del missier, f., mäntylä, t. y bruine de bruin, w. (2010). executive fuctions in decision making...

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Executive functions in decision making: An individual

differences approach

Fabio Del MissierUniversity of Trieste, Italy

Timo Ma ntylaUniversity of Umea, Sweden

Wa ndi Bruine de BruinCarnegie Mellon University, Pittsburgh, PA, USA

This individual differences study examined the relationships between threeexecutive functions (updating, shifting, and inhibition), measured as latentvariables, and performance on two cognitively demanding subtests of theAdult Decision Making Competence battery: Applying Decision Rules andConsistency in Risk Perception. Structural equation modelling showed that

executive functions contribute differentially to performance in these two tasks,with Applying Decision Rules being mainly related to inhibition andConsistency in Risk Perception mainly associated to shifting. The resultssuggest that the successful application of decision rules requires the capacity toselectively focus attention and inhibit irrelevant (or no more relevant) stimuli.They also suggest that consistency in risk perception depends on the ability toshift between judgement contexts.

Keywords: Cognitive control, Decision making, Decision-making competence,Executive functions, Individual differences.

Correspondence should be address to Fabio Del Missier, Department of Psychology,

University of Trieste, Via S.Anastasio, 12, I-34134, Trieste (TS), Italy. E-mail: [email protected]

The authors thank Mim` Visentini, Giovanna Mioni, and Rino Rumiati for their support

and help in data collection. We also thank two anonymous Thinking & Reasoningreviewers and

Edward T. Cokely for their detailed and insightful comments on a previous version of this

paper. Fabio Del Missier thanks Consorzio Universitario di Pordenone for financial and

logistic support. The research was also supported by a grant of the University of Trieste (FRA

grant, Passolunghi & Del Missier).

THINKING & REASONING, 2010, 16 (2), 6997

2010 Psychology Press, an imprint of the Taylor & Francis Group, an Informa business

http://www.psypress.com/tar DOI: 10.1080/13546781003630117

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Decision making has traditionally been conceived as a complex interplay of

high-level process, involving option generation, evaluation of risks and

consequences, and choice of a course of action in line with personal

preferences (e.g., Baron, 2008; Hastie & Dawes, 2001). According to this

view, decision making may require a high degree of cognitive control

(Tranel, Anderson, & Benton, 1994). Consistent with this idea, a close link

between frontal/executive functions and decision-making processes has been

suggested by patient studies (e.g., Eslinger & Damasio, 1985; Manes et al.,

2002), brain-imaging research (e.g., Clark, Cools, & Robbins, 2004; De

Martino, Kumaran, Seymour, & Dolan, 2006), and behavioural experiments

(e.g., Hinson, Jameson, & Whitney, 2003; Shiv & Fedorikhin, 1999). For

example, some experimental studies have provided support for the idea that

decision procedures sensitive to long-term consequences of options entailworking memory resources and control processes (Hinson et al., 2002, 2003;

Shiv & Fedorikhin, 1999, 2002). However, these studies did not identify the

specific executive processes involved in decision procedures.

According to dual-process theories, decision making is supported by

heuristic and analytic processes (e.g., Epstein & Pacini, 1999; Evans, 2003,

2007; Evans & Over, 1996; Goel, 1995; Kahneman, 2003; Kahneman &

Frederick, 2005; Peters, Hess, Va stfja ll, & Auman, 2007; Reyna, 2004;

Sloman, 1996). Although dual process theories differ in many respects (for a

review, see Evans, 2008), they generally assume that heuristic decision makingdepends on learned associations and intuitive heuristics, while analytic

decision making is guided by rules and principles. Heuristic decision making

would rely on fast automatic processes, whereas analytic decisions would

entail slower control processes and working memory. Despite its intuitive

appeal and propulsive role, the research conducted within the dual-process

framework has not yet provided detailed insights into the nature of the control

processes involved in different kinds of decision-making tasks: Dual process

theories nicely describe what the two systems do but it is not clear how the

systems actually operate (De Neys & Glumicic, 2008, p. 1250; see also Evans,2007; Gigerenzer & Regier, 1996; Keren & Schul, 2009; Osman, 2004).

One of the reasons underlying our poor knowledge of the nature of

control processes in decision making is the scarce attention devoted to

individual differences and measurement instruments (cf. Lopes, 1987; Parker

& Fischhoff, 2005). Traditionally, decision-making processes, such as the

selection of decision rules to choose between options (Bro der, 2003; Larrick,

Nisbett, & Morgan, 1993; Payne, Bettman, & Johnson, 1993) and the

evaluation of risks associated with options (Mandel, 2005), have been

studied in isolation, mainly focusing on systematically understanding

deviations from normative standards (e.g., Kahneman, Slovic, & Tversky,

1982). As a result, relatively little is known about how individual decision-

making skills are related to each other, to cognitive abilities and to

70 DEL MISSIER, MANTYLA, BRUINE DE BRUIN

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real-world outcomes (cf. Bruine de Bruin, Parker, & Fischhoff, 2007).

Moreover, past research made only sporadic attempts to develop and

validate measures of individual differences in decision-making competence,

which are crucial to investigating the connections between cognitive

processes and decision behaviour.

Stanovich and West (1998, 2000, 2008) conducted an important stream of

individual differences studies involving reasoning and decision making.

They found moderate correlations between performance in some tasks (e.g.,

resistance to overconfidence and hindsight bias) and measures of cognitive

ability. Following this line of research, Bruine de Bruin et al. (2007; see also

Parker & Fischhoff, 2005) developed and validated a battery of decision

tasks aiming to measure individual differences in decision-making compe-

tence. The decision-making tasks, including Applying Decision Rules andConsistency in Risk Perception, were selected from the judgement and

decision-making literature, representing skills relevant to normative theories

of decision making. Using a diverse sample and a variety of performance

criteria, the Adult Decision Making Competence (A-DMC) battery was

found to have appropriate reliability and validity. The availability of this

validated A-DMC measure of individual differences now makes it possible

to examine in a more reliable way the connection between cognitive skills

and decision-making tasks.

