In research on decision-making much attention during last few decades has been devoted to personal information processing styles. This interest is related to the growing popularity of Dual-Process Theories (DPT) in which two cognitive systems are emphasized. The first is intuitive, quick, unconscious and affect-based, whereas the second is logical, conscious, slow and reason-based, also labeled referred as “rational” (e.g., Epstein, 1994; Kahneman, 2003). Various measurement techniques have been developed to diagnose the personal style of information processing. Two classes of these measurements can be distinguished: self-reported inventories and task solving tests. In the study presented here, both types of measurements were used, i.e., self-reported Rational-Experiential Inventory (the REI) proposed by Pacini and Epstein (1999) and the Cognitive Reflection Test (the CRT) developed by Frederick (2005).

The important contribution from the present research is that these measurements of information processing have been confronted with the fundamental assumption of rational choices accepted in utility theory (UT), i.e., the transitivity of preferences (Von Neumann and Morgenstern, 1953). Despite a high interest in personal styles of information processing in decision research, to our knowledge neither measurement of DPT has been directly confronted with the concept of transitivity of preferences in UT¹. So the first goal of this study was to validate two DPT measures of rationality: the REI and the CRT in light of the transitivity of preferences, the measure of rationality in UT.

The second goal of the study is to investigate the influence of individual differences in information processing on the strategies applied to selections among multi-attribute options. The following properties of strategies were investigated: requirements for trade-offs (compensatory vs. non-compensatory), maximization vs. satisficing and option-wise vs. attribute-wise information processing. These properties were selected because they allow differentiating among decision strategies related to the classical concept of rationality, to the concept of bounded rationality and to simple heuristics. It was expected that high scores on the Rationality subscale of the REI (the REI-R) and in the CRT would be related either to option-wise compensatory strategies and to maximization or to option-wise non-compensatory strategy and to satisficing. In contrast, low scores on the REI-R and in the CRT would be related to dimension-wise non-compensatory strategies².

The third goal was to test whether the strategies based on option-wise information processing favor the transitivity of preferences, independently of the requirement of trade-offs. Therefore, another important contribution from the presented research is the test of preferences' transitivity in the light of information processing behind various decision strategies.

The distinction between two means of cognition, emphasized within DPT, is not a new idea. Immanuel Kant (1781) introduced the concept of a posteriori and a priori judgments. A posteriori judgments are derived from experience and are based on phenomena that are related to sensation. These judgments don't lead to accurate representations of objects “as they are in themselves” and relations between them. In contrast, a priori judgments are derived from analytical thinking, or are synthetic a priori truths based on abstract reasoning noumena, i.e., objects as they are in themselves, independently of the senses. The concept of extensional and intuitive reasoning, introduced by Tversky and Kahneman (1983), is very similar to Kant's theory. This is also the fundamental concept in DPT proposed by Kahneman (2003; Kahneman and Frederick, 2005) who emphasized two cognitive systems: (1) intuitive, quick, unconscious, affect-based and (2) logical, conscious, slow, reason-based.

Frederick (2005) developed the CRT to probe individual differences in the dominant information processing system. The CRT consists of three mathematical questions (e.g., In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?). To answer these questions correctly one has to use System 2. On the other hand, wrong answers produced by System 1 come to mind automatically. High performance in the CRT means that System 2 “wins” with System 1 and indicates ability for analytical thinking. It was shown in number of studies that score in the CRT correlates positively with scores in IQ tests, SAT total score (Frederick, 2005; Obrecht et al., 2009; Toplak et al., 2011; Liberali et al., 2012), the ability to delay gratifications and the percentage of risky choices consistent with the normative model (Frederick, 2005). Similarly, Cokely and Kelley (2009) found that participants who scored highly in the CRT made choices in line with expected value. At the same time, a low score in the CRT positively correlated with the answers that reflected the conjunction and gambler's fallacies, neglect of base rate and sample size, framing and more (Toplak et al., 2011). The CRT also measures numeracy skills, i.e., the skills that enable understanding and number use (e.g., Frederick, 2005; Reyna et al., 2009). In light of DPT, the most important property of the CRT is that the score in the CRT correlates with the Stroop effect (Stroop, 1935), as shown by Toplak et al. (2011). This indicates that analytical information processing with the aid of System 2 requires conscious overcoming of automatic responses evoked by System 1. Therefore one may conclude that the CRT is a good measure of poor vs. high information processing.

Alternatively, Pacini and Epstein (1999) proposed a self-reported inventory, the REI (the Rational-Experiential Inventory), to identify individual differences in information processing. This inventory consists of two subscales: Experiential (the REI-E, “I like to rely on my intuitive impressions”) and Rational (the REI-R, “I enjoy problems that require hard thinking”). The REI-R has been found to be a strong predictor of performance consistent with the normative rules in tasks such as missing-a-flight vignette, the thematic and abstract versions of Wason task and the jelly bean task (Witteman et al., 2009). Ayal et al. (2011; Ayal et al., 2012) reported that participants, who scored high on the REI-R less frequently chose low-diversified portfolios and less frequently had reversed preferences for normatively identical options in two different situations. On the basis of the above findings, one may conclude that a high score on the REI-R is a good predictor of rational behavior.

