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The Quarterly Journal of Experimental Psychology

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Attention and attribute overlap in preferentialchoice

Sudeep Bhatia

To cite this article: Sudeep Bhatia (2016): Attention and attribute overlap inpreferential choice, The Quarterly Journal of Experimental Psychology, DOI:10.1080/17470218.2016.1174720

To link to this article: http://dx.doi.org/10.1080/17470218.2016.1174720

Accepted author version posted online: 04Apr 2016.Published online: 25 Apr 2016.

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Attention and attribute overlap in preferential choiceSudeep Bhatia

Department of Psychology, University of Pennsylvania, Philadelphia, PA, USA

ABSTRACTAttributes that are common, or overlapping, across alternatives in two-alternativeforced preferential choice tasks are often non-diagnostic. In many settings,attending to and evaluating these attributes does not help the decision makerdetermine which of the available alternatives is the most desirable. For this reason,many existing behavioural theories propose that decision makers ignore commonattributes while deliberating. Across six experiments, we find that decision makersdo direct their attention selectively and ignore attributes that are not present in orassociated with either of the available alternatives. However, they are as likely toattend to common attributes as they are to attend to attributes that are unique toa single alternative. These results suggest the need for novel theories of attentionin preferential choice.

ARTICLE HISTORYReceived 16 October 2015Accepted 22 March 2016

KEYWORDSJudgment and decisionmaking; Multi-attributechoice; Attention; Processtracing

Many everyday value-based decisions involve a choicebetween two or more alternatives defined on a set ofattributes. These attributes determine the desirabilityof the alternatives, and in order to make the correctchoice, decision makers need to attend to, and sub-sequently evaluate and aggregate, the decision attri-butes associated with the choice alternatives thatthey are deliberating over.

The aggregation of attribute values can be difficult,and this aspect of the decision process has been thefocus of considerable scholarly enquiry (Busemeyer& Townsend, 1993; Dawes, 1979; Fishburn, 1967;Gigerenzer & Goldstein, 1996; Keeney & Raiffa, 1993;Stewart, Chater, & Brown, 2006; Tversky, 1972). Choos-ing the right attributes to attend to and evaluate isalso, however, an important and difficult problem.The relevance of different attributes for the decisiontask can vary across choice sets. In order to makequick choices, decision makers need to direct theirattention carefully, so that they process only the infor-mation that is relevant for making the choice.

In this paper we study attribute attention in two-alternative forced choice with binary attributes. Hereattributes can be either present or absent in analternative. Present attributes are attributes that thealternatives possess. For example, a diligent job

candidate can have the attribute or quality of beinghard working, and a luxurious resort can have the attri-bute of a swimming pool. Absent attributes are attri-butes that the alternative does not possess. It ispossible that a certain, less diligent, job candidate isnot especially hard working, or that a less luxuriousresort does not have a swimming pool. If attributesare present in the alternatives then they can beeither unique to a single alternative or common andoverlapping across the two alternatives. The goal ofthese forced choice tasks is to select the alternativethat is the most desirable, irrespective of the absolutedesirability of the two alternatives. For this purpose,common attributes are often non-diagnostic. Particu-larly, when the values of the attributes in a choiceproblem are independent of each other, commonattributes do not help the decision maker determinewhich of the available choice alternatives is moredesirable. In these settings, focusing exclusively onunique attributes is necessary to ensure the quickestand least effortful decisions. Indeed, a number of exist-ing theories of decision making have suggested thatdecision makers either completely ignore commonattributes, or pay proportionally less attention tothese attributes, compared to those that are uniquein the available alternatives (Bordalo, Gennaioli, &

© 2016 The Experimental Psychology Society

CONTACT Sudeep Bhatia bhatiasu@sas.upenn.edu Department of Psychology, University of Pennsylvania, Philadelphia, PA 19104, USA

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2016http://dx.doi.org/10.1080/17470218.2016.1174720

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Shleifer, 2012, 2013; Houston, Sherman, & Baker, 1989,1991; Kőszegi & Szeidl, 2013).

How do decision makers select the attributes thatthey attend to in two-alternative binary-attributeforced choice tasks? Is attribute attention completelyindiscriminate; that is, is each attribute equally likelyto be attended to, regardless of whether it iscommon, unique, or absent across the alternatives?If not, then do decision makers focus their attentionand attend to only unique attributes, or do theyfollow a simpler strategy that at times leads to ineffi-cient decisions? Although attention is selective, anumber of well-known findings in decision-makingresearch suggest that attention allocation is notalways completely efficient. Information that is irrele-vant to the task at hand can at times become thefocus of attention. This is perhaps best demonstratedthrough the dilution effect, which finds that judg-ments are sensitive to non-diagnostic information(LaBella & Koehler, 2004; McKenzie, Lee, & Chen,2002; Nisbett, Zukier, & Lemley, 1981). Particularly,the presence of cues that are not correlated with thejudgment criterion can reduce the weights placedon correlated diagnostic cues leading to weakenedbeliefs and reduced confidence in the judgment.Other work finds that numerical anchors, cues thatare associated with favoured responses, dominancerelationships between alternatives, and a number ofother irrelevant features of the decision task can biasresponses (Huber, Payne, & Puto, 1982; Nickerson,1998; Tversky & Kahneman, 1974; see also Weber &Johnson, 2009 for a review).

In six experiments we test whether decisionmakers are able to successfully ignore commonoverlapping attributes, in simple binary forcedchoice. Our experiments involve three differentmeasures of attribute attention and consider prefer-ential choice problems from two separate domains.We find that decision makers do ignore absent attri-butes, indicating that their attention is selective.However, they are as likely to attend to commonattributes as they are to unique attributes. This influ-ences the quality of their decisions, so that decisionmakers typically take longer in choices involvingboth common and unique attributes than onlyunique attributes. Additionally we find that theobserved attentional strategies in our forcedchoice tasks are similar to those used in free choicetasks, in which decision makers can choose not toselect either of the two available alternatives.Common attributes are always diagnostic in free

choice, suggesting that decision makers may beusing a single attentional strategy for differenttypes of choice, a strategy that is efficient whenchoice is free, but often inefficient when it isforced. We conclude this paper with a discussion ofthese efficiencies and their implications regardingthe determinants of attribute attention in preferen-tial choice.

Attention in multi-attribute choice

Consider a choice between a bag of chips and abanana, for an afternoon snack. Each of these alterna-tives can be described in terms of a set of attributes.For example, the chips can be seen as being“crunchy” and “savoury” whereas the banana can beseen as being “healthy” and “sweet”. In choices suchas these, decision makers determine the relative desir-ability of the choice alternatives by examining thedesirability of their component attributes. If decisionmakers like crunchy and savoury snacks then theywill choose chips. If on the other hand, they wantsomething healthy or sweet, they will selectbananas. This structure also applies to other types ofchoices. Thus, for example, a choice between twojob candidates would be determined by the desirabil-ity of the component attributes of these candidates(attributes such as “hard working”), and a choicebetween two vacation resorts would be determinedby the desirability of the component attributes ofthese resorts (attributes such as “swimming pool”).

More generally, a two-alternative multi-attributedecision problem can be seen as a choice betweenalternatives x and y, which are written as a vectorsof n independent attributes, so that x = (x1, x2, . . . , xn)and y = (y1, y2, . . . , yn). Each of these attributes has acertain desirability or value, Vi, with the overall desirabil-ity of an alternative equal to the sum of the desirabilityof its associated attributes (see Keeney & Raiffa, 1993, foran overview). In this paper we consider choices invol-ving only binary attributes, where xi = 1 if x is associatedwith attribute i and xi = 0 if x is not associated with attri-bute i, and yi = 1 if y is associated with attribute i and yi= 0 if y is not associated with attribute i. For this settingwe can write the set of the attributes associated with x,as Ax = {i | xi = 1} and the set of the attributes associatedwith y, as Ay = {i | yi = 1}. Subsequently the desirability ofx can be written as U(x) = ∑

i[Ax Vi , and the desirabilityof y can be written as U(y) = ∑

i[Ay Vi . The goal of thestandard multi-attribute choice task is to select thechoice alternative with the highest desirability, with x

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being the correct choice if U(x) >U(y) and y being thecorrect choice if U(y) >U(x).

In order to solve this task, the decision maker needsto attend to the attributes, determine their values, Vi,and then aggregate these values into a measure ofthe relative desirability of the two alternatives (seeBhatia, 2013; Roe, Busemeyer, & Townsend, 2001). Asimple way to approach this would be to consider alln attributes equally. However, if attending to eachattribute involves a cost (such as time), then thisapproach is inefficient. It is likely that many of the nattributes do not provide any information aboutwhich of the two alternatives is more desirable.

Which attributes should decision makers considerwhen attribute attention is costly? In two-alternativechoices with binary attributes, where total value isadditive in attributes, efficient attention can be easilycharacterized. Particularly, since decision makers onlyneed to determine the most desirable of the alterna-tives—that is, whether U(x) > U(y) or U(y) > U(x)—they should only consider attributes that are uniqueto the available alternatives—that is, attributes thatare associated with only one of the available alterna-tives [attributes i [ (Ax /Ay) < (Ay /Ax)]. Common attri-butes that are associated with both of the alternatives(attributes i such that i [ Ax ∩ Ay) are relevant fordetermining the absolute desirability of the alterna-tives, but not the relative desirability of the alterna-tives. Additionally, absent attributes that areassociated with neither of the two alternatives (attri-butes i such that i ∉ Ax < Ay) are clearly irrelevant tothe decision.