Studies on control processes in decision making could also have beenlimited by methodological problems that, until recently, plagued research on

executive functions. The expression executive functioning has seen a

variety of interpretations, and the construct validity of most neuropsycho-

logical tests of executive functioning, such as the Wisconsin Card Sorting

Test (WCST) is not well established (Miyake et al., 2000; Royall et al., 2002;

Salthouse, 2005). Furthermore, commonly used individual-differences

measures of executive functioning, including the WCST, suffer from low

reliability and, perhaps as a result, show very low intercorrelations

(Denckla, 1996; Duncan, 1986; Miyake et al., 2000; Rabbitt, 1997;Salthouse, 2005).

Individual-differences studies of executive control have recently adopted

a methodological approach that has reduced these methodological

problems. Instead of using complex frontal tests, such as the WCST,

these recent studies have examined executive functioning by means of latent

variable analyses on simpler control tasks (Friedman et al., 2006; Ma ntyla ,

Carelli, & Forman, 2007; Ma ntyla , Kliegel, & Ro nnlund, in press; Miyake

et al., 2000; Salthouse, Atkinson, & Berish, 2003; see also Salthouse, 2005).

Their main strategy has been to use multivariate analyses for examining

individual differences in more specific control functions. Specifically, the

structure of executive functioning has typically been examined at the level of

latent variables (i.e., identifying what is statistically shared among the

EXECUTIVE FUNCTIONS IN DECISION MAKING 71

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multiple exemplar task scores for each executive function), rather than at the

level of manifest variables (i.e., analysing individual task scores). By

statistically extracting what is common among tasks selected to tap a

putative executive function, the resulting latent variable is a purer and

probably more reliable measure of the theoretical construct, which can be

related to a target manifest variable (e.g., performance in a decision task).

Recent research has adopted a latent variable approach for examining the

role of executive functions in a several domains of cognition, including

complex frontal lobe tasks (Miyake et al., 2000), fluid intelligence

(Friedman et al., 2006), attentional difficulties (Friedman et al., 2007), and

duration judgements (Carelli, Forman, & Ma ntyla , 2008).

Following these recent lines of work, the present study adopted an

individual differences approach to investigate cognitive control processesthat are assumed to play a role in decision making. In particular we

examined, through a latent-variable approach, the contribution of distinct

executive functions to performance on two cognitively demanding subtests

taken from a validated decision-making battery. We focused on three

control functions: updating working memory representations, shifting

between tasks and information sets, and inhibiting responses and stimuli

(hereafter referred to as updating, shifting, and inhibition, respectively).

These functions have frequently been postulated in the literature (e.g.,

Baddeley, 1996; Miyake et al., 2000; Nigg, 2000; Rabbitt, 1997; Smith &Jonides, 1999) and they have been reliably identified as important elements

of executive control (e.g., Friedman et al., 2006, 2007, 2008; Garon, Bryson

& Smith, 2008; Miyake et al., 2000; Shimamura, 2000). However, Miyake

et al. (2000) conceived of these executive functions as a non-exhaustive

conceptualisation of control processes, at a relatively low level of analysis,

which proved to be appropriate for reaching a better understanding of the

relationship between control processes and complex cognitive tasks. As a

result, we are not claiming that these are the only executive functions

relevant to decision-making competence or that these functions areprimitives of cognitive control.

The updating function is thought to be involved in the active revision and

monitoring of working memory representations. It is usually assessed by

tests that require performing a revision of working memory content by

replacing older, no longer relevant information, with newer information (see

the Materials section for a detailed description of tests of executive

functions). The shifting function is assumed to play a role when the

individual has to switch between tasks or mental sets, and it is measured by

tests in which participants perform repeated shifts from one task (or mental

set) to another. The inhibition function is needed to actively suppress

responses or thoughts or, in general, to keep the individuals attention

focused on goal-relevant information in the face of interference


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(cf. Friedman et al., 2008). Tests of voluntary inhibition require stopping

prepotent responses and resisting interfering stimuli or thoughts.

We selected as target decision tasks the Applying Decision Rules (ADR)

and Consistency in Risk Perception (CRP) subtests from the A-DMC

battery (see the Materials section for a detailed description). ADR and CRP

measure significant aspects of decision-making competence: respectively, the

ability to correctly apply choice strategies when selecting from a set of

alternatives and the capacity to consistently judge the probability of the

occurrence of various risky events. ADR and CRP were selected for two

concurrent reasons. First, from the theoretical viewpoint, these two tasks

can be distinguished according to their postulated control requirements,

allowing for specific predictions about executive involvement to be

formulated. Second, previous research showed that, in addition to havinga good reliability and validity, ADR and CRP are the most cognitively

demanding and analytical A-DMC tasks. That is, they show the strongest

correlations with measures of fluid and crystallised intelligence (Bruine de

Bruin et al., 2007), which partly depend on efficiency in executive control

(e.g., Friedman et al., 2006; Salthouse et al., 2003).

Indeed, a precursor of ADR was found to be related with a generic

composite measure of executive functioning (Giancola, Martin, Tarter,

Pelham, & Moss, 1996). Furthermore, both ADR and CRP are also better

handled by participants who self-report relying more on rational decision-making styles (cf. Bruine de Bruin et al., 2007). Moreover, ADR and CRP

display the highest correlations with the other A-DMC subtasks, and show

the highest loadings on the one-factor solution of A-DMC, suggesting that

they may reflect core analytical A-DMC skills (Bruine de Bruin et al.,

2007). This idea is supported by a recent re-analysis of Bruine de Bruin

et al.s original data, which identified ADR and CRP as cognitive (vs

experiential) decision tasks (Bruine de Bruin, Parker, & Fischhoff, 2009).

To summarise, the study described in the present paper aims to understand

which control processes are more involved in two different decision-makingtasks capturing significant aspects of analytical decision competence (ADR

and CRP). Its broader goal is to promote an approach capable of establishing

a closer link between decision making and research in executive functioning,

which could allow a further specification of theories of individual differences

in decision making (e.g., Stanovich & West, 2000, 2008).

AN INDIVIDUAL DIFFERENCES STUDY ON COGNITIVECONTROL IN DECISION MAKING

We conducted a multi-indicator individual differences study, with the aim of

testing our hypotheses on the relationships between executive functions and

decision-making performance via structural equation modelling. Starting


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from previous research and from a cognitive task analysis, we hypothesised

that either inhibition or updating could play a prevailing and substantial

role in ADR, while we expected that shifting could play such a role in CRP.