In light of the cited findings, it is not surprising that the scores on the REI-R and in the CRT are positively correlated (Liberali et al., 2012; Thoma et al., 2015). On the other hand, these two measurements reflect two different methodological approaches: the score in the CRT results from actual performance, while the REI is a self-declarative measurement. Thus, it was interesting to check how both measurements account for transitivity of preferences and for strategies applied for selection among multi-attribute options.

Deviations in actual behavior from the fundamental assumptions of rational choices accepted in UT (Von Neumann and Morgenstern, 1953) have been studied for many years (e.g., Edwards, 1954; Simon, 1955, 1972, 1978, 1986; Kahneman and Tversky, 1972, 1973; Tversky and Kahneman, 1973, 1974, 1983; Shafir et al., 1993) and much attention has been paid to deviations from transitivity of preferences (e.g., May, 1954; Tversky, 1969). The transitivity axiom requires a systematic order of preferences across options. This means that for any three options A, B, and C, if A is preferred to B and B is preferred to C than A has to be preferred to C. The assumption of preference transitivity is the basic requirement of rational choice (Fishburn, 1991; Müller-Trede et al., 2015). Since in DPT rationality is related to information processing with the aid of System 2, there should be a relation between measures of the dominant style in information processing and the transitivity of preferences. So in the present study we checked whether DPT measurements account for transitivity of preferences.

The second goal of the study was to investigate the influence of individual differences in information processing on strategies applied in selection among multi-attribute options. In the light of information processing, the following properties of decision strategies are important: requirements for trade-offs (compensatory vs. non-compensatory), maximization vs. satisficing and option-wise vs. attribute-wise information processing.

As for the trade-offs' requirement, compensatory and non-compensatory decision strategies can be distinguished. The basic compensatory strategy is the Multi-Attribute Utility (MAU) model. According to this strategy, the decision maker estimates the score (utility) on all the attributes and assigns weights to them. The utility of each attribute is multiplied by its weight. The option with the highest weighted sum should be chosen. There are also other linear models that are less sophisticated, e.g., Franklin's Rule, Tallying (Gulliksen, 1950), but all of them require: (1) linear integration of information, (2) inter-dimensional trade-offs, and (3) a separate, global evaluation of each option. Does such a model always lead to rational choices? Imagine that one has to evaluate the health of three individuals considering three essential, equally important organs, as described in Table 1. According to the linear model, Person 2 has the highest weighted sum and, therefore, should be considered the healthiest. Yet clearly we are not able to survive without any one of the above organs. From this perspective, the healthiest is Person 3, even though s/he has the lowest global evaluation. Is choosing Person 3 an irrational decision? A solution to the above problem may be the strategy that doesn't require trade-offs, as proposed by Simon (1955, 1972, 1978). It still requires option-wise evaluations, but the optimization criterion is relaxed. According to Simon's concept of Bounded Rationality (Simon, 1957), people make decisions that may not be optimal but are still satisficing. Simon's idea is that it is sufficient to pick an option that satisfies aspirations The decision maker searches through options only until one that meets aspirations is found. So instead of the maximization of additively integrated utilities from all attributes, the comparison of scores for these attributes with the satisficing threshold is the criterion for choice (conjunction rule—CON).

The most important difference between MAU and CON is that they imply different criteria for decision: either averaging or meeting minimal cutoffs on all the relevant attributes. On the other hand, applying either strategy requires the systematic processing of all relevant information, which entails relatively high cognitive effort. This can be avoided if one uses another class of non-compensatory strategies, i.e., lexicographic strategies, which are much simpler than CON.

In these strategies, options are not treated separately but compared on the basis of attributes in the following way: (1) the decision maker orders attributes by importance and (2) chooses the option that is the best on the most important attribute, e.g., Person 1 from Table 1, if healthy heart is the most important attribute. If options are equally good on the most important attribute, the second most important attribute is considered, etc. There are many non-compensatory models based on attribute-wise comparisons such as Lexicographic) Rule (LEX, e.g., Luce, 1956; Tversky, 1969; Fishburn, 1970; Luce et al., 2000), Elimination by Aspects (Tversky, 1972), Minimax, Take-The-Best heuristic³ (Gigerenzer and Goldstein, 1996) or Priority Heuristic (Brandstatter et al., 2006). Even though lexicographic models differ among themselves, all of them are based on the same idea that choices are made on the basis of comparative judgments and incomplete, selective information processing. This is in contrast to MAU and CON strategies, where choices are based on global evaluations that include all the relevant information, made independently for each option.