More formally, we have U(x) > U(y) if and only if∑

i[Ax/Ay Vi .∑

i[Ay/Ax Vi , making evaluations ofunique attributes both necessary and sufficient fordetermining the correct response in two-alternativeforced choice. Knowing the value of Vi if i is associatedwith both the alternatives does not in any way helpthe decision maker determine U(x) > U(y) or U(y) > U(x). If an attribute i is common, Vi could take on anyvalue and not influence which of the two alternativesis more desirable.

The above analysis uses insights from decisiontheory, which have guided the study of multi-attributechoice for many decades (Keeney & Raiffa, 1993).However we would obtain a similar characterizationof efficient attention if we were to study theproblem using Bayesian or information theoreticmethods, which are typically used to examine infor-mation acquisition for experimental purposes (seeChaloner & Verdinelli, 1995; Kiefer, 1959 for work on

optimal experimental design). These methods oftencharacterize the usefulness of a piece of information(in this case, knowing the value of Vi for a particulari) in terms of its ability to discriminate between thehypotheses in consideration [U(x) > U(y) or U(y) > U(x)]. According to these approaches, decision makersshould attend to attributes only if knowing theirvalues changes the posterior probabilities of thehypotheses or the relative likelihoods of the hypoth-eses. In the simple case studied here, theseapproaches would recommend that decision makersavoid sampling attributes associated with both avail-able alternatives, as knowing the values of thesecommon attributes would not change the decisionmaker’s beliefs about which of the two alternativesis more desirable.

It is important to note that the above insights donot hold when the values of the attributes interactwith each other—that is, when total value is not addi-tive in attributes. For this reason we cannot claim thatattending to common attributes is always inefficient.Nonetheless, the simple additive setting outlinedhere is the standard way of modelling multi-attributechoice and has been the focus of much enquiry indecision-making research (see Keeney & Raiffa,1993). It is thus not surprising that a number ofapproaches have proposed, either explicitly orimplicitly, that decision makers avoid attending tocommon attributes when making their decisions. Forexample, one of the best known lay decision-makingstrategies, Benjamin Franklin’s rule, involves cancellingout and ignoring common attributes in pairwisechoice (see Gigerenzer & Goldstein, 1999). Likewise,in the field of multi-criteria decision analysis, somestrategies involve the use of attribute differences orratios in the calculation of relative desirability, withattributes that are shared across alternatives playinglittle or no role in the decision (Triantaphyllou, 2013).From a behavioural perspective, some recent theoriesof economic choice have proposed that decisionmakers attend to attributes proportionally to the dis-persion of the alternatives on the attributes. Thesestrategies imply that common attributes, on whichalternatives have zero dispersion, receive the leastattention (Bordalo et al., 2012, 2013; Kőszegi &Szeidl, 2013). Likewise, psychological models such asthe cancellation and focus heuristic suggest thatdecision makers cancel out and ignore common attri-butes in sequential choice (Houston et al., 1989, 1991).This can also be seen as being a property of the well-known additive difference model, in which attributes

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on which alternative differences fall below a certainthreshold are ignored, though it is important to notethat this model does not make explicit predictionsregarding attention (Tversky, 1969; see also Leland,1998; Rubinstein, 1988, for closely related models).Most of the above theories also predict that theamount of attention to common attributes shouldbe equivalent to the amount of attention to absentattributes (as choice alternatives have equal amountsof both of these types of attributes).

Related claims have been made in multi-cue judg-ment research. Here scholars have suggested thatthe usefulness of a cue for a particular judgmentdepends on the ability of that cue to discriminatebetween alternatives. Decision makers who usecues that are present in most alternatives will typi-cally be unable to distinguish two given alternativesfrom each other (Gigerenzer & Goldstein, 1999;Newell, Rakow, Weston, & Shanks, 2004; Rakow,Newell, Fayers, & Hersby, 2005). Although the focusof this work is on cue attention as a function of thestatistical structure of the general decision makingenvironment, rather than the specific choice setoffered to the decision maker in a single trial (as inthis paper), this work nonetheless supports theidea that attention towards common attributes isdetrimental to the decision.

In this paper, we test whether decision makers doin fact ignore common attributes and focus only onunique attributes. In all of our experiments, wepresent decision makers with pairs of choice alterna-tives described by lists of attributes and ask decisionmakers to make choices between the two alternatives.These lists are structured so that attributes are associ-ated with only one of the alternatives (and are thusunique) or both of the alternatives (and are thuscommon and overlapping). We also include attributesthat are absent from both of the alternatives as a base-line measure for attribute attention. In four of ourexperiments, we measure attribute attention indirectlyby the ability of decision makers to recall the attributespresented in these lists, after the lists have been dis-played to them. In the remaining two experimentswe measure attribute attention by using mouseclicks and viewing times, and overall decision times,respectively. Finally, although the first five of ourexperiments involve forced choices, in our sixth exper-iment we also include a free choice condition.Common attributes in free choices are always diag-nostic, and an examination of attribute attention infree choice can test whether decision makers are

able to successfully modify their attentional strategiesbased on the type of choice task that they are offered.

EXPERIMENT 1

In Experiment 1 we offered participants choicesbetween two alternatives, defined on a set of attri-butes. After decision makers had seen the alternativesand the attributes, we tested whether they werebetter at recalling the attributes that were common,unique, or absent in their choice set. We used recallas a proxy for attribute attention, as attributes thatare successfully recalled are ones that decisionmakers spent more time attending to and deliberatingover. If attribute attention is indiscriminate, then therecall of an attribute should not depend on whetherit is common, unique, or absent. If, on the otherhand, attention is selective then we should expect sys-tematic differences in the ability of participants torecall different attributes, based on their associationwith the available alternatives.

Method

ParticipantsOne hundred participants were recruited throughAmazon Mechanical Turk (59% male, Mage = 30.55years, SD = 8.57) and performed the experimentonline. All participants were English speakers livingin the United States.

Materials and procedureAfter giving informed consent, participants were pre-sented with a single forced choice between twoalternatives defined on binary attributes. Particularly,they were asked to imagine that they had to hire anemployee for their company and that they had achoice between two applicants. The applicants weredefined by 10 employment-related attributes, suchas “intelligent”, “motivated”, and so on. The choicealternatives offered to the decision makers had oneunique attribute each, one common attribute, andseven absent attributes.

The alternatives were presented in a table format,with the first column displaying the attributes andthe second column indicating which of the attributesare associated with the alternative. If an attribute wasassociated with the alternative then there was an “X”in the table cell corresponding to that alternative’sattribute. If not, then this cell was left empty. Partici-pants were told that this “X” indicates that the

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candidate possesses that attribute whereas theabsence of an “X” next to an attribute indicates thatthe candidate does not process that attribute. Theorder that the attributes and alternatives were pre-sented in was randomized. Additionally, the attributesthat were unique, common, or absent from the choiceset were perfectly counterbalanced across partici-pants, so that each attribute was associated with thefirst applicant, the second applicant, and both appli-cants an equal number of times. Note that thisdisplay format controls for display frequency: All attri-butes are listed an equal number of times, andcommon attributes are not mentioned more timesthan unique or absent attributes. Biases in attributeattention therefore cannot be attributed to differencesin display frequency across different choice sets.Figure 1 shows an example of a choice display offeredto participants.

After being shown the applicants and their com-ponent attributes, as in Figure 1, participants weretaken to a new screen where they were asked torecall and list as many attributes presented in the pre-vious screen as they could remember. They were expli-citly told to list both the attributes associated with theapplicants and the attributes not associated with theapplicants (though they were not required to listthese two sets of attributes in any particular order).After the attribute recall task was complete, partici-pants proceeded to a final screen where they madetheir choices. Each participant answered only onequestion, and the entire experiment, including intro-duction and debriefing, took approximately fiveminutes.

Results

We found that participants were much more likely torecall the attributes that were associated with theavailable applicants (that is, unique and common attri-butes) than the attributes that were not associatedwith the available applicants (that is, absent attri-butes). Interestingly, Participant 85 explicitly men-tioned this at the end of the study, as a way tojustify his inability to recall all of the attributes. Hesaid that he “only paid attention to the qualities theapplicants had, not the ones they didn’t”. Overall, par-ticipants recalled an average of 91% of the uniqueattributes, 84% of the common attributes, and 15%of the absent attributes. The recall probabilities ofthe 10 attributes when they are unique, absent, andcommon are presented in Table 1.

We can compare the recall of attributes when theyare common, unique, or absent with a mixed-effectslogistic regression that uses each participant’ssuccess or failure to recall each attribute at a separatedata point. There are 10 attributes in each choice, anda total of 100 participants, generating 1000 obser-vations. For each of these observations, we use therecall of the attribute as a dependent variable (recall= 1 if the attribute was listed in the recall task by theparticipant; recall = 0 otherwise). We also usedummies for each of the attributes as independentvariables, allowing us to have fixed effects on an attri-bute level. We specify two more independent vari-ables, unique and absent (unique = 1 if the attributeis unique, and unique = 0 otherwise; absent = 1 if attri-bute is absent, and absent = 0 otherwise), which indi-cate whether the attribute in consideration wasunique or absent in the choice set offered to the par-ticipant (common attributes serve as a basis for com-parison as the mean recall for common attributes isbetween that for unique attributes and absent attri-butes, and they correspond to data points whereboth unique = 0 and absent = 0). Finally we allow forrandom effects on a participant level, generating 100different groupings on our dataset. This regressioncontrols for attribute-level influences on recallthrough the fixed-effects terms, and participant-levelinfluences on recall through the random-effectsterms. Examining whether the variables unique andabsent have a significant effect on recall would tellus whether recall is significantly higher for uniqueattributes than for common attributes and whetherrecall is significantly lower for absent attributes thanfor common attributes, controlling for attribute-specific and participant-specific influences.