The capacity to effectively apply decision rules is essential in multi-

attribute choice contexts (Bettman, Luce, & Payne, 1998; Payne & Bettman,

2004). While it is usually assumed that the application of decision strategies

depends on cognitive control and working memory (e.g., Payne et al., 1993),

to the best of our knowledge no specific research on this topic has been

published (possibly because past studies focused instead on strategy

selection: e.g., Bro der, 2003; Larrick et al., 1993; Payne et al., 1993). The

ADR task in the A-DMC battery specifically evaluates the ability to apply

decision rules of varying complexity (lexicographic, satisficing, equal

weights, etc.). Participants are presented with different multi-attributedecision problems involving choices between DVD players with different

features, and they are asked to select one or more options according to a

different decision rule (see Appendix A for one example). The application of

decision rules (see Bettman et al., 1998) usually requires selectively focusing

on goal-relevant information while carrying out an ordered stream of

operations and inhibiting irrelevant (or no more relevant) information.

Thus, inhibition may play a major role in ADR (cf. Friedman et al., 2008).

For example, the lexicographic decision rule involves first comparing

options on the attribute that is deemed the most important, then (if no clearwinner emerges) comparing the best options on the second most important

attribute (but ignoring or inhibiting unsatisfying options and already-

considered attributes), and so on. On the other hand, some ADR problems

require the execution of mental operations (comparisons and computations)

and the temporary maintenance of intermediate results, such as a reduced

choice set from which a preferred option will be selected. Thus updating

could be also involved, at least in the more complex problems composing

this task. Shifting is expected to play a less-significant role in ADR, because

this task requires the application of different rules or combination of rules(lexicographic, satisficing, etc.) to different problems (and thus there is no

need to reinstate previously encountered problems or rules).

The ability to follow basic principles of probability theory when judging

probabilities of different events is generally deemed to be an important

prerequisite to decision under uncertainty. The CRP task in the A-DMC

battery requires a participant to specify the probability of various events

that could happen to him/her in different time frames (see Appendix A for

one example). A series of judgements has to be provided in sequence, while

event type and time frame change. Some of these judgements are logically

related. Performance is then assessed by evaluating the congruency of the

participants judgements with basic probability principles. To summarise,

CRP essentially requires that participants maintain coherence in a series of


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conceptually related probabilistic judgements while switching between

different event descriptions and time frames. Past research showed that

the shifting executive function is involved in mentally switching from one

information set to another (Rende, Ramsberg, & Miyake, 2000). Thus

individuals with greater shifting ability should be better able to shift back

and forth between related probability judgements, facilitating comparisons

between different probability judgements, and increasing the likelihood that

they will recognise ones that are related. As a result, they should be better

able to give consistent judgements to probabilistic judgements that ask

about related events varying only in time frame or descriptive detail.

Evidence in line with this hypothesis also comes from Ma ntyla et al. (in

press), who examined metamemory judgements in relation to executive

functions, finding a relationship between set shifting (but not updating andinhibition) and metacognitive judgements on memory problems. Therefore

we hypothesised that the shifting executive function is significantly related to

consistency in risk perception. On the other hand, inhibition and updating

should play a minor role in this task, because single CRP judgements do not

appear to require a great deal of selective processing or integration/

maintenance, and an external memory of the previous responses is always

available on the questionnaire.

Analytic approach

We used structural equation modelling to test our hypotheses about the

relationships between executive functions and decision-making perfor-

mance. Following previous work, data analysis was carried out in two stages

(cf. Kline, 1998, Miyake et al., 2000): (1) the identification of a measurement

model of executive functioning (stage 1), and (2) the estimation of structural

models of decision tasks based on the measurement model. The second stage

can be reached only if the first one allows the identification of a valid

measurement model (e.g., Hair, Black, Babin, & Anderson, 2009).In the first stage we identified a measurement model that aims to capture

the structure of executive functions, starting from a candidate three-

component model that, as noted earlier, has been repeatedly supported (e.g.,

Friedman et al., 2006, 2008; Miyake et al., 2000). In other words, we tested a

hypothesis on the structure of executive functions. To this aim, we used two

tasks for each of the three functions (see Figure 1, and the Method section

for a detailed description of variables included in the model). According to

this model, the three executive functions are distinct but relatedconstructs.

Through structural equation modelling, we compared the fit of the

candidate measurement model with two reference models, which departed

from the idea that inhibition, shifting, and updating are distinct but related

constructs. The first reference was a one-component model (assuming unity


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of executive functions) and the second reference was a three-component

unrelated model (assuming independence of executive functions). The

endorsed measurement model was then kept fixed in the next stage of data

analysis (cf. Hair et al., 2009; Kline, 1998).

In the second stage of analysis we focused on the contribution ofexecutive functions to performance in different decision tasks (structural

models) while keeping the measurement model fixed. This means that, for

each decision task (ADR and CRP), we tested structural models that share

the measurement model (i.e., the structure of executive functions), but differ

in a principled way in the posited relationships between each executive

function and performance in the target decision task (which is always a

manifest dependent variable). This approach, similar to the one followed by

Miyake et al. (2000), is summarised in Figure 1 (assuming the measurement

model that we actually used). In the second stage we also started from acandidate model for each decision task, which embodied a selective

relationship between executive functions and the target decision task. In

particular, the candidate model was specified by combining the measure-

ment model identified in the first stage with a structural model substantiat-

ing our selective hypothesis on the relationships between executive functions

and the target decision task (see the previous section). Thus we tested the

shifting hypothesis for CRP and assessed two alternative hypotheses for

ADR (inhibition and updating). The candidate model was always compared

with two reference structural models: a no-path model (assuming complete

independence between executive functions and decision performance), and a

full-path model (assuming that each executive function significantly

contributes to decision performance). In order to be convincingly supported,

Figure 1.Abstract structure of the models tested in our study. Ellipses represent latent variables,

while rectangles represent manifest variables. According to the measurement model (solid

arrows), the three executive functions (shifting, updating, and inhibition) are clearly separable

but correlated. Dashed arrows represent potential relationships between executive functions

and decision tasks, which may or may not be included in specific structural models (depending

on the hypotheses).


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the candidate model should show a significantly better fit than the no-path

model and should not have a worse fit than the full-path model.

METHOD

Participants

A total of 116 undergraduates of the Trieste and Padua universities took

part in the study. The sample comprised 90 females and 26 males (mean

age 23.45, SD 5.04). Participants were awarded course credits for their

collaboration.

