loss condition Inthe Gain condition, we calculated final payment by taking each participant’s average earnings per trialand dividing that value by ten In the Loss condition, participants were truthfully told that they hadreceived a $10 ‘‘endowment’’ for the task and that every gamble they played would subtract from this

Fig 6 Presentation of gamble information in Experiment 2.

amount The same formula used to determine payment in the Gain condition was also used in the Losscondition, only rather than simply taking the average of all gamble outcomes divided by ten, thisamount was then subtracted from the initial ‘‘endowment’’ of $10 Participants in both conditionswere provided with their respective method and told that, on average, they could expect to earnaround $5 Finally, in order to ensure that they understood the manner in which they were expected

to indicate a choice, they were shown animated example trials and completed an example trial prior tothe main task As in Experiment 1, participants were not informed that their mouse movements werebeing recorded, and were given no special instructions about mouse movement whatsoever Partici-pants completed the task with their preferred hand

All participants completed all 46 trials in their respective conditions The order in which gamblesappeared was randomized once (for both conditions), and then this single order was reversed forcounterbalancing across participants The left/right presentation order of gambles within a pair wasalso counterbalanced between participants Following completion of all experimental trials, partici-pants were reminded of the date and location of their payment collection window before beingdismissed

3.3 Results

Experiment 2 represents an increase in the complexity of stimuli relative to Experiment 1, whichallows us to ask more complex questions about the psychological processes underlying participants’decisions This increased complexity also allows us to showcase the diversity of analytic techniquesmade possible by continuous response tracking, including derivative measures such as velocity andacceleration Whereas analyses in Experiment 1 were based on stimulus similarity (Difference), here

we will base our analyses on a simple comparison of risk attitudes, which is a pervasive construct indecision research using gamble stimuli such as these In particular, we will compare trials where the

‘‘Safe’’ option was chosen to those trials where the ‘‘Risky’’ option was chosen, where risk is alized by gamble variance, per convention in the field.2Additionally, we will compare measures takenacross Gain and Loss conditions For these comparisons, we excluded the three trials with a dominantoption to keep such ‘‘obvious’’ choices from inflating any measures

operation-3.3.1 Aggregate-level data analysis

As in Experiment 1, the choice data (Table 2) provide an initial assessment of whether either themethod or the stimuli are idiosyncratic in a way that prevents further generalization These data showthat participants preferred the Safe gamble in the domain of Gains, by a margin of three to one In theLoss domain, participants preferred the Risky option, although the relative strength of this preferencewas not quite as extreme These results are in line with typical risk attitudes across gains and losses(Tversky & Kahneman, 1981), and again affirm that the methodology did not adversely affect behavior,and that the stimuli created for this task were not abnormal

Table 2 Choice proportions for Experiment 2 (E2) and Experiment 3 (E3).

Because most of our stimulus pairs did not differ greatly in expected value, we assumed that gamble variance was an

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Again as in Experiment 1, we first plotted the time-normalized trajectories aggregated across trialsand participants (Fig 7).3Specifically, to produceFig 7, we separated an individual’s trials into Risky andSafe choices For each participant, we then averaged across the corresponding trajectories within each ofthese response conditions At this point, each participant is represented by a single Risky trajectory and asingle Safe trajectory, unless they did not make a single choice of one type across all trials For example, aparticipant who made all Safe choices would have a Safe trajectory aggregated across 43 trials but wouldnot have a Risky trajectory Finally, the plots shown inFig 7were generated by then aggregating theseindividual x- and y-vectors across all participants within the associated Domain-Response combination

to produce each plotted trajectory Because a few participants in each Domain had fully consistent vealed risk attitudes and never made one type of choice (Risky or Safe), sample sizes varied slightlyacross conditions (Table 2for sample sizes)

re-Closer inspection ofFig 7reveals a number of interesting phenomena For the Gain condition (darklines), the response trajectories are clearly more direct for the Safe choices (solid lines) compared tothe Risky choices (dotted lines) In fact, the Safe choice trajectories never tend towards the Risky op-tion, but the Risky choice trajectories suggest participants briefly consider the Safe option beforechanging course towards the Risky option they ultimately chose In the Loss condition (light lines),the relative curvature across Risky and Safe choice trajectories is reversed—greater curvature is asso-ciated with selection of the Safe option Comparisons across Gains and Losses makes clear that the eas-iest and most definite choice, as inferred from the directness of the response trajectory, was selection

of a Safe Gain, whereas the most difficult and conflicted choice was selection of the Risky Gain Any

X−coordinate

Risky GainSafe GainRisky LossSafe Loss

Fig 7 Response trajectories for Gain and Loss domains Plots are time-normalized to 101 time steps, plotted as offset (in pixels) from trial initiation point Placement of response box is approximate Total y-distance of all trajectories is approximately 300 pixels Dashed lines show aggregated trajectories for choice of Risky option, and solid lines show aggregated trajectories for choice of Safe option, separately for Loss trials (light lines) and Gain trials (dark lines).