Using this approach, we do find that decisionmakers are significantly less likely to recall an attributeif it is absent from the choice set than if it is commonin the choice set (β =−4.41, z =−11.38, p < .001). Wedo not, however, find that decision makers are signifi-cantly more likely to recall an attribute if it is uniquein the choice set than if it is common in the choice set(β = 0.68, z = 1.61, p = .11).

It may be argued that this experiment fails todetect a difference between the recall of unique andcommon attributes due to power. This point can beaddressed by comparing the Bayesian information cri-terion (BIC) score of the above logistic regression withthe score of a simpler regression model with onlyabsent as the main independent variable (i.e., aregression that ignores differences between

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common and unique attributes). The BIC score forthese models would be calculated using the followingformula:

BIC = −2L+ k · ln (n)

Here L is the log-likelihood of the model in con-sideration, k is the number of its parameters, and nis the total number of data points. The BIC score is auseful way to compare model fits controlling formodel flexibility, and models with lower BIC scoresare those that achieve the best fits with the fewestparameters. Using this approach, we find that theBIC score of the above logistic regression, which hasboth unique and absent as independent variables, is852.92. In contrast the BIC score for a regression

with only absent as an independent variable is848.58. These scores show that the best performingmodel is one that only uses the absent variable topredict recall and ignores differences between attri-butes that are unique and attributes that arecommon. This further indicates that decision makersare not more likely to recall an attribute if it isunique in the choice set than if it is common in thechoice set.

Discussion

This experiment provided strong evidence thatdecision makers attend to attributes selectivelywhen making their decisions. Particularly, participantswere much better at recalling attributes if they were

Figure 1. Displays used in Experiments 1 and 5 (top panel), in Experiments 3 and 6 (middle panel), and in Experiment 2 (bottom panel).

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associated with the available alternatives (i.e.,common and unique attributes) than if they werenot associated with any of the available alternatives(i.e., absent attributes). Changing the attributes associ-ated with different alternatives changed which of theattributes were most likely to be recalled.

This experiment also provided a test of differences inattribute attention between common and unique attri-butes. It found that while unique attributes wereslightly more likely to be recalled than common attri-butes, the difference in recall probability was not stat-istically significant. For this reason, the bestperforming statistical model in terms of the BIC was amodel that lumped common and unique attributesinto a single category. Additionally, the difference inthe recall probabilities of common versus unique attri-butes was much smaller than the difference in therecall probabilities of common versus absent andunique versus absent attributes. This implies thateven though unique attributes may be slightly moresalient, decision makers do not ultimately ignorecommon attributes in forced binary choice. This indi-cates that their attention may not be perfectly efficientand also provides evidence against a number of exist-ing theories of decisionmaking (e.g., Bordalo, Gennaioli,& Shleifer, 2013; Houston et al., 1989; Kőszegi & Szeidl,2013), which predict that attribute attention is aproduct of the dispersion of the available alternativeson the attributes. According to these theories,common attributes should be attended to as frequentlyas absent attributes, and both should be attended tomuch less frequently than unique attributes.

EXPERIMENTS 2 AND 3

The goal of Experiments 2 and 3 is to test the robust-ness of the results in Experiment 1. Experiment 2 uti-lizes a different choice domain—choices between

vacation resorts rather than potential employees—and additionally modifies the presentation of thechoice stimuli, so as to include an explicit symbol toindicate attribute absence (instead of leaving the cor-responding table cell blank). Experiment 3 considerssettings with a higher number of unique andcommon attributes and correspondingly smallernumber of absent attributes. The use of a separatechoice domain and different types of presentationformats is necessary to test whether the results ofExperiment 1 are a product of a general decision-making strategy, rather than a strategy applicableonly to a small class of choice alternatives presentedin a highly specific manner. Likewise the use of set-tings with a greater number of common and uniqueattributes and fewer absent attributes is necessary totest whether the results of Experiment 1 hold whendecision makers are offered richer choice alternatives,which are associated with multiple attributes.

Method

ParticipantsOne hundred participants were recruited throughAmazon Mechanical Turk for Experiment 2 (60%male, Mage = 33.45 years, SD = 10.88) and for Exper-iment 3 (61% male, Mage = 32.48 years, SD = 9.88)each. All participants were English speakers living inthe United States.

Materials and procedureExperiments 2 and 3 were identical to Experiment 1 interms of their procedure and implementation. Theonly differences between these studies and Exper-iment 1 involved the choice options given to partici-pants (in both studies) as well as the presentation ofthe choice options (in Experiment 2).

In Experiment 2, participants were asked to makea choice between hypothetical vacation resorts,defined on attributes such as “casinos”, “famousspa”, “beaches”, and so on. This is in contrast toExperiment 1, which involved choices between jobapplicants. A second difference involved the typesof tables used to display the options. These tablesdid use an “X” to indicate that an attribute wasassociated with an alternative. However, instead ofleaving table cells blank if the attribute was notassociated with an alternative, Experiment 2 used along dash sign, “—”, as shown in Figure 1. Again,as in Experiment 1, participants were told that an“X” indicates that a resort has that attribute

Table 1. The average recall probabilities of the different attributeswhen they are unique, common and absent, in Experiment 1

Attribute Unique Common Absent

Hard worker 1.00 1.00 .29Experience .90 .80 .16Recommendations .84 .70 .03Intelligent 1.00 .58 .20Creative .91 .71 .15Motivated .95 .89 .08Friendly .95 1.00 .13Go-getter .80 1.00 .13Organized 1.00 1.00 .18Good education .95 .91 .16Average .91 .84 .15

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whereas a “—” indicates that a resort does not havethat attribute. As in Experiment 1, there were a totalof 10 attributes, with one attribute being unique toeach alternative, one attribute being common tothe two alternatives, and the remaining seven attri-butes being absent from the alternatives.

Experiment 3 utilized the same attributes and pres-entation format as those in Experiment 1, but variedthe total number of unique, common, and absent attri-butes in the two choice options. Unlike Experiment 1,Experiment 3 presented choice alternatives with twounique attributes each, two common attributes, andfour absent attributes. This is shown in Figure 1.Again, the attributes that were unique, common, orabsent in each choice set were counterbalanced.Finally, as above, each participant answered onlyone question, and the two experiments, includingintroduction and debriefing, took approximately fiveminutes.

Results

The results of Experiment 2 were nearly identical tothose of Experiment 1, except for the fact that themild difference between the recall probabilities ofunique and common attributes, observed in Exper-iment 1, reversed. Particularly, participants recalledan average of 80% of the unique attributes, comparedto an average of 85% of the common attributes.Additionally, as in Experiment 1, absent attributeswere much less likely to be recalled than commonand unique attributes, with participants recalling anaverage of 17% of the absent attributes. The recallprobabilities of the 10 attributes when they areunique, absent, and common are presented in Table 2.

As in Experiment 1, we can use a mixed-effectslogistic regression to examine the differences inrecall probabilities, controlling for attribute-level andparticipant-level heterogeneity. Using this approach,we do find that decision makers are significantly lesslikely to recall an attribute if it is absent from thechoice set than if it is unique in the choice set (β =−3.42, z =−13.30, p < .001). We do not, however, findthat decision makers are significantly more likely torecall an attribute if it is common in the choice setthan if it is unique in the choice set (β = 0.36, z =1.00, p = .32). As above, a BIC score analysis indicatesthat the BIC score for this regression (BIC = 946.08) ishigher than the BIC score for a similar regressionwith only absent as the independent variable (BIC =940.22), further demonstrating that there are no

statistically relevant differences between unique andcommon attributes in terms of their effects on recall.

Experiment 3 also finds similar results. Particularly,participants recalled an average of 73% of theunique attributes, 69% of the common attributes,and 19% of the absent attributes.

With the above-mentioned mixed-effects logisticregression we find that decision makers are signifi-cantly less likely to recall an attribute if it is absentfrom the choice set than if it is common in thechoice set (β =−2.54, z =−10.97, p < .001). We donot, however, find that decision makers are signifi-cantly more likely to recall an attribute if it is uniquein the choice set than if it is common in the choiceset (β = 0.17, z = 0.83, p = .41). This is further reflectedin a higher BIC score for this regression (BIC =915.81) than for a similar regression with only absentas the independent variable (BIC = 908.21). The recallprobabilities of the 10 attributes when they areunique, absent, and common are presented in Table 3.

Discussion

Experiments 2 and 3 replicated the result of Exper-iment 1 using different types of choice alternativesand presentation formats, as well as choice alterna-tives with a higher number of unique and commonattributes and fewer number of absent attributes. Par-ticularly, these studies found that decision makerswere much more likely to recall unique andcommon attributes than absent attributes, indicatingthat attribute attention is selective. Additionally,there were no statically relevant differences betweenthe recall probabilities of unique and common attri-butes. This indicates that attribute attention may notbe perfectly efficient. These results also contradictthe predictions of some existing theories of multi-attri-bute choice (Bordalo et al., 2013; Houston et al., 1989;Kőszegi & Szeidl, 2013), which suggest that decisionmakers ignore common attributes relative to uniqueattributes.

