THINKING & REASONING, 2010, 16 (2), 69–97

Executive functions in decision making: An individual differences approach Fabio Del Missier University of Trieste, Italy

Timo Ma¨ntyla¨ University of Umea˚, Sweden Downloaded By: [Del Missier, Fabio] At: 13:27 18 May 2010

Wa¨ndi Bruine de Bruin Carnegie Mellon University, Pittsburgh, PA, USA

This individual differences study examined the relationships between three executive functions (updating, shifting, and inhibition), measured as latent variables, and performance on two cognitively demanding subtests of the Adult Decision Making Competence battery: Applying Decision Rules and Consistency 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 and Consistency in Risk Perception mainly associated to shifting. The results suggest that the successful application of decision rules requires the capacity to selectively focus attention and inhibit irrelevant (or no more relevant) stimuli. They also suggest that consistency in risk perception depends on the ability to shift 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 Mimı` Visentini, Giovanna Mioni, and Rino Rumiati for their support and help in data collection. We also thank two anonymous Thinking & Reasoning reviewers 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). Ó 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 entail working 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 making depends 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 decisionmaking skills are related to each other, to cognitive abilities and to

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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 competence. The decision-making tasks, including Applying Decision Rules and Consistency 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 been limited 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 neuropsychological 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

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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 processes that 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 are primitives 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 individual’s 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 having a 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 decisionmaking 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-making tasks 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 COGNITIVE CONTROL 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 multiattribute 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-attribute decision 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 clear winner emerges) comparing the best options on the second most important attribute (but ignoring or inhibiting unsatisfying options and alreadyconsidered 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 participant’s 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 and inhibition) 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 performance. 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 threecomponent 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 related constructs. 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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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).

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 of executive 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 a candidate 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 measurement model identified in the first stage with a structural model substantiating 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,

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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

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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 ¼ 23.45, SD ¼ 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 10–20 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 psychological laboratories of the universities of Trieste and Padua. We selected two tests that are thought to tap each of the three target executive functions: plus–minus and number–letter (shifting), Stroop and stop-signal (inhibition), 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: plus–minus (trial 1), letter-memory, Stroop, number–letter, stop-signal, n-back, plus–minus (trial 2).1 After each test participants received a short break. A longer pause was allowed between Stroop and number–letter 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 1

The plus–minus 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 ¼ .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 discussion with 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 participants’ 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 more options 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 2 In 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 of the A-DMC carried out on a sample of undergraduates (Marklund, 2008). 3 The 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 year’s 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 participant’s 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 year’s 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 the next year’’ cannot be greater than the probability of dying ‘‘from any cause—crime, illness, accident, and so on—during the next year’’), and (iii) the judged probabilities of complementary events should add up to 100% (e.g. probability of moving ‘‘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 Plus–minus. 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. Number–letter. 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 number–letter 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 number–letter 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 a fourth key when the letter is a consonant (G, K, M, R). In the final block of trials the number–letter pairs are presented in clockwise order in the four quadrants of the screen, and participants respond to the number when the number–letter pair appears in the upper quadrants and to the letter when the number–letter 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 number–letter 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 to respond 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 to actively 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 to inhibit 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 96 word 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 the colour 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.

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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 fixed and 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, Akaike’s Information Criterion (AIC), the standardised root mean-squared residual (SRMR), Bentler’s Comparative 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

4

The 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 values lower 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 a formula 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): AIC ¼ Fml þ (2v/n þ 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 (plus–minus, number–letter) did not differ from normality after the substitution of three outlier values with the nearest non-outlier values (two cases for plus–minus and one case for number–letter, respectively). The decision-making measures were arcsin transformed to achieve the normality of their distributions. Reliability of measures was computed with the split-half (odd–even) correlation adjusted by the Spearman-Brown prophecy formula (RT measures) or with Cronbach’s 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 zeroorder correlations for the executive functioning measures agree with previous studies (e.g., Friedman et al., 2006, 2008; Miyake et al., 2000). TABLE 1 Descriptive statistics of untransformed executive tests and decision-making measures Task Executive functioning Plus–minus (s)a,b Number–letter (ms)a,b Letter-memoryc n-backc Stop-signalc Stroop (ms)a Decision making Applying Decision Rulesc Cons. in Risk Perceptionc,d

N

Mean

Min

Max

SD

Skew.

Kurtosis

Reliability

116 116 116 116 116 116

18.46 649 0.85 0.85 0.64 185

75.25 122 0.50 0.72 0.00 34

59.59 1515 1.00 0.95 1.00 347

13.28 272 0.11 0.05 0.26 65

1.06 0.78 70.93 70.43 70.71 0.17

1.10 0.55 0.69 70.12 70.13 70.11

.60 .84 .40 .73 .84 .78

116

0.64

0.10

1.00

0.21

70.62

0.11

.70

113

0.74

0.35

1.00

0.14

70.47

70.02

.73

a These variables were reversed (higher scores indicate better performance), but we report the descriptive statistics before their reversal in order to increase readability. b Three plus–minus outlier values and one number–letter outlier value were substituted by the nearest non-outlier values. c These variables were arcsin-transformed, but we report the descriptive statistics before the transformation in order to increase their readability. d The 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).