Procedure

A series of individual differences measures were collected in two sessions: (1)

A-DMC session, (2) executive functioning session. The tasks were presented

in separate sessions in order to avoid fatigue effects, and each participant

completed the two sessions within 1020 days. In the A-DMC session small

groups of participants completed the A-DMC tasks (including ADR and

CRP), in the same order as in the original questionnaire. Participants

completed the executive functioning session individually, in the psycholo-

gical laboratories of the universities of Trieste and Padua. We selected twotests that are thought to tap each of the three target executive functions:

plusminus and numberletter (shifting), Stroop and stop-signal (inhibi-

tion), letter-memory and n-back (updating; see also Figure 1). These tests,

which are frequently used to measure the three executive functions (see next

section), were administered in the following fixed order: plusminus (trial 1),

letter-memory, Stroop, numberletter, stop-signal, n-back, plusminus

(trial 2).1 After each test participants received a short break. A longer

pause was allowed between Stroop and numberletter tasks. The entire

executive functioning session lasted approximately 1 hour and 15 minutes(pauses included). Ethical and privacy protection standards were followed

throughout data collection and analysis.

Materials

Decision-making tasks

The A-DMC is a set of seven decision tasks that has been recently

validated and proposed as an instrument to measure individual differences

in decision-making competence (Bruine de Bruin et al., 2007). A-DMC

1The plusminus test was composed of two separate trials whose results were averaged.


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originates from a decision-making battery tailored for adolescents (Y-DMC:

Parker & Fischhoff, 2005), and it comprises a series of tasks that appear to

tap different aspects of decision competence. Performance was found to be

weakly correlated across the different A-DMC tasks (significant correlations

ranging from .15 to .43, mean of significant correlations .16). Bruine de

Bruin et al., (2007) reported that the overall A-DMC index (average of

standardised measures of performance in the different tasks) and each

individual subtask showed good to acceptable reliability and nomological

validity (with the exception of Path Independence). The original A-DMC

questionnaire was initially translated into Italian and underwent a first pilot

test.2 The accuracy of the translation was checked with the back-translation

method, applied by a professional translator. A small number of minor

discrepancies were detected, which were resolved after a joint discussionwith the translator. After a second pilot test the final version of the Italian

A-DMC was employed in the present study.3 We will now describe the ADR

and the CRP subtests, which are of interest here.

Applying Decision Rules (ADR). This A-DMC task evaluates partici-

pants ability to apply decision rules of varying complexity. Participants are

presented with 10 different multi-attribute decision problems involving

choices between DVD players with different features (such as picture

quality). For each problem, participants are asked to select one or moreoptions according to a different decision rule (lexicographic, satisficing,

equal weights, etc.), from a table presenting numeric ratings of features.

Scores represent the percent of responses across items that reflect

normatively correct answers that would have been obtained from an

errorless application of the prescribed decision rules.

Consistency in Risk Perception (CRP). This A-DMC task is devised to

assess participants capacity to follow the rules of probability theory when

providing probability judgements for risky events. Ten events are described,and participants are asked to judge the probability that each event could

2In the Italian version of the A-DMC dollars were replaced by euros. In order to maintain

the original figures, we avoided converting nominal values. However, euro values appeared to

be completely reasonable to participants of our pilot test. Minor word changes were applied

whenever the original wording made reference to cultural/social aspects that could be

unfamiliar or appear strange to Italian participants (e.g., Halloween was replaced by Carnevale

in a sunk cost problem). As can be seen by the descriptive statistics reported in Table 1, the

results of our study generally agree with those reported by previous studies. Moreover, our

A-DMC results show a good agreement with the results of a pilot test of a Swedish version ofthe A-DMC carried out on a sample of undergraduates (Marklund, 2008).

3The Italian version of the A-DMC used in our study is available from the first author of

this paper. A Swedish version is available from the second author of this paper.


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happen in 1 years time (e.g., What is the probability that you will get into a

car accident while driving during the next year?). Then the same events are

presented again, but this time participants are asked to evaluate their

probability of occurrence in 5 years time (e.g., What is the probability that

you will get into a car accident while driving during the next 5 years?).

Judgements of probability are expressed by ticking a graduated ruler that

displays a scale from 0% (no chance) to 100% (certain). Consistency in risk

perception is then evaluated by assessing the congruency of the participants

judgements with three principles: (i) the judged probabilities of the same

event in different time frames should be consistent (e.g., the probability of

getting in a car accident could not be greater in 1 years time than in 5 years

time), (ii) the judged probability of a subset event cannot exceed that of its

superset event (e.g., the probability of dying in a terrorist attack during thenext year cannot be greater than the probability of dying from any

causecrime, illness, accident, and so onduring the next year), and (iii)

the judged probabilities of complementary events should add up to 100%

(e.g. probability ofmoving your permanent address to another state some

time during the next year and probability of keeping your permanent

address in the same state during the next year). Performance is evaluated

by measuring the proportion of consistency checks (on a total of 20)

successfully passed by participants probabilistic judgements.

Executive functioning tasks

Plusminus. This paper-and-pencil task is commonly used to evaluate

the capacity to resist task interference when shifting between tasks (Jersild,

1927; Miyake et al., 2000; Spector & Biederman, 1976). Participants are

initially asked to add three to each of a series of numbers. Subsequently they

are asked to subtract three from each of another series of numbers. The final

task requires alternatively summing and subtracting three from each of a

third series of numbers. In our version of the task (as in Miyake et al., 2000),each series was composed of 30 two-digit numbers between 10 and 99

(randomly generated without replacement). Participants have to keep in

memory their current goal because no external cues are provided to remind

them. Performance (a shift cost measure) is measured by taking the

difference between the RT needed to complete the third (alternating) series

and the mean RTs of the first two series. We asked participants to execute

the three tasks twice, using different series of numbers, in order to obtain a

more reliable assessment and allow the computation of a reliability measure.

Thus our performance measure was the mean shift cost of these two trials

(participants accuracy was over 98%). Before the first administration of

each of the three tasks (sum, subtract, sum/subtract), a short training series

was presented. Participants were asked to work both quickly and accurately,


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and RTs needed to complete each series of numbers were recorded using a

stopwatch.

Numberletter. This computerised task is usually employed as an

indicator of the shifting capacity (Miyake et al., 2000; Rogers & Monsell,

1995). We used a version of the task that closely follows the one adopted by

Miyake et al. (2000). In the first block of trials a series of numberletter

pairs (e.g., 5B) is presented in the upper quadrants of the screen.