Before proceeding, let us compare the recall prob-abilities in Experiment 3 with those in Experiment 1,to examine the effect of increasing the number ofpresent or absent attributes, and the changes tostimuli presentation this generates, on participantbehaviour. Experiment 3 and Experiment 1 are identicalexcept for the fact that Experiment 3 has twice as manypresent attributes (and fewer absent attributes). For thisreason its display involves more “X”s, and these “X”s andtheir corresponding present attributes stand out less

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(see Figure 1). It could be that this standing out (figure/ground contrast) plays a role in directing attention andgenerating the observed behavioural patterns. We dofind that the recall probabilities of absent attributes inExperiment 3 are higher than those in Experiment 1(19% vs. 15%), but that these differences pale in contrastto the recall probabilities of present attributes, whichfrequently exceed 70%. This suggests that the totalnumber of present or absent attributes can influencerecall probability, but that their effect is minor andcannot account for all of the differences observed inthis paper. It could be useful, in future work, to considera variant of Experiment 3 with no absent attributeswhatsoever, to ensure that these patterns persist andthat the findings of Experiments 1 and 3 are robust.

EXPERIMENT 4

While the results of Experiments 1–3 are useful forcharacterizing the nature of attribute attention in pre-ferential choice, they measure attribute attentionindirectly. Particularity, the recall of attributes afterthe decision alternatives have been displayed isused as a proxy for attribute attention during thedisplay of the decision alternatives. In order to morerigorously examine how decision makers allocateattention, it would be useful to observe attentionduring the decision process itself. This is the goal ofExperiment 4, which uses a Mouselab interface (Will-emsen & Johnson, 2011) that allows us to observeinformation acquisition during deliberation.

Method

ParticipantsOne hundred participants were recruited throughAmazon Mechanical Turk (61% male, Mage = 31.81years, SD = 9.89) and performed the experiment

online. All participants were English speakers livingin the United States.

Materials and procedureThe specific choice alternatives used were identical tothose in Experiment 1. Unlike Experiment 1, however,the names of the attributes (e.g., “good education”,“intelligent”, etc.) were hidden behind grey boxes.Decision makers needed to click on the grey boxes inorder to find out which attributes the boxes represented.Clicking on a grey box would open it up, uncovering itscorresponding attribute. Clicking on the next grey boxwould close the first box and open up the second.

Information about whether an attribute behind agrey box was associated with the alternatives wasfreely available. Thus decision makers could choosewhether they wanted to uncover grey boxes corre-sponding to unique attributes, common attributes,or absent attributes. Examining the number of timesthat decision makers clicked on the grey boxes inorder to uncover the different attributes, and thetotal amount of time that decision makers spentlooking at the attributes in the grey boxes, can quan-tify attribute attention in the choice task.

An example of the display used in Experiment 4 isshown in Figure 2. The left panel shows the display toparticipants when none of the boxes have beenclicked. The right panel shows the display to participantswhen one of the boxes is clicked. It is only by clickingthat participants are able to determine the specific attri-bute in a box. As in Experiment 1, attributes associatedwith different alternatives were indicated by an “X” intheir corresponding cell, and participants were toldthat the presence of this “X” indicated that the candidatepossessed the attribute and that the absence of this “X”indicated that the candidate did not possess the attri-bute. Additionally, choice was made on a separatescreen after examination of all of the attributes. Finally,the order that the attributes and alternatives were pre-sented in was randomized, and the attributes thatwere common, unique, and absent were counterba-lanced. Participants were given detailed instructions(including illustrations and examples) regarding thispresentation format; however, there were no practiceproblems. Each participant answered only one question.

Results

We found that participants were much more likely toclick the attributes that were associated with the avail-able applicants (that is, unique and common

Table 2. The average recall probabilities of the different attributeswhen they are unique, common and absent, in Experiment 2

Attribute Unique Common Absent

Adventure sports .94 .82 .19Beautiful scenery .82 .86 .21Beaches .50 .63 .06Activities for family .89 .90 .23Exciting nightlife .70 .85 .20Good weather .94 1.00 .14Casinos .82 .92 .20Great local cuisine .77 .88 .15Famous Spa .74 .90 .15Wildlife excursions .85 .78 .19Average .80 .85 .17

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attributes) compared to the attributes that were notassociated with the available applicants (that is,absent attributes). On average, participants clickedunique attributes 1.71 times, common attributes 1.65times, and absent attributes 0.49 times. We obtainedidentical results for the total viewing time of each attri-bute. We found that participants spent more timelooking at unique and common attributes thanabsent attributes. On average, participants spent anaverage of 3.80 s viewing each unique attribute, anaverage of 3.30 s viewing each common attribute,and an average of 0.69 s viewing each absent attri-bute. The average clicking frequencies and viewingtimes of the 10 attributes when they are unique,absent, and common are presented in Table 4.

A rigorous way to examine attention to attributeswhen they are common, unique, or absent involvesa mixed-effects regression that uses each participant’sclicking data or viewing time data for each attribute ata separate data point. For this, we can again use theapproach outlined in Experiment 1, which controlsfor attribute-level influences on recall through fixed-effects terms, and participant-level influences on

recall through random effects terms, and specifiesunique and absent as independent variables that indi-cate whether an attribute is unique or absent for a par-ticipant in a particular choice set. With this approachwe do find that decision makers are significantly lesslikely to click on an attribute if it is absent from thechoice set than if it is common in the choice set (β=−1.16, z =−16.94, p < .001). Likewise we find thatdecision makers are significantly less likely to spendtime viewing an attribute if it is absent from thechoice set than if it is common in the choice set (β=−2.64, z =−12.59, p < .001). We do not, however, findthat decision makers are significantly more likely toclick on an attribute if it is unique in the choice setthan if it is common in the choice set (β = 0.06, z =0.74, p = .46). Likewise we do not find that decisionmakers are significantly more likely to spend timeviewing on an attribute if it is unique in the choiceset than if it is common in the choice set (β = 0.46, z= 1.94, p = .06), though note that this difference isonly marginally above the threshold used for statisti-cal significance.

As in the previous studies, we can compare the BICscores of the above regressions with similar scores fora simpler regression model that only permits absent asthe dependent variable. With regards to clicks, we findthat the above regression has a higher BIC score (BIC= 2217.60) than a simpler regression model (BIC =2211.24), indicating that a simpler model thatignores differences between unique and commonattributes performs better than a model that permitsthese differences. We find similar results for viewingtimes, with lower BIC scores for the simpler regression(18,232.92 vs. 18,235.95).

It is also possible to examine the order in whichparticipants click on the various attributes. Although

Table 3. The average recall probabilities of the different attributeswhen they are unique, common and absent, in Experiment 3

Attribute Unique Common Absent

Hard worker .84 .82 .33Experience .73 .58 .14Recommendations .61 .50 .15Intelligent .73 .65 .18Creative .74 .87 .11Motivated .63 .65 .15Friendly .77 .78 .24Go-getter .73 .91 .17Organized .67 .57 .25Good education .81 .60 .19Average .73 .69 .19

Table 4. The average mouse clicks and viewing times for the different attributes when they are unique, common and absent, in Experiment 4

Attribute

Mouse clicksViewing times

(ms)

Unique Common Absent Unique Common Absent

Hard worker 1.95 1.64 0.53 4620.33 3121.00 553.04Experience 1.60 1.60 0.51 3411.90 2545.10 611.90Recommendations 1.74 1.78 0.46 3571.95 3059.33 795.94Intelligent 1.95 1.00 0.47 3166.95 2498.56 764.28Creative 1.26 2.40 0.56 4273.37 2974.70 748.03Motivated 2.05 1.40 0.41 4330.30 3008.70 520.67Friendly 1.52 1.50 0.54 4714.10 2671.60 749.57Go-getter 1.47 1.64 0.47 2640.84 6312.73 541.77Organized 1.77 1.89 0.54 3016.86 3166.67 851.46Good education 1.75 1.64 0.39 4212.35 3623.00 743.93Average 1.71 1.65 0.49 3795.89 3298.14 688.06

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existing theories about attention to common attri-butes do not make strong predictions regardingwhich attributes are attended to first, attentionalorder has been shown to be a theoretically relevantconstruct, predicting, for example, findings such asthe endowment effect and present bias (Johnson,Häubl, & Keinan, 2007; Weber et al., 2007). For thisanalysis, we formalize attentional order for unique,common, and absent attributes, using the averagerank of these attributes for each participant. Forexample, for a participant that clicks on the twounique attributes at least once, we can calculate theaverage ranks of each of this participant’s unique attri-bute clicks in the list of all clicks, and then averagethese ranks to get a measure of the order in whichunique attributes are clicked by this participant. Thiscan be repeated for common and absent attributes,and a comparison can be made between averageclick orders to determine which attributes this

participant is most likely to click on early versus latein the decision. This is similar to the Mouselab analysisin Johnson et al. (2007), and, as with this analysis, andunlike the analyses performed thus far in this paper, itrequires participant-level rather than attribute-levelcomparisons.