3

To prepare the data for subsequent analyses, we recoded the x-coordinates of the mouse movement trajectories as necessary to

choice in the Loss domain produced conflict between these two relative extremes, with selection ofthe Risky Loss seeming slightly easier and less equivocal This interaction between Domain and Re-sponse is especially noteworthy in that it parallels the choice data in the current experiment as well

as an abundance of previous research (cf prospect theory’s risk seeking for losses and risk aversion forgains;Kahneman & Tversky, 1979)

Another distinct advantage of collecting continuous positional data is the ability to calculate atives such as velocity (Fig 8) and acceleration (not shown) To do so, we determined the Euclideandistance traveled in x,y-coordinates per time step (velocity), calculated over a moving window of se-ven time steps.4The qualitative pattern suggested by most of the trajectories is consistent with a quickinitial movement to start the trial, followed by a relatively slow and consistent movement during most ofthe trial, followed by a terminal increase in speed of movement towards the selected option Most prom-inent, perhaps, is the difference between the Risky and Safe choices in the Gain condition (Fig 8a), wherethe former shows the most pronounced example of the pattern just described, but the latter shows rel-atively smooth and consistent progression towards the Safe response across the trial In contrast, boththe Risky and Safe trajectories in the Loss domain (Fig 8b) show similar trends, although the terminalvelocity is greater for Safe choices The Risky Gain trajectory also shows an earlier terminal increase

deriv-in speed relative to all other trajectories These trajectories provide evidence agaderiv-inst the possibility thatparticipants simply withheld any mouse movement until a decision was made, subsequently completing

a quick and single movement detached from underlying cognitive processing If theoretical ations warrant, additional derivatives (like acceleration or jerk) can also be explored in more detail

4

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3.3.2 Individual-level data analysis

One challenge in working with such rich data is that these data are most easily presented in gate form—presenting the mouse paths for each individual could be overwhelming and largely unin-telligible on trials with substantial noise Although the aggregated data nicely demonstrate prospecttheory’s risk aversion in gains and risk seeking in losses, it is possible that this pattern only representssome virtual average participant that does not truly exist For example, if half of the participants pro-ceeded directly to select the Risky choice while the other half moved directly to the Safe choice andhesitated before moving to select the Risky choice, the aggregate path would lie somewhere in themiddle and not reflect any observed behavior

aggre-In order to refute this possibility, we moved to individual-level analyses as in Experiment 1, by culating MAD for each participant’s average Safe and Risky response trajectories We then calculated adifference score by subtracting the deviation on the average Safe choice from the deviation on theaverage Risky choice, for each participant A bimodal distribution of difference scores would suggestour results were just a product of averaging across subjects, whereas a unimodal distribution wouldshow that the aggregate paths were representative of most participants (cf.Spivey et al., 2005) Be-cause our participants were not required to select both Risky and Safe responses, those that did notexhibit a given response were excluded from this analysis Histograms of the difference scores fromthe remaining participants (Fig 9) show that most participants exhibited the same pattern seen inthe aggregate data In the Gain condition the modal response was positive, showing greater MAD inRisky trials than in Safe trials In the Loss condition the modal response was negative, which againmatched the pattern depicted in the aggregate data Finally, the mean and variance of the empiricaldistributions were used to create reference normal distributions; Kolmogorov–Smirnov tests of nor-mality showed that neither empirical distribution showed a statistically significant difference fromthe corresponding normal distribution (Gains, p = 52; Losses, p = 84)

cal-Having established that the patterns inFig 7are not artifacts of aggregation, the task shifts toquantifying the differences seen in the aggregate plots One method is to perform traditional signifi-cance tests comparing the trajectories at each of the 101 time steps (Dale et al., 2007; Spivey et al.,2005;Duran et al., 2010) For example, we compared the Risky trajectory x-coordinates with the Safe

Fig 9 Histograms of difference scores The difference (Risky–Safe) in mean maximum deviation from a straight path, in pixels,

trajectory x-coordinates, in separate paired-samples tests for each of the Gain and Loss conditions

Ris-ky and Safe responses consistently diverged (p < 0.05) from the 29th to 96th time steps for the Gaindomain, and from the 36th to 93rd time steps for the Loss domain Whereas we would expect the tra-jectories not to differ at the beginning or end due to common starting and final coordinates (afterreflecting the counterbalanced trajectories across x = 0), we see that the majority of the movementduring the ‘‘heart’’ of each trial showed statistically significant divergence This same technique can

be applied to the velocity profiles shown inFig 8 These profiles similarly showed statistically icant differences (p < 05) for 47% of time steps in the Gain condition, but only 5% of time steps in theLoss condition (represented by the black bars inFig 8)

signif-Many other metrics can be calculated using the positional data to investigate specific claims; wereport several illustrative calculations shown inFig 10that support the claim of significant differencesbetween the trajectories As in Experiment 1, these calculations were made on each individual trajec-tory, and then averaged across trials within each participant’s appropriate Domain-Response condi-tion This is helpful especially in situations where individual trends might be lost in the aggregationnecessary to produce interpretable plots such as those inFig 7

First, we calculated the total x,y-distance traveled by each trajectory (Distance inFig 10; cf.Dale

et al., 2007;Duran et al., 2010) Globally, participants traveled farther when making Risky responses,F(1, 179) = 25.36, p < 01, and when choosing amongst Losses, F(1, 179) = 14.44, p < 01 However, theseeffects were not independent of one another Confirming the trend seen in the aggregate trajectories,participants took a more circuitous route when making Risky responses in the realm of Gains, whereasthe opposite was true in the realm of Losses, as supported by a test of the interaction: F(1, 179) = 76.95,

p < 01 The total distance provides a nice summary statistic, but we can further ‘‘unpack’’ its meaningwith additional measures For example, a demonstrably large distance would be achieved by a trajec-tory that repeatedly wavered back and forth between the response options before making a selection

0200400600800

01234

Risky Safe

Response(b) Xflips

020406080

Risky Safe

Response(d) MADtime

Fig 10 Response dynamics metrics for choices among gamble pairs in Experiment 2: Distance (a), X flips (b), AAD (c), and

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