Participants are asked to press a first key when the number in the pair is

odd (3, 5, 7, 9) and a second key when the number is even (2, 4, 6, 8). In the

second block of trials another series of numberletter pairs is presented in

the lower quadrants of the screen. This time participants are instructed to

press a third key when the letter in the pair is a vowel (A, E, I, U) and afourth key when the letter is a consonant (G, K, M, R). In the final block of

trials the numberletter pairs are presented in clockwise order in the four

quadrants of the screen, and participants respond to the number when the

numberletter pair appears in the upper quadrants and to the letter when

the numberletter pair is presented in the lower quadrants. Thus, in half of

the trials participants shift between the two response sets previously

practised. In each trial the next numberletter pair was presented 150 ms

after the preceding response. Participants were given detailed written

instructions that fully explained each phase of task. They were asked torespond both quickly and accurately. Then 32 trials (plus 10 trials of

practice) were presented for each of the first two blocks of trials, and 128

trials were presented for the third block of trials (plus 12 trials of practice).

Performance was measured by taking the difference between the mean RT of

the shift trials of the third block of trials and the average RT of the first two

blocks of trials. RTs were computed on correct responses (whose percentage

was higher than 95% in each block of trials).

Letter-memory. This task is commonly used to measure the capacity toactively update working memory contents (Miyake et al., 2000; Morris &

Jones, 1990). In each trial a series of letters is presented, one by one, in the

centre of the computer screen (2000 ms per letter). Participants have to

rehearse the last three letters presented. When the presentation ends they

have to report the last three letters of the series. The length of the series of

letters varied randomly in each trial (5, 7, 9, or 11). After two practice trials

participants underwent 12 test trials. Performance was measured by taking

the proportion of final letters correctly recalled.

n-back. The n-back task is frequently used to measure individuals

capacity to update and actively manipulate working memory contents (cf.

Owen, McMillan, Laird, & Bullmore, 2005). We employed a version of this


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task that has been proven to be sensitive to individual differences in

updating (e.g., Ma ntyla , Karlsson, & Marklund, 2009). Participants were

presented with a series of high-frequency words (between three and seven

letters). Each word was presented for 2000 ms, centred on the computer

screen. Participants were required to press a key whenever the word

presented on the screen was the same as the one presented three serial

positions earlier in the series (3-back). This happened for 24 of the 96 stimuli

presented (25%). The stimuli also included 25% of foils (i.e., words repeated

at intervals of 2, 4, and 5). Participants underwent a practice session before

the test trials, and performance was measured as the proportion of correct

responses.

Stop-signal. This task has been often used to measure the capacity toinhibit a learned response. In each trial a stimulus letter (X or O) was

presented in the centre of the screen, and participants were required to

identify each by pressing a different specific key. They were also instructed

to withhold the response when they heard a beep (i.e., a stop signal)

immediately after the presentation of the stimulus letter. A fixation point

appeared on the screen 1000 ms before the stimulus presentation, and the

stop signal was delivered between 400 and 600 ms after the target (see also

Logan, 1994; Salthouse et al., 2003). We asked participants to be both fast

and accurate. After 20 training trials participants underwent 72 test trials.This number of trials was sufficient to obtain a reliable assessment of

individual differences in our previous studies (e.g., Ma ntyla et al., 2007,

2009) and allowed the task duration to be kept short. Task performance was

examined in terms of the proportion of correct responses in stop trials (cf.

Miyake et al., 2000).

Stroop. This task (Stroop, 1935) is commonly employed to assess

individual differences in inhibitory capacity. We used a version of the task

requiring manual responses (see also Ma ntyla et al., 2009). A series of 96word triples was presented on the computer screen. The central word of the

triple (stimulus word) was printed in colour (blue, green, yellow, red) at the

centre of the screen. In half of the trials the colour of the printed word was

congruent with the stimulus word (e.g., the word red was printed in red),

while in the other half it was incongruent (e.g., the word red was printed

in blue). The two adjacent words also referred to colour names (blue, green,

yellow, red) but were always printed in black. Participants were asked to

identify thecolour in which the central word was printed by pressing one of

two keys to respond. The first key was on the right side of the computer

keyboard and marked with a right arrow, while the second, on the left side

of the keyboard, was marked with a left arrow. Participants were instructed

to press the right arrow to indicate that the colour of the central word


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corresponded to the word presented in the right side of the screen, while

pressing the left arrow meant that the colour of the central word was

designated by the black word presented in the left side of the screen. We

asked participants to be both fast and accurate, and they underwent a

short series of training trials before starting the test. The difference between

mean RTs in incongruent and congruent trials was used as the dependent

variable.

RESULTS

As previously explained, in the first stage of data analysis we identified a

measurement model, which specifies the structure of the executive functions.

Then, in the second stage, the endorsed measurement model was kept fixedand we evaluated the models for the two decision tasks. All the models were

tested through the SEPATH program of the STATISTICA package

(version 8). We estimated the models through the maximum likelihood

technique, starting from the correlation matrix. Following previous

structural equation modelling studies, we evaluated the models through

multiple fit indices: the w2 statistic, Akaikes Information Criterion (AIC),

the standardised root mean-squared residual (SRMR), Bentlers Compara-

tive Fit Index (CFI), and the Adjusted Population Gamma Index (APGI).

Finally, we took into account standardised residuals and used the w2

difference test to compare the fit of nested models.4

4The w2 statistic is a common measure of badness of fit of a candidate model (compared to a

saturated model), and a small value of w2 corresponds to a small difference between the

correlation matrix generated by the candidate model and the observed matrix. A model with

acceptable fit is associated with a non-significant w2 at the conventional alpha level (i.e., p 4

.05), but more stringent alpha levels are preferred (i.e., p 4 .10 or greater). The SRMR index

also takes into account the difference between observed and predicted correlations, and valueslower than .08 indicate a good fit. AIC is a modified w2 statistic that takes into account also the

complexity of the model. Simpler models, with more degrees of freedom, are preferred and

associated with lower AIC values (which indicate better fit). CFI measures the fit of a candidate

model (compared to a baseline null model), and higher values of this index indicate better fit

(good fit when CFI 4 .90). APGI is an adjusted estimate of the population AGFI (Jo reskog &

So rbom, 1984) that would be obtained if we could analyse the population correlation matrix

(Steiger, 1989). Good fit is indicated by values above .95. The w2 difference test is used to

appraise the difference of fit between two nested models. The difference between the w2 statistics

of the two models (fuller vs nested) is evaluated in relation to the difference between their

degrees of freedom. If the difference w2 is significant (at the .05 alpha level), then the fuller model

has a significantly better fit than the nested one. AIC in STATISTICA 8 is computed with aformula that takes into account the maximum likelihood discrepancy function for a model

(Fml), the degrees of freedom for the model (v) and the sample size ( n): AICFml (2v/n 1).