Now out of the 100 subjects in this study, only 85subjects clicked on both unique attributes, and theaverage rank of these clicks was 4.14 (SD = 2.82). Like-wise only 87 subjects clicked on the common attri-bute, and the average rank of these clicks was 3.67(SD = 2.77). Finally, only 28 subjects clicked on allabsent attributes, with an average click rank of 5.99(SD = 1.72). These averages indicate that commonattributes are likely to be clicked on earlier in thedecision, followed by unique attributes, and then byabsent attributes. Using a paired t-test to compareclick order for the 85 subjects who clicked on bothall of the unique attributes and all of the common

Figure 2. Example of display used in Experiment 4. The left panel shows the display when none of the boxes have been clicked. The right panelshows the display when one of the boxes is clicked.

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attributes, we find that the click order for these twotypes of attributes is not significantly different (t =1.91, p = .20). Repeating this analysis for the 28 sub-jects that clicked on all absent attributes, all uniqueattributes, and all common attributes, we again findno difference in click order (p > .10 for all compari-sons). This could, however, be due to the relativelysmall sample size for this analysis: If more than 28 par-ticipants clicked on the absent attributes at least once,we may have been able to observe statistically rel-evant differences in click order between absent andpresent attributes.

Discussion

Experiment 4 examined attribute attention using theMouselab interface. In this study, information aboutwhether or not an attribute was associated with analternative was available to the participants.However, participants had to click on the grey boxesthat covered the various attributes to determinewhat the attributes actually were. This study foundthat decision makers were significantly more likely toclick and view the attributes that were associatedwith the available alternatives (that is, common orunique attributes) than the attributes that were notassociated with the available alternatives (that is,absent attributes). There were no statistically relevantdifferences in clicking frequencies and viewing timesbetween common and unique attributes. Thissuggests that decision makers are unable to ignorecommon attributes, which are often non-diagnosticfor the purposes of the choice.

It is useful to note that the viewing times measuredin this study may be overestimates, as they corre-spond to the entirety of the time between twoclicks. Additionally, they may be noisy and imperfectmeasures of attribute attention: Decision makersneed not be actively viewing and processing the attri-bute when its box is uncovered. Nonetheless theseviewing times serve as a suitable proxy for relativeattribute attention for current purposes, as it is unli-kely that the extent of this overestimate and noisevaries across different types of attributes.

Additionally note that many process-tracingstudies using tools like Mouselab examine multiplephases in decision makers’ search for information.For example, sometimes decision makers first openall boxes before focusing in on the attributes or cuesthat are relevant for the decision. The average clickcounts for the attributes in this study indicate that,

on average, there is only one major phase of infor-mation acquisition: The average click count forabsent attributes is very small, indicating that thetypical decision maker does not even open this typeof attribute, and subsequently does not display ageneral orientation phase.

Overall, these results reproduce the findings ofExperiments 1–3 using a novel measure of attentionand provide further evidence that attention, whilebeing selective, is nonetheless not perfectly efficient.Additionally, these results contradict the predictionsof several theories of multi-attribute choice (Bordaloet al., 2013; Houston et al., 1989; Kőszegi & Szeidl,2013), which propose that common and absent attri-butes are both ignored during the choice process.

EXPERIMENT 5

Experiments 1–4 utilized attribute recall and mousetracking. These measures of attribute attentionprovide strong evidence that decision makers areable to ignore absent attributes but not common attri-butes when making their decisions: Common andunique attributes are recalled with almost equal prob-ability and are additionally clicked on and viewed withalmost equal frequency. Absent attributes, in contrast,are seldom recalled, clicked on, or viewed.

The recall and mouse-tracking measures used inExperiments 1–4 suffer from some important limit-ations. While they may serve as reasonable proxiesof attribute attention, an increased recall or viewingtime for an attribute does not indicate that thedecision maker is necessarily spending more timethinking about the attribute. Experiment 5 attemptsto address this by using a third method. It presentschoices similar to those used in Experiments 1, 3,and 4, but varies the number of common versusabsent attributes in the choice. Additionally, itmeasures total decision time instead of attributerecall or click-based information acquisition. If, inaddition to ignoring absent attributes, decisionmakers are able to ignore common attributes, thenincreasing the number of common attributes in a par-ticular choice should not significantly alter decisiontime. In contrast, if decision makers attend to andprocess common attributes, total decision timeshould increase with the number of common attri-butes in a choice task. Along with providing an newtype of test of decision makers’ attention, this designcan also be used to verify whether decision makers’observed attentional strategies are in fact detrimental

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for the choice at hand. Short decision times are acharacteristic of efficient decision making, anddecisions that sample more information than theyneed to, and subsequently take longer than theyneed to, are commonly seen as being inefficient.

Method

ParticipantsFifty participants (64% male, Mage = 21.32 years, SD =2.35) performed the experiment in a behavioural lab-oratory at a British university. Participants wererecruited from the university’s experimental partici-pant pool. Our use of a laboratory environment inthis study (compared to performing the experimentonline as in other studies in this paper) was necessi-tated by the fact that we wished to study decisiontimes, which require additional experimental control.

Materials and procedureOnce again, the decision task asked participants tochoose between two job applicants defined on 10different attributes. The attributes used were identicalto those of Experiments 1, 3, and 4. However, unlikethese studies, this experiment asked each participantto make 30 different binary forced choices. Each ofthese binary choices offered participants two appli-cants, with one unique attribute each. These 30choices were composed of 10 sets of three choices.The choices within each set were similar in that thetwo options they offered had the same compositionof unique attributes. The only difference betweenthese choices was the number of common versusabsent attributes. The first choice in each set did nothave any common attributes (with the remainingeight attributes being absent), the second choicehad one common attribute (with the remainingseven attributes being absent), and the third choicehad two common attributes (with the remaining sixattributes being absent). Thus, for example, the firstset used in this experiment offered participantsthree choices between an applicant with “good rec-ommendations” and an applicant who is a “go-getter”. In the first of the three choices in this set,the applicants had none of the other eight attributes.Thus the choice was between an applicant who hadonly good recommendations and an applicant whowas only a go-getter. In the second of the threechoices, both applicants were also creative. Thus thechoice was between an applicant who had good rec-ommendations and was creative, and an applicant

who was a go-getter and was creative. In the third ofthe three choices, the applicants also had had agood education. Thus the choice was between anapplicant who had good recommendations, was crea-tive, and had had a good education, and an applicantwho was a go-getter, was creative, and had had agood education. Again there were 10 different setsof these three types of choices. The attributes thatwere unique and common across the choices andacross the sets were counterbalanced, and the orderin which the choices, choice alternatives, and attri-butes were presented was randomized.

Note that this experiment did not capture recall ormouse-tracking data. Thus in each of the 30 choices,participants were given the two choice options onthe screen (presented as in Figure 1) and were thenasked to make their choice on the same screen. Thisexperiment did, however, collect decision time datafor each choice.

Results

The primary dependent variable in this experiment isdecision time. If decision makers ignore bothcommon and absent attributes, then varying thenumber of common versus absent attributes withineach set should not affect the time that decisionmakers spend deliberating during the choice. Thusdecision times within each set of three choicesshould be constant.

For choices without common attributes, theaverage decision time was 6.05 s (SD = 4.42). Thistime increased to 9.33 s (SD = 4.71) in choices with asingle common attribute, and to 11.24 s (SD = 4.86)in choices with two common attributes. Overall, thedifference in decision times in the setting withoutcommon attributes and the setting with a singlecommon attribute is statistically significant, whenassessed using a linear regression with participant-level random effects and set-level fixed effects (β =3.41, z = 4.52, p < .001). The difference in decisiontimes in the setting with a single common attributesand the setting with two common attributes is simi-larly statistically significant (β = 1.91, z = 2.59, p < .01).Figure 3 illustrates these differences. Both theseregressions also controlled for the trial number ofthe problem at hand (trial number = 1 for theproblem presented first, and trial number = 30 forthe problem presented last), to make sure that theseresults were not due to the fact that earlier decisionstake longer on average than later decisions.

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These differences can also be examined with acombined regression, whose main independent vari-able is the total number of common attributes in thechoice at hand. As above, this regression would useparticipant-level random effects and set-level fixedeffects. After running this regression we find that thetotal number of common attributes has a significantpositive effect on decision time (β = 2.65, z = 6.92, p< .001), indicating that choice sets with multiplecommon attributes take longer than choice sets withfew common attributes. These results do not changeif we take a log-transform of the decision time data,or if we exclude decision time outliers.

Discussion

Experiment 5 attempted to test whether decisionmakers are able to ignore common attributes whiledeliberating. For this purpose it gave each participantmultiple binary forced choices, with each choicevarying the number of common versus absent attri-butes between the two alternatives. If, like absentattributes, common attributes are able to beignored, then making an absent attribute a commonattribute should not affect decision outcomes, suchas decision time. On the other hand, if decisionmakers are more likely to attend to common attri-butes, then increasing the number of common attri-butes in a decision should make choices takerelatively longer. This study found that the numberof common attributes in the decision did have a sig-nificant positive effect on decision time, suggestingthat common attributes are not ignored during delib-eration. This indicates that attribute attention may notbe perfectly efficient. It also provides evidence againsta number of existing theories of decision making,

which predict that attribute attention is a product ofthe dispersion of the available alternatives on the attri-butes. According to these theories, decision makerspay as much attention to common attributes as toabsent attributes, implying that making absent attri-butes common should not affect decision outcomessuch as decision time.

In addition to providing a test of attribute atten-tion, this study also tests whether decision makers’observed attentional strategies can be detrimental tothe decision. Both common and absent attributesare non-diagnostic, and thus changing whether anattribute is common or absent should not slowdown the decision. By finding that decisions do takelonger with more common attributes, Experiment 5illustrates the pernicious effect of common attributeson important decision outcomes like decision time.Ultimately, the same decision could have been madequicker, if decision makers were able to ignorecommon attributes in the same way that theyignored absent attributes.