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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 independent). For estimation, we fixed the correlations between executive functions at one 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. Bentler’s Comparative Fit Index (CFI) and the Adjusted Population Gamma Index (APGI) reached their respective thresholds. The threecomponent independent model was unacceptable according to various measures of fit (p 5 .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 (p 5 .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 (N ¼ 116) Model

df

w2

p

SRMR

AIC

CFI

APGI

Three-component correlated Three-component correlated (revised) Three-component independent One-component

6 7 12 9

8.51 8.52 27.62 14.43

.203 .289 .006 .108

0.056 0.055 0.112 0.070

0.33 0.32 0.40 0.33

0.91 0.95 0.46 0.81

0.98 0.99 0.93 0.97

The endorsed model is indicated in bold. SRMR: standardised root mean-squared residual (good fit if 5.08); AIC: Akaike’s 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 (p 5 .05), as well as the updating-inhibition interfactor correlation. The shifting-updating correlation was instead marginally significant (p ¼ .08). However, the correlation between shifting and inhibition was not significant and very close to zero (7.04, p ¼ .89). This suggested that the shifting-inhibition free parameter was not needed in the model. Thus, we reestimated 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, and employed 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 threecomponent 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 p 5 .05 level), those next to the smaller arrows on the left are residual variances, and those on curved double-headed arrows are inter-factor correlations. Standard errors are in parentheses, after the corresponding coefficients. The updating-inhibition correlation is significant (p 5 .05), while the updatingshifting correlation is marginally significant (p ¼ .06).

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TABLE 3 Fit indices for Applying Decision Rules (N ¼ 116) Model

df

w2

p

SRMR

AIC

updating coefficient

inhibition coefficient

shifting coefficient

Full-path Updating Inhibition Shifting No-path

24 26 26 26 27

12.47 14.55 14.95 28.39 33.42

0.97 0.96 0.96 0.34 0.18

0.055 0.059 0.063 0.099 0.114

0.18 0.16 0.16 0.28 0.31

.07 (.31) .46*** (.09) – – –

.44^ (.31) – .54*** (.11) – –

.17 (.21) – – .32* (.14) –

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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: ^p 5 .10; *p 5 .05; **p 5 .01; ***p 5 .001.

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 p 5 .0001; updating p 5 .0001; shifting p 5 .05). According to the w2 difference test, however, the full-path model was significantly better than the shifting model (p 5 .001). The same test did not show a significantly better fit of the fullpath model versus the inhibition model (p ¼ .29) or updating model (p ¼ .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 ¼ .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 5

CFI 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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TABLE 4 Fit indices for Consistency in Risk Perception (N ¼ 113) Model

df

w2

p

SRMR

AIC

updating coefficient

inhibition coefficient

shifting coefficient

Full Path Updating Inhibition Shifting No-path

24 26 26 26 27

16.39 22.53 23.99 17.06 24.35

0.87 0.66 0.58 0.91 0.61

0.065 0.081 0.087 0.066 0.089

0.22 0.24 0.25 0.19 0.23

7.27 (.33) .15^ (.11) – – –

.26 (.33) – .08 (.13) – –

.53* (.22) – – .38** (.13) –

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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: p 5 .10 ^; p 5 .05 *; p 5 .01 **; p 5 .001***.

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: p 5 .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 ¼ .18; inhibition: p ¼ .55). The full-path model did not attain a significantly better fit than the shifting model (non-significant w2 difference test: p ¼ .72). However, the full-path model had a better fit than the updating or the inhibition models (p 5 .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 DISCUSSION In this paper we have presented an individual differences study that investigated the relationship between executive functions and two

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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 two different 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 shiftingrelated 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 implications. 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 especially valuable 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 should be 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 bound the 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 particularly stringent 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 the generality 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 higherorder 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 2009 Revised manuscript received 22 December 2009 First published online 23 March 2010

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APPENDIX A A-DMC items taken from Applying Decision Rules and Consistency in Risk Perception Applying Decision Rules The following questions are about other people choosing between DVD players, like the ones above. Please read each question carefully, because they ask for different answers. For each question, think about how each person makes their choice, then pick the DVD they choose. But be careful, because the DVD players will change from question to question.

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Question 2: Features

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DVD A B C D E

Picture Quality

Sound Quality

Programming Options

Reliability of Brand

Price

2 5 5 3 4

5 4 3 5 4

5 4 2 2 4

5 5 5 2 5

$369 $369 $369 $369 $369

Sally first selects the DVD players with the best Sound Quality. From the selected DVD players, she then selects the best on Picture Quality. Then, if there is still more than one left to choose from, she selects the one best on Programming Options. Which one of the presented DVD players would Sally prefer? __________

Consistency in Risk Perception A. The following questions ask about events that may happen some time during the next year.

1. What is the probability that you will get into a car accident while driving during the next year?

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APPENDIX B Pearson correlations for the executive functions and decision-making measures Task 1. 2. 3. 4. 5. 6. 7. 8. Downloaded By: [Del Missier, Fabio] At: 13:27 18 May 2010

^

Plus–minus Number–letter Letter-memory n-back Stop-signal Stroop Applying Decision Rules Cons. in Risk Perception

1

2

– .21* – .16^ .17^ .08 .13 .19* 7.10 .03 –.03 .05 .12 .33*** .13

3

4

– .24* – .23* 7.02 .28** .11 .34*** .26** .09 .14

5

6

– .20* – .16^ .27** 7.03 .08

p 5 .10; *p 5 .05; **p 5 .01; ***p 5 .001. Pairwise deletion of missing data.

7

8

– .34*** –