This formula makes the AIC more stable across differing sample sizes.


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Data transformations and descriptive statistics

Descriptive statistics of untransformed variables are presented in Table 1.

After an arcsin transformation, commonly used for proportion correct

measures (see, e.g., Miyake et al., 2000), the executive functioning measures

(letter-memory, n-back, stop-signal) achieved normality. The distributions

of untransformed RT-based executive functioning measures (plusminus,

numberletter) did not differ from normality after the substitution of three

outlier values with the nearest non-outlier values (two cases for plusminus

and one case for numberletter, respectively). The decision-making

measures were arcsin transformed to achieve the normality of their

distributions. Reliability of measures was computed with the split-half

(oddeven) correlation adjusted by the Spearman-Brown prophecy formula(RT measures) or with Cronbachs alpha (proportion correct measures). It

was generally in line with previous studies (e.g., Bruine de Bruin et al., 2007;

Miyake et al., 2000).

As can be seen in Table 1 and Appendix B, descriptive statistics and zero-

order correlations for the executive functioning measures agree with

previous studies (e.g., Friedman et al., 2006, 2008; Miyake et al., 2000).

TABLE 1Descriptive statistics of untransformed executive tests and decision-making measures

Task N Mean Min Max SD Skew. Kurtosis Reliability

Executive functioning

Plusminus (s)a,b 116 18.46 75.25 59.59 13.28 1.06 1.10 .60

Numberletter (ms)a,b 116 649 122 1515 272 0.78 0.55 .84

Letter-memoryc 116 0.85 0.50 1.00 0.11 70.93 0.69 .40

n-backc 116 0.85 0.72 0.95 0.05 70.43 70.12 .73

Stop-signalc 116 0.64 0.00 1.00 0.26 70.71 70.13 .84

Stroop (ms)a 116 185 34 347 65 0.17 70.11 .78

Decision makingApplying Decision

Rulesc116 0.64 0.10 1.00 0.21 70.62 0.11 .70

Cons. in Risk

Perceptionc,d113 0.74 0.35 1.00 0.14 70.47 70.02 .73

aThese variables were reversed (higher scores indicate better performance), but we report the

descriptive statistics before their reversal in order to increase readability.bThree plusminus outlier values and one numberletter outlier value were substituted by the

nearest non-outlier values.cThese variables were arcsin-transformed, but we report the descriptive statistics before the

transformation in order to increase their readability.dThe number of valid cases for CRP did not reach 116 because some items of the subtest were

not completed by three participants. The entire subtest score for those participants was

discarded.


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Correlations are low and positive with some sign of specificity. Descriptive

statistics and the zero-order correlation for the A-DMC tasks are generally

in line with previous research (Bruine de Bruin et al., 2007).

Structure of executive functions: Measurement model

We started from a candidate three-component measurement model, in which

the three executive functions are clearly distinct but correlated. As already

explained, this model has been supported by previous studies. The candidate

model was compared with two reference models: (a) a unitary model

(assuming the unity of executive functions), and (b) a three-component

independence model (in which the three executive functions are indepen-

dent). For estimation, we fixed the correlations between executive functions atone in the unitary model and at zero in the independence model (see Miyake

et al., 2000). The results are summarised in Table 2.

The three-component correlated model showed a good fit on all the indices.

The fit of this model was fully acceptable: the w2 statistic was not significant at

the .20 level and the standardised root mean-squared residual index (SRMR)

was low. Bentlers Comparative Fit Index (CFI) and the Adjusted Population

Gamma Index (APGI) reached their respective thresholds. The three-

component independent model was unacceptable according to various

measures of fit (p5 .01, SRMR greater than .08, CFI much lower than.90). Moreover, the w2 difference test showed that the three-component

correlated model had a significantly better fit than the three-component

independent model (p5 .01). Finally, the one-component model achieved an

inferior evaluation on the majority of indices (only AIC and APGI are at the

same level), although if it was not inferior according to the w2 difference test.

To summarise, the candidate measurement model was supported by measures

of fit and by the comparison with two reference models.

TABLE 2

Fit indices for the measurement model (N116)

Model df w2 p SRMR AIC CFI APGI

Three-component correlated 6 8.51 .203 0.056 0.33 0.91 0.98

Three-component correlated (revised) 7 8.52 .289 0.055 0.32 0.95 0.99

Three-component independent 12 27.62 .006 0.112 0.40 0.46 0.93

One-component 9 14.43 .108 0.070 0.33 0.81 0.97

The endorsed model is indicated in bold. SRMR: standardised root mean-squared residual

(good fit if5.08); AIC: Akaikes Information Criterion (lower values indicate a better fit); CFI:Comparative Fit Index (good fit when 4.90); APGI: Adjusted Population Gamma Index (good

fit when 4.95). Non-significant w2 statistics (i.e., p 4 .05 or, better, p 4 .10) indicates

acceptable fit.


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The structural coefficients of executive functioning measures were all

significant (p5 .05), as well as the updating-inhibition interfactor correla-

tion. The shifting-updating correlation was instead marginally significant

(p .08). However, the correlation between shifting and inhibition was not

significant and very close to zero (7.04, p .89). This suggested that the

shifting-inhibition free parameter was not needed in the model. Thus, we re-

estimated the model fixing that parameter at zero. This simpler version of

the correlated model, with one additional degree of freedom, achieved an

equivalent level of fit than the original three-component correlated model

according to all the indices (see Table 2). The estimated coefficients of this

final model are presented in Figure 2, together with their standard errors. In

conclusion, we considered this revised three-component correlated model as

the best measurement model of executive functions for our data, andemployed it in the second stage of analysis.