EXPERIMENT 6

The studies thus far have attempted to test for differ-ences in attribute attention across unique, common,and absent attributes. They have involved forcedchoices, in which common attributes are non-diagnos-tic, and have found that unique and common attri-butes are attended to roughly equally, whereasabsent attributes are largely ignored.

In Experiment 6 we study both attention inforced choices and attention in free choices, usinga design similar to that of Experiments 1–3. In freechoices, decision makers have the option to notchoose either of the two alternatives, which requiresthat decision makers compute not only the relativedesirability of the choice alternatives, but also theabsolute desirability of the alternatives. It may,after all, be better to avoid choosing either of thetwo alternatives if they are both undesirable. As dis-cussed above, the overall value of a choice alterna-tive is often the sum of the values of all itscomponent attributes—that is, a sum of the valuesof attributes that are unique to the alternative, aswell as attributes that are shared with other alterna-tives. As a result of this, decision makers need tofocus on common attributes in order to make agood decision. Absent attributes are typically irrele-vant for evaluating the absolute desirability of analternative.

Figure 3. Average (ave.) decision time (in seconds) as a function of thenumber of common attributes in Experiment 5. Error bars indicate ±1standard error.

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Comparing attention in free choices with attentionin forced choices can provide some preliminaryinsights regarding why decision makers attended tocommon attributes in our experiments. Free choicesare fairly widespread (indeed, most everydaydecisions permit the possibility of choice deferral).Both unique and common attributes are diagnosticin these settings, implying that it is often efficient fordecision makers to pay attention to common attri-butes. It may be the case that decision makers fail tomodify their attentional strategies appropriatelywhen given forced choices instead of free choices. Ifthis explanation were correct, we would expect theallocation of attention to be similar across bothtypes of choices. Experiment 6 provides a direct testof this prediction.

Method

ParticipantsOne hundred participants (58% male, Mage = 31.11years, SD = 11.35) recruited from Amazon MechanicalTurk performed the experiment online. All participantswere English speakers living in the United States.

Materials and procedureThe choice alternatives and attributes used in thisexperiment were identical to the alternatives andattributes in Experiment 3, with participants given achoice between two job applicants, each definedon 10 attributes. As in Experiment 3, there weretwo unique attributes for each applicant, twocommon attributes, and four absent attributes.Additionally, half the participants were assigned tothe forced choice condition and had to choose oneof the two applicants. The other half of the partici-pants were assigned to the free choice conditionand had the option to choose one of the two appli-cants, or to not choose either of the two applicantsand instead continue the hypothetical job search.Prior to being presented with the choice alternatives,participants in the two conditions were told whetheror not they would have the opportunity to defer theirdecision. As in Experiments 1–3, the presentation ofthe choice alternatives was followed by a recalltask, in which participants had to list as many ofthe attributes as they could remember. After thistask they were taken to the choice screen in whichthey made a decision between the two applicants(in the forced choice condition) or a decisionbetween the two applicants and the option to

choose neither of the applicants (in the free choicecondition). Each participant answered only onequestion.

Results

We begin by examining overall choice and recall pat-terns across the two conditions. We find that the prob-ability of recalling an attribute in the forced choicecondition is 50%, whereas the probability of recallingan attribute in the free choice condition is 51%. Thisis not a significant difference (z = 0.56, p = .58), whenexamined using a mixed-effect logistic regression con-trolling for attribute-level influences using fixedeffects and participant-level influences using randomeffects. Overall choice is deferred 24% in the freechoice condition, implying that decision makersmade an active choice 76% of the time in thiscondition.

Let us now examine the relationship between recalland attribute uniqueness, commonality, and absencein the forced choice condition. We find that theresults of this condition are nearly identical to thoseof Experiment 3, except for the fact that the mildand non-significant difference between the recallprobabilities of unique and common attributes isagain reversed. Particularly, participants recalled anaverage of 68% of the unique attributes comparedto an average of 72% of the common attributes.Additionally, as in Experiment 3, absent attributeswere much less likely to be recalled than commonand unique attributes, with participants recalling anaverage of 16% of the absent attributes. The recallprobabilities of the 10 attributes in the forced choicecondition, when they are unique, absent, andcommon, are presented in Table 5.

As in earlier studies, we can use a mixed-effectslogistic regression to examine the differences inrecall probabilities more rigorously. Using thisapproach, we find that decision makers are signifi-cantly less likely to recall an attribute if it is absentfrom the choice set than if it is common in thechoice set (β=−2.63, z =−8.86, p < .001). We do not,however, find that decision makers are significantlymore likely to recall an attribute if it is common inthe choice set than if it is unique in the choice set(β = 0.34, z = 1.09, p = .27). This is also reflected in ahigher BIC score for this regression (BIC = 564.71)than for a simpler regression model that ignores thedifference between common and unique attributes(BIC = 559.81).

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We obtained a similar set of results in the freechoice condition. Particularly, participants recalled anaverage of 62% of the unique attributes, an averageof 74% of the common attributes, and an average of29% of the absent attributes. Our mixed-effects logis-tic regression finds that decision makers are signifi-cantly less likely to recall an attribute if it is absentfrom the choice set than if it is unique in the choiceset (β =−1.61, z =−6.58, p < .001), and additionallysignificantly more likely to recall an attribute if it iscommon in the choice set than if it is unique in thechoice set (β = 0.69, z = 2.36, p < .05). Unlike all theprior studies, this difference between unique andcommon attributes is reflected in a lower BIC scorefor this model (BIC = 676.70) than for a simplerregression model that ignores the differencebetween common and unique attributes (BIC =677.48), suggesting that common and unique attri-butes do have divergent effects on recall probabilities.The recall probabilities of the 10 attributes in the freechoice condition, when they are unique, absent, andcommon, are also presented in Table 5.

Thus far, our analysis has examined the two con-ditions separately and has found some evidence fora higher recall probability of common attributes com-pared to unique attributes in free choices than inforced choices. We can test this more rigorously bycombining the two conditions and applying theabove type of mixed-effects logistic regression withan interaction term. A positive significant interactionbetween the type of attribute (common vs. unique)and the condition (forced vs. free) would indicatethat being given free choices instead of forcedchoices increases the relative attention to commonattributes compared to unique attributes. Using thismethod, we find that there is no significant interactioneffect (β = 0.36, z = 0.83, p = .40), indicating that rela-tive recall probabilities of common and unique attri-butes are roughly identical across the two conditions.

Discussion

We find that the patterns in attribute recall probabil-ities observed earlier in this paper emerge in bothforced and free choices in Experiment 6. Particularly,decision makers pay roughly equal attention tocommon and unique attributes, and moreover paymore attention to these attributes than to absent attri-butes. These results replicate those of Experiment 3, asthe forced choice conditions in Experiment 6 andExperiment 3 are identical. Additionally, these results

suggest that decision makers may be using similarattentional strategies in both forced and freechoices. Common attributes are diagnostic in freechoices, and the fact that decision makers do notappear to significantly change how they allocatetheir attention across these two settings implies thatthe attention to common attributes observed in ourexperiments may be due to an error in selecting theright attentional strategy in forced choice.

GENERAL DISCUSSION

The experiments presented in this paper examineattention to decision attributes in two-alternativeforced choice tasks, with binary attributes. Exper-iments 1–3 and 6 measure attribute attentionindirectly by the ability of decision makers to recallthe relevant decision attributes after they have beendisplayed. Experiment 4 measures attribute attentionthrough mouse clicks and viewing times on a Mouse-lab interface. Experiment 5 measures attribute atten-tion indirectly, using overall decision times. These sixexperiments find that decision makers are as likelyto attend to common attributes as they are tounique attributes. Common attributes are often non-diagnostic; that is, they do not affect the relative desir-ability of the two alternatives. These experiments alsofind that attribute attention is selective. Particularly,decision makers are significantly more likely toattend unique or common attributes than absent attri-butes. Changing the attributes that are associatedwith the alternatives in the choice set can sub-sequently alter attribute attention.

These results contradict a number of existingbehavioural theories. Some of these theoriespropose that decision makers completely cancel outcommon attributes in multi-attribute choice(Houston et al., 1989, 1991). Others propose thatdecision makers’ attention depends on the dispersionof the alternatives on each attribute, with attributesthat are present in identical amounts in the twoalternatives being given the least amount of attention(Bordalo et al., 2012, 2013; Koszegi & Szeidl, 2013). Yetothers suggest that decision makers place less weighton attributes on which alternative differences are verysmall (Tversky, 1969; also Leland, 1998; Rubinstein,1988), which can in some settings be seen as ahypothesis regarding attribute attention. The factthat we observe nearly equivalent attention tocommon and unique attributes in our experimentssuggests that these theories provide an incomplete

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account of attribute attention in simple binary-attri-bute forced choice.

These limitations of existing theories suggest theneed to build new models of attribute attention,with increased descriptive power, which are able toexplain why decision makers display the types ofattentional patterns documented in this paper. Ulti-mately attribute attention is one of the most impor-tant components of the decision process, and it isnecessary to rigorously understand the ways inwhich attribute attention depends on the task athand, in order to fully characterize preferentialdecision making.

Cognitive constraints and the structure of theenvironment

The attentional strategy observed in this paper can beconsidered to be associative, in that it directs attentiontowards all attributes that are associated with thealternatives in the choice set and ignores all attributesthat are not associated with the alternatives in thechoice set (see Bhatia, 2013; Khader, Pachur, & Jost,2013, for a discussion of this type of strategy). Whilethe associative attentional strategy is not completelyefficient when attributes are independent, it mayvery well be a reasonable way to direct attentiongiven decision makers’ cognitive constraints and thestructures of the decision environments that theyare usually exposed to.

Non-additive utilityResearch on multi-attribute preferential choicenearly always considers settings in which decisionmakers’ preferences are additive in attributevalues, and this additive structure is generally seen

as providing the standard model of multi-attributechoice (see Keeney & Raiffa, 1993). It is this additivestructure that makes common attributes unnecess-ary in two-alternative forced choice, and sub-sequently justifies the attribute-cancellationassumptions in lay decision rules like BenjaminFranklin’s heuristic and in related behavioural the-ories such as those discussed above (e.g., Bordaloet al., 2012, 2013; Houston et al., 1989, 1991;Koszegi & Szeidl, 2013). Indeed even theories thatdo not explicitly ignore common attributes stillrely on the assumption of additivity. Thus promi-nent accounts of multi-attribute choice, such asthose involving lexicographic decision making(Fishburn, 1974; Gigerenzer, Hoffrage, & Kleinbölt-ing, 1991; Tversky, 1969), the equal weighting ofattributes (Dawes, 1979), the tallying of attributes(Alba & Marmorstein, 1987; Russo & Dosher, 1983),weighted additive rules (Keeney & Raiffa, 1993),the sequential sampling of attributes (Bhatia, 2013;Roe et al., 2001; Usher & McClelland, 2004), andneural network-based recurrent activation (Glöck-ner & Betsch, 2008; Holyoak & Simon, 1999), allassume that the desirability of an alternative is asimple weighted sum of its component attributes.

However, there are settings in which the alterna-tives offered to participants have non-additive com-ponents. This is the case with certain economicbundles, which contain complementary goods suchas printers and print cartridges. Here the presence ofa print cartridge in a bundle with a printer addsnon-linearly to the desirability of that bundle, regard-less of whether that print cartridge is common acrossthe bundles in the choice set. Although choicesbetween these types of economic bundles are typi-cally not considered within multi-attribute choiceresearch, they are nonetheless present in many day-

Table 5. The average recall probabilities of the different attributes when they are unique, common and absent, in the forced and free choiceconditions of Experiment 6

Attribute

Forced choice Free choice

Unique Common Absent Unique Common Absent

Hard worker .79 .82 .21 .62 .89 .55Experience .42 .71 .39 .67 .70 .32Recommendations .73 .60 .08 .65 .56 .33Intelligent .73 .85 .06 .90 1.00 .26Creative .70 .54 .29 .55 .67 .26Motivated .55 1.00 .06 .79 .58 .16Friendly .80 .50 .24 .56 .90 .46Go-getter .61 .77 .08 .63 .75 .21Organized .61 .78 .06 .33 .71 .12Good education .88 .67 .14 .48 .64 .22Average .68 .72 .16 .62 .74 .29

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to-day decision-making environments. It is necessaryto attend to common goods in choices betweenthese types of economic bundles, in order to selectthe bundle with the highest overall desirability. Dueto the task-switching costs (Monsell, 2003), it is likelythat decision makers could be using the same atten-tional strategy, the associative attentional strategy, inchoices between bundles with non-additive goods,in which attention to common goods is efficient, asthey do in choices between alternatives with additiveattributes, in which attention to common attributes isinefficient.

Note that it is also possible that participants’ evalu-ations of the stimuli in our experiments are non-addi-tive. For example, it may be the case that thedesirability of an applicant who is both motivatedand intelligent is more than the sum of the desirabil-ities of applicants who are only motivated and appli-cants who are only intelligent. This could be onereason why participants attend to common attributes.However, such an explanation would also predict thatparticipants would attend to absent attributes (as bothcommon and absent attributes are diagnostic whenutility is non-additive). The fact that we are seeingabsent attributes being ignored implies that thisexplanation cannot account for all of our results.

Absolute desirabilityPreferential choice tasks do not always involve con-siderations of relative option desirability, as withforced binary choice. Decision makers also sometimesneed to evaluate the absolute desirability of the avail-able alternatives. This is the case with free choices inwhich decision makers can obtain as many of theavailable alternatives as they would like, as discussedin Experiment 6. It is also the case in contingent valua-tion tasks, such as those eliciting buying and sellingprices or likability ratings. It is in these settings thatthe associative attentional strategy, which directsattention towards an attribute if and only if it ispresent in the alternatives, is efficient. More formally,as the absolute desirability of an alternative x iswritten as U(x) = ∑

i[Ax Vi , decision makers need toconsider all the attributes in Ax = {i | xi = 1}, in orderto determine U(x). Again, given that task switching iseffortful (Monsell, 2003), it is probably difficult fordecision makers to change attentional strategiesbetween tasks involving evaluations of both absoluteand relative desirability (such as free choice tasks) andtasks involving evaluations of only relative desirability(such as forced choice tasks). If the associative

attentional strategy is not too detrimental in forcedchoices, it may be the case that decision makers usethis strategy consistently in all value-based decisions.

The results of Experiment 6 provide evidence tosupport this claim. Experiment 6 finds that decisionmakers display similar patterns of attention allocationin free and forced choices. More specifically, commonattributes are attended to almost as frequently inforced choices, in which these attributes are non-diag-nostic, as they are in free choices, in which they arediagnostic. Additionally, absent attributes areignored in both types of choices. Given these simi-larities, it is possible that decision makers are using asingle attentional strategy, the associative attentionalstrategy, in both settings. However, these similaritiescould also be due to similarities in presentationformat and other aspects of the experimental designthat these conditions have in common.

Real-world environmentsThere is another reason why decision makers use theobserved associative attentional strategy. It may, infact, be an efficient way of allocating attention inenvironments that decision makers are exposed toin the real world, as it could be that there are relativelyfew common attributes in these environments. Theintuition for this claim for this adaptive rationalityclaim (e.g., Gigerenzer & Goldstein, 1996; Payne,Bettman, & Johnson, 1993; see also Anderson, 1990;Oaksford & Chater, 2007) is as follows: The universeof choice alternatives that could be available in anychoice task is large and diverse. Subsequently theset of attributes on which these alternatives aredefined is also very large. This implies that any twoavailable alternatives, x and y, are most likely associ-ated with only a small subset of all possible attributes;that is, x and y are sparse vectors. If the distribution ofattributes in these alternatives is independent, thendue to their sparseness, these alternatives are unlikelyto overlap on any of their attributes. In other words theavailable choice alternatives for large attribute spacesmost probably do not have common attributes. Inthese settings, the tendency of the associative atten-tional strategy to direct attention to common attri-butes is not detrimental, and associative attention islargely efficient.

Consider, for example, picking any two items atrandom in a grocery store. These stores carry a largerange of diverse items, and it is relatively unlikelythat two randomly chosen items would have manyoverlapping attributes. The probability and extent of

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overlap would reduce further as the store gets largerand larger. The same holds for other types ofdecisions—for example, whether to spend a bonussalary on a new television or on a vacation.

More formally, let us consider a setting in whichthere are n possible attributes in the attribute space,and choice alternatives x and y are associated withan average of mx and my of these n attributes. Weassume that the probability of an alternative beingassociated with a given attribute is described by a Ber-noulli distribution with the probability of successequal to mx/n for x and my/n for y. Both attributesand alternatives are assumed to be independent sothat the association of one alternative with an attri-bute does not affect that alternative’s associationwith other attributes, or the association of the otheralternative with any of the attributes. Additionally,for simplicity, the association probability of an alterna-tive with an attribute is assumed to be identical for allattributes.

With these assumptions we can write the prob-ability of both the alternatives having a given attri-bute—that is, the probability that the given attributeis common, as (mx · my)/n

2. Correspondingly the prob-ability of this attribute being either absent or unique is1− (mx · my)/n

2. From this, we can write the probabilityof all attributes being absent or unique, and none ofthe attribute being common, as [1− (mx · my)/n

2]n.This is the probability that a given pair of alternativesdo not overlap on any attribute at all. We can showthat [1− (mx · my)/n

2]n is increasing in n, with [1−(mx · my)/n

2]n approaching 1 as n approaches infinity.1

Thus, as the number of possible attributes, n, getslarger, the probability that there are no common attri-butes also gets larger, and for large enough n, it is verylikely that there are no common attributes to attendto. This implies that in everyday decision environ-ments, which consist of large attribute spaces, associ-ative attribute attention is almost always efficient.

Of course, there is one important limitation of theabove argument: The distribution of attributes acrossalternatives is not necessarily independent. Some-times, decision makers have to make choicesbetween two similar choice options. This means thatit is not always the case that the probability of therebeing a common attribute falls to zero in large attri-bute spaces. Despite this limitation, the above analysisis useful: It provides a formal study of one possible

environmental structure and its interaction with a par-ticular decision strategy, and establishes that there areindeed environments where the strategies observedin this paper are beneficial for decision making.Future work should attempt to more rigorouslycharacterize the interplay between environmentalstructure and the observed attentional strategies, inorder to better understand why these strategies areused by decision makers.