Executive functions in decision-making tasks

In the second stage of data analysis, we tested our hypotheses about control

processes entailed in successful decision performance in Applying Decision

Rules and Consistency in Risk Perception through structural equation

models. In each of these models the measurement model was the three-

component correlated model identified in the first stage (i.e., all the

Figure 2.Three-component measurement model of the executive functioning data. Numbers on

arrows are standardised coefficients (all significant, at least at the p5 .05 level), those next to

the smaller arrows on the left are residual variances, and those on curved double-headed arrowsare inter-factor correlations. Standard errors are in parentheses, after the corresponding

coefficients. The updating-inhibition correlation is significant (p5 .05), while the updating-

shifting correlation is marginally significant (p .06).


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coefficients and terms of the model were fixed at the estimates reported in

Figure 2).

Applying Decision Rules (ADR)

The application of decision rules is assumed to involve working memory

functions. In particular, we hypothesised that a major role could be played

by the inhibition executive function, needed to ensure goal-oriented

processing through the inhibition of irrelevant (or no longer relevant)information. Alternatively, the mental operations required by this A-DMC

task could require the support of the updating executive function. The

results of structural equation modelling on Applying Decision Rules are

presented in Table 3.5

All the single-factor models (updating, inhibition, and shifting) achieved

a better fit than the no-path model (w2 difference tests: inhibition p5 .0001;

updating p5 .0001; shifting p5 .05). According to the w2 difference test,

however, the full-path model was significantly better than the shifting model

(p5

.001). The same test did not show a significantly better fit of the full-path model versus the inhibition model (p .29) or updating model

(p .35). In single-factor models, inhibition was the strongest predictor of

decision performance, as shown by standardised coefficients (see Table 3).

Moreover, only the inhibition coefficient was marginally significant (p .07)

in the full-path model, in which all the predictors (shifting, updating, and

inhibition) are considered.

Thus, although shifting and updating do appear to be related to ADR

performance in single-factor models, their influence is no more significant

when all the predictors are included in the model. Considering the whole

TABLE 3

Fit indices for Applying Decision Rules (N116)

Model df w2 p SRMR AIC

updating

coefficient

inhibition

coefficient

shifting

coefficient

Full-path 24 12.47 0.97 0.055 0.18 .07 (.31) .44^ (.31) .17 (.21)

Updating 26 14.55 0.96 0.059 0.16 .46*** (.09)

Inhibition 26 14.95 0.96 0.063 0.16 .54*** (.11)

Shifting 26 28.39 0.34 0.099 0.28 .32* (.14)

No-path 27 33.42 0.18 0.114 0.31

The endorsed model is indicated in bold. Estimated coefficients are followed by respective

standard errors (in parentheses). Significance levels of one-tailed tests are as follows: ^p5 .10;

*p5 .05; **p5 .01; ***p5 .001.

5CFI and APGI were not used in the following analyses because they did not contribute to

the discrimination of the best model.


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pattern of results, inhibition seems to have a prevailing role in the successful

application of decision rules, while shifting seems to be much less involved in

this task.

Consistency in Risk Perception (CRP)

This decision task requires maintaining consistency in probabilistic

judgements while switching between event descriptions and time frames.We hypothesised that participants with a higher shifting capacity should be

able to express more consistent judgements than participants less able in

shifting. The results of structural equation modelling are presented in Table 4.

The candidate model (shifting) was clearly better than the no-path model,

according to all the fit indices (including the w2 difference test: p5 .01).

Moreover, according to the w2 difference test, the shifting model showed a

better fit than the updating or inhibition models, which did not expose

significant improvements versus the no-path model (updating: p .18;

inhibition: p .55). The full-path model did not attain a significantly betterfit than the shifting model (non-significant w2 difference test: p .72).

However, the full-path model had a better fit than the updating or the

inhibition models (p5 .05 in both cases). Finally, only the shifting

coefficient was significant in the full-path model, in which all the predictors

were included. These results show that shifting plays an important role in

the expression of consistent risk judgements, while inhibition and updating

do not.

GENERAL DISCUSSIONIn this paper we have presented an individual differences study that

investigated the relationship between executive functions and two

TABLE 4

Fit indices for Consistency in Risk Perception (N113)

Model df w2 p SRMR AIC

updating

coefficient

inhibition

coefficient

shifting

coefficient

Full Path 24 16.39 0.87 0.065 0.22 7.27 (.33) .26 (.33) .53* (.22)

Updating 26 22.53 0.66 0.081 0.24 .15^ (.11)

Inhibition 26 23.99 0.58 0.087 0.25 .08 (.13)

Shifting 26 17.06 0.91 0.066 0.19 .38** (.13)

No-path 27 24.35 0.61 0.089 0.23

Note: The endorsed model is indicated in bold. Estimated coefficients are followed by respective

standard errors (in parentheses). Significance levels of one-tailed tests are as follows: p5 .10 ^;

p5 .05 *; p5 .01 **; p5 .001***.


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decision-making tasks (ADR and CRP), building on recent advances in the

measurement of decision-making skills and in the assessment of executive

functions. Our main aim was to provide new insights into the nature of

control processes relevant to decision-making competence, measured by two

cognitively demanding subtests of the A-DMC battery. Here we first trace

the general implication of the findings for the research on control processes

in decision making. Then we will illustrate how our results contribute to the

explanation of performance and errors in the specific decision tasks we

considered, and outline potential applied implications. Finally, the main

limitations of the present study will be discussed in relation to future

research directions.

In accordance with our expectations, significant relationships between

executive functions and the two target decision-making tasks were observed.However, going beyond previous work, the present study was able to show

more specific associations between executive functions and two cognitively

demanding decision-making tasks, which were selected as valid indicators of

analytic decision making. These results suggest that there is specificity in the

control requirements of different decision-making tasks. In particular,

shifting is mainly involved in the capacity to provide consistent judgements

on risky events, while inhibition appears to play a significant role in the

accurate implementation of decision rules. Thus our study indicates which

control processes are most operative in successful performance on twodifferent decision tasks, suggesting that some decision errors can be partially

traced back to the ineffectiveness of different types of control process. In

other words, our results qualify existing theoretical accounts of the

relationship between cognitive abilities and decision making by identifying

different sources of cognitive control limitations that mainly affect different

decision tasks (cf. Stanovich & West, 2000, 2008).

The shifting executive function was found to be related to the capacity to

express consistent judgements of risky events (CRP). This finding agrees

with the results of recent studies that showed a relation between shifting-related performance and metacognitive judgements requiring mental

flexibility (e.g., Ma ntyla et al., in press; Souchay & Isingrini, 2004).