Attentional biases

The findings documented in this paper can be seen asillustrating a type of attention bias in preferentialchoice. These types of biases are well known and areoften able to account for deviations from traditionaleconomic rationality. For example, Birnbaum and col-leagues (Birnbaum, 2008; Birnbaum & Chavez, 1997)have argued that attention is disproportionatelydirected towards low gamble outcomes, providingone explanation for violations of expected utilitytheory, and Bhatia (2014) has shown how these viola-tions can be attributed to randomness in attentionallocation. Similarity, Yechiam and Hochman (2013a,2013b) have shown that disproportional attentiontowards losses relative to gains provides a powerfulpsychological explanation for loss aversion. Relatedly,Weber et al. (2007) have noted that decision makersare more likely to focus on immediate outcomes inreward sequences, predicting immediacy biases andother violations of exponential discounting.

Attention has also been used to explain the depen-dence of choice on the way that preferences are eli-cited—that is, the response modes in the decisiontask. Tversky et al.’s classic account of preferencereversals in risky choice, for example, assumes thatdecision makers pay more attention to monetarypayoffs in matching tasks than in choice (Tversky,Sattath, & Slovic, 1988). Multi-attribute choice rever-sals across logically identical task frames have beenexplained in a similar manner, with acceptanceframes guiding attention towards positive attributesand rejection frames guiding attention towards nega-tive attributes (Shafir, 1993).

Similar work has used attention to study the effectof focal alternatives on final choices. For exampleHouston et al. (1989, 1991) have used Tversky’sfeature-based attention model of similarity to

1The increasingness of [1− (mx·my)/n2]n can easily be established by taking the first derivative (with positive n). The limit can be obtained by

examining the limit of ln{[1− (mx · my)/n2]n} and applying L’Hôpital’s Rule.

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account for reversals in choice as the focus of compari-son in the choice task is varied. This model can alsoaccount for order effects in preferential choice. Morerecently, the effect of numerical anchors has beenexplained using attentional biases that favour theanchored response (Chapman & Johnson, 1994;Strack & Mussweiler, 1997). A similar explanation hasbeen used to predict the effects of endowments andother reference points on final choices. According tothis account, decision makers are more likely toattend to the attributes of reference points, makingthem seem more attractive than their competitors(Carmon & Ariely, 2000; Johnson et al., 2007).

It may be the case that existing theories of atten-tional bias may be able to characterize the types ofattentional strategies observed in this paper. Perhapsthe theory most relevant to the results of this paperis Bhatia’s (2013) associative accumulation model,which attempts to use attribute attention to explainthe effects of irrelevant decoy alternatives andsalient alternatives such as reference points onchoice. This model states that decision makersattend to attributes in proportion to the associationof these attributes with available alternatives. Sub-sequently altering the set of alternatives in a choicetask in a logically irrelevant manner (such as byadding dominated decoys) leads to seeminglyirrational reversals in choice.

There are, however, some differences betweenthe associative attentional strategies described inBhatia’s (2013) account and the attentional strategyobserved in the participants in our experiments.Most notably, Bhatia’s (2013) model assumes thatthe attention towards an attribute has an increasingrelationship with the associations of the attributewith the alternatives in the choice set. Thus whiledecision makers are predicted to ignore absent attri-butes, they are also predicted to pay more attentionto common attributes than to unique attributes. Wedid not observe this in our experiments. In all of ourtasks, we found that decision makers paid the sameamount of attention to common attributes as theydid to unique attributes.

The difference between our experimental resultsand Bhatia’s (2013) predictions could be due to thenature of the tasks considered in this paper. In orderto characterize efficient attention, we examined onlytwo-alternative choices with binary attributes.Bhatia’s analysis however pertains to three-alternativechoice with continuous attributes. Future work shouldexamine attribute attention in larger choice sets with

continuous attributes, so as to build more general the-ories of attribute attention in preferential choice.

Additional avenues for future work

The discussion in this section has outlined the neces-sity of developing and testing theories of attributeattention that are able to account for the effectsobserved in this paper. There are also, however,many ways in which the experimental techniques inthis paper can be improved upon, to further validatethe observed attentional patterns and to better under-stand their underlying properties. First, it is necessaryto examine additional measures of attention. Thoseused in this paper—namely recall, mouse tracking,and decision time—are indirect and imperfectproxies of what the decision maker is actually thinkingabout. For example, while recall probability is posi-tively associated with the depth and extent of cogni-tive processing, it is also influenced by variousattribute-level factors, such as the frequency withwhich the attribute occurs in the natural environment(though the fixed-effects terms in the logisticregressions performed in this paper do help controlfor these attribute-level biases). Additionally, in Exper-iments 1–3 in this paper, decision makers would needto look at the various attributes to see whether theywere unique, common, or absent in the alternatives.Merely looking at the attributes could influencerecall and subsequently add noise to our recallmeasure. Likewise, although our mouse clicking andviewing time information in Experiment 4 bypassesmany of these problems, it does not, by itself,provide a noiseless account of what the decisionmaker is thinking about, or even looking: Decisionmakers often attend to objects other than those thatare on the screens in front of them. Lastly, althoughthe overall decision time measure in Experiment 5does allow us to determine when decision makersare processing additional information in the choiceproblem, it does not tell us exactly what this infor-mation is. We are only able to state that decisionmakers are attending more to some things in one con-dition than in another, but not conclusively state thatit is the attributes themselves that are getting theincreased attention.

There are two ways in which these limitations canbe addressed. The first involves better behaviouralmeasures of attention, such as eye tracking (see e.g.,Noguchi & Stewart, 2014). Unlike the mouse-trackingtools used in this paper, eye tracking and related

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measures would be able to directly assess whatdecision makers are looking at. The second involvesneural measures of attention and cognitive proces-sing, such as blood-oxygen-level-dependent (BOLD)activation (see Lim, O’Doherty, & Rangel, 2013).Unlike eye tracking, which is only able to capturevisual attention, these measures would also be ableto determine what decision makers are thinkingabout. Future work should attempt to examine thephenomena studied in this paper using these twoalternative approaches.

Another limitation of the studies in this paper istheir one-shot nature. Experiments 1–4 and 6 allinvolve only one decision problem. Although this isnecessary for measures such as recall (in which is itimportant for participants not to know about therecall test that follows stimuli presentation), it limitsthe insights of this paper to novel decision settingsin which decision makers do not have much experi-ence with the choice problem at hand. These settingsare vulnerable to increased error, as well as the effectsof curiosity, which could be driving attention towardsthe common attributes. Future work should thusattempt to replicate the experiments in this paper inrepeated-choice settings with feedback. It is possiblethat after obtaining enough experience with a particu-lar choice problem, decision makers may be able tolearn to ignore non-diagnostic common attributes.

A repeated-choice study with feedback is also valu-able as it would allow for the experimenter to controlthe reward structure in the task. This is necessary toensure additive utility, which is the only setting inwhich common attributes are non-diagnostic. Cur-rently we cannot rigorously claim that decisionmakers are aggregating attribute values indepen-dently, and subsequently we cannot claim that theobserved attentional strategies are inefficient. With arepeated-choice study we could test these claimsand subsequently enhance the theoretical impli-cations of our results.

The studies could also be improved by controllingfor the manner in which the associations of the attri-butes with the alternatives are conveyed to partici-pants. Currently the presence of an attribute in analternative is indicated on an attribute-by-alternativematrix with signs like “X”. This is the standard way ofpresenting this information in multi-attribute andmulti-cue decision-making research. It is also closelyrelated to the way in which the presence or absenceof features in objects is conveyed in the real world.However, it is possible that this type of stimuli

presentation, rather than some innate behaviouraltendency, is the reason why decision makers attendto present attributes and ignore absent attributes. Tocontrol for this, it would be necessary to counterba-lance the use of signs like “X” so that in some con-ditions they indicate attribute presence but in otherconditions they indicate attribute absence, or elseuse neutral signs (involving other symbols or differentcolours) for presence and absence. If the observedattribute attention biases continue to emerge inthese types of designs then these biases could beseen as being a much more integral and prevalentfeature of multi-attribute decision making.

A final limitation of the experiments in this paperinvolves the fact that the attentional biases that theystudy do not influence decision makers’ choices. Thisis due to the fact that these biases pertain to decisionmakers’ attention towards irrelevant information—information that should not, in theory, alter the wayin which the decision makers evaluate the options. Itmay, however, be the case that there are some set-tings in which this type of biased attention can influ-ence the actual decision outcome. For example,some researchers have found that drawing attentiontowards missing options or missing information canaffect choice probabilities (Huber & McCann, 1982;Schulte-Mecklenbeck & Kühberger, 2014). Futurework should examine whether it is possible for theattentional strategies documented in this paper toinfluence decision outcomes in a similar manner.

CONCLUSION

This paper provides an empirical examination of attri-bute attention. Across six experiments we find thatdecision makers focus attention on attributes thatare unique to each of the alternatives as well as attri-butes that are common to the two alternatives—thatis, attributes that are associated with one or both ofthe alternatives. Attributes that are not associatedwith either of the two alternatives are ignored.Although this strategy does direct attention selec-tively, it is not always efficient. Common attributesare often non-diagnostic for determining which ofthe available alternatives is most desirable. Ourresults contradict some existing accounts of attributeattention in preferential choice, while also presentingnovel insights about how more powerful descriptiveand explanatory theories of attribute attention maybe constructed.

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Acknowledgement

Thanks to Russell Golman for valuable insights.

Funding

Thanks to the Economic and Social Research Council [grantnumber ES/K002201/1] for funding.

ORCID

Sudeep Bhatia http://orcid.org/0000-0001-6068-684X

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