Individuals with greater shifting ability, being more able to switch from one

context to another, may be more sensible to the need to harmonise

probabilistic judgements related to different time frames and situations, and

they may also be more able in accomplishing this task. Thus participants

with better shifting skills may have the appropriate mindset and cognitive

resources for deploying more consistent risk assessment strategies, involving

more systematic evaluation procedures. Inhibition was instead significantly

associated with the accurate application of decision rules. This result can be

explained in terms of the functional support of inhibition to goal-directed

processing. In most goal-directed tasks, inhibition plays an important role in


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keeping task-relevant information active by suppressing interfering or

irrelevant information (Carretti, Cornoldi, De Beni, & Romano , 2005;

Friedman et al., 2008). Thus inhibition may support the goal-directed and

selective information processing required by the successful application of

multi-attribute choice procedures.

The results of the present study suggest interesting applied implica-

tions. First, if different executive functions are mainly required for the

successful accomplishment of some decision-making task, training these

functions may improve some aspects of decision-making performance.

Thus it could be useful to examine the effects of training and

rehabilitation of executive functions (e.g. Dahlin, Stigsdotter Neely,

Larsson, Ba ckman, & Nyberg, 2008; Olesen, Westerberg, & Klingberg,

2003) on decision making. Beneficial side-effects could be especiallyvaluable in vulnerable segments of the population, such as older adults

and individuals with executive/frontal problems. Another practical

implication of our findings is that some decision tasks can be challenging

for individuals with limited executive control capacity. A variety of

decisions about health, finance, and everyday living require the

application of rather complex choice strategies and the expression of

consistent probabilistic judgements (e.g., Finucane & Lees, 2005;

Finucane, Mertz, Slovic, & Schmidt, 2005; Finucane et al., 2002; Parker

& Fishhoff, 2005). To facilitate the decision making, these tasks shouldbe presented in a format that simplifies information processing and

minimises demands on specific executive functions. Decision makers can

be helped through an appropriate design of information display (e.g.,

Bettman, 1975; Bettman, Payne, & Staelin, 1986) or through the use of

decision aids that can mechanise part of the task (e.g., Edwards &

Fasolo, 2001). However, information design and decision-aiding measures

should not be aimed only at a general reduction of cognitive load, but

should also be directed at counteracting specific executive difficulties.

Limitations and future work

Four limitations of the present study need to be acknowledged and

discussed. The first limitation is the correlational nature of the research,

which might allow alternative interpretation of our findings (i.e., the

relationships we highlighted might be spurious). Although alternative

interpretations of correlational researches are possible, we think that the

selectivity of the relationships observed in our study strongly speaks against

the existence of spurious associations stemming from the influence a

common cognitive factor. Thus there are reasons to think that our findings

reflect genuine relationships between executive functions and decision

performance. Future research might examine whether individual differences


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in executive functioning really provide a predictive contribution to

decision-making performance that goes beyond the contribution of

individual differences in more general cognitive measures (such as fluid

intelligence and numeracy; e.g., Bruine de Bruin et al., 2009; Cokely &

Kelley, 2009; Mata, Schooler, & Rieskamp, 2007). This line of research

might offer very interesting insights both for decision-making scholars and

for researchers interested in executive functioning and intelligence.

Preliminary findings obtained in our lab seem to support the idea that

individual differences in executive functioning can provide a specific

predictive contribution, at least for some decision tasks (Del Missier,

Ma ntyla & Bruine de Bruin, 2009).

A second limitation of the research is represented by the use of a

relatively small sample of undergraduate participants, which might boundthe external validity of our findings. However, this potential concern is

attenuated by the observation that our descriptive A-DMC results

generally agree with findings obtained in previous studies with diverse

populations (Bruine de Bruin et al., 2007, 2009; Parker & Fischhoff,

2005). If anything, we expect that the relationships we identified in a

rather homogeneous sample of young educated participants can emerge

more strongly in heterogeneous samples, where individual differences in

executive functioning are certainly more pronounced. From this point of

view, the use of a sample of undergraduates assured a particularlystringent test of our hypotheses. In any case we think that further

research on more heterogeneous samples will have the merit of increasing

the external validity of the present findings.

A related limitation concerns the stability of structural equation models,

possibly due to the relatively small sample size and the adoption of two

indicators for each latent construct. Even though we selected executive

functioning tasks that previous studies considered as appropriate indicators

of the respective latent constructs (see the Materials section), increasing the

number of executive measures in future studies should help to examine thegenerality of our findings.

A final limitation of the present study concerns our set of measures.

Even though we focused on three executive functions that have been

frequently postulated and investigated in the literature (e.g., Friedman

et al., 2006, 2007, 2008; Garon et al., 2008; Ma ntyla et al., 2007, 2009, in

press; Miyake et al., 2000; Nigg, 2000; Rabbitt, 1997; Shimamura, 2000;

Smith & Jonides, 1999), we do not imply that these are the sole functions

relevant to decision-making competence. Moreover, studies adopting a

lower-level decomposition of executive functioning can possibly be carried

out with success. Additionally, given that the conceptualisation of

executive functioning constructs is still being debated, some of these


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functions can be conceived in different ways (for inhibition see, e.g.,

Friedman et al., 2008; Friedman & Miyake, 2004; Nigg, 2000). Taking all

these aspects into consideration, we deem the present work as a first step

in the exploration of the relationship between executive functioning and

decision making. Further steps could investigate different aspects of

cognitive control or the adoption of different potential theoretical

decompositions/conceptions of executive functions. As noted earlier, the

two target A-DMC tasks used in the present study have been selected for

theoretical and methodological reasons, and they measure two significant

aspects of analytical decision-making competence. However, other

judgement and decision-making tasks need to be considered by future

research and this will hopefully advance our understanding of the role of

control processes in decision making.To conclude, the present study tried to relate executive functions and

decision making, two important research areas in the realm of higher-

order cognition. While these two areas are usually considered to be

tightly connected, the relationships between executive control and

decision-making processes are rarely articulated in sufficient detail and

they are usually not supported by specific empirical evidence. We hope

that the present study helps to bridge this gap and stimulates further

research in the field.

Manuscript received 30 June 2009Revised manuscript received 22 December 2009

First published online 23 March 2010

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