The relation between applied strategies and information processing as well as transitivity of preferences requires explanation. It follows from previous research that people who base their decisions predominantly on System 1 are focused on perceptual features of a task (Sloman, 1996; Kahneman, 2003) and are prone to the biases that stem from context-dependent judgments (Payne et al., 1988, 1993). Such people therefore either use simple lexicographic rules or switch between different strategies. On the other hand, focusing on abstract aspects of a problem protects one against such judgmental biases. As mentioned earlier, Ayal et al. (2011) found that people who scored highly on the REI-R were less prone to reverse preferences for normatively identical options set in different contexts. So one may conclude that people with dominant System 2 consider all relevant aspects and consistently apply the same criterion for similar choices. For example, a person may consistently believe that either averaging (MAU) or meeting aspirations (CON) leads to the most accurate decision.

As for transitivity, the common view is that lexicographic rules lead to intransitivity of preferences, as a result of shifting attention among various dimensions. Since some information is ignored, judgment is partial. Tversky (1969) proposed a different explanation of intransitivity. He assumed that people differ not only in the relative importance assigned to various attributes but also in Just Noticeable Difference (JND) in scores across various attributes. He gave the example of three job candidates: X, Y, Z, who differed with respect to two attributes: intelligence and experience. Under the assumption that IQ is more important than experience, the candidate who scores higher in IQ than the others should be chosen. If such a difference, however, is not salient, one will look at differences in experience. This may lead to intransitive preferences, when the difference in IQ between X and Y as well as between Y and Z is not salient and then they are ordered due to the other dimension that points to X. On the other hand, the difference between X and Z in IQ scores may be noticeable—thus Z is chosen over X—resulting in intransitive preferences. This structure is called a lexicographic semi-order (LS) that results in intransitivity, “where a semi-order (LS) (Luce, 1956) or a just noticeable difference structure is imposed on a lexicographic ordering” (Tversky, 1969, p. 32).

The important feature of Tversky's explanation is that this can be extended to intransitivity that results from additive models. He gave an example of the Additive Difference (ADD) model. In the ADD, differences in scores for each dimension are calculated for both options and then these differences are summed. Differences in JND for various attributes can lead to the intransitivity of preferences. Note, LS can be treated as a specific case of ADD—where at least one difference in scores is described as a step function. So both models, ADD and LS, can result in intransitive preferences, when differences in scores are described by non-linear functions.

From Tversky's reasoning (1969), it follows that the compensatory principle does not prevent the intransitivity of preferences, when sensitivity to various dimensions is described by different non-linear functions and judgment is comparative. The important question is whether the linearity requirement is necessary, when information processing is option-wise and then each option is evaluated independently as in MAU and in CON strategies. If the utility of scores is defined by a monotonic function, one may expect transitive orderings of independently formed global evaluations. For MAU it is assumed that the higher the score, the higher its utility. For CON one can assume that all utilities of scores are described by step functions. Therefore, Hypothesis 3 was formulated as follows:

One aim of these studies was to check the relation between DPT measurements and the transitivity of preferences. It was found that people who obeyed transitivity scored highly on the REI-R and also in the CRT. This is an important and new result, which implies that both measures are good predictors of respect for transitivity. Even though both DPT measurements were very frequently used in previous studies (e.g., Ayal and Hochman, 2009; Cokely and Kelley, 2009; Pachur and Galesic, 2013; Graffeo et al., 2015), to our knowledge such a direct test has not been reported. One example of an indirect test is the research by Ayal et al. (2015). In Experiment 1, they found that the number of biases made could be predicted from the score on the REI and from the induced thinking mode. In Experiment 2, they found that: (1) an induced analytical thinking mode improved transitivity in analytical tasks, and (2) an induced intuitive thinking mode improved transitivity in intuitive tasks. However, in Experiment 2 the REI wasn't used. Therefore, in neither of these studies was the direct relation between the REI and transitivity checked. In case of the CRT, Primi et al. (2016) checked the relation between scores in the CRT and the transitivity of inferences, i.e., the validity of conclusions in light of given premises. They found not significant correlation with the CRT (r = 0.24, p = 0.67, N = 59). However, the transitivity of inferences should not be confused with the transitivity of preferences. For example, one prominent difference is that the transitivity of preferences depends on sensitivity to differences in scores on attributes (Tversky, 1969).

It should be underlined that the positive relation between scores on the REI-R and the CRT and the transitivity of preferences was observed for abstract choices only. The key advantage of abstract frames is that they reduce conflict of values. Therefore, people perceive choices as logical tasks: experience, knowledge about the world, beliefs and other factors do not disturb decision processes. So, System 1 is not activated. For example, in an abstract frame one has to accept the importance of the attributes given in the instruction since one has neither experience nor knowledge about the situation or its attributes. So a frame of this kind should be the best experimental condition to examine individual differences in the dominant style of information processing, what should result in the transitivity of preferences These results are in line with those reported by Toplak et al. (2011).

Respondents who had transitive preferences in abstract choices, also scored highly on the REI-R and in the CRT. Lack of such relations in specific choices was most likely caused by the small fraction of LEX-users, who had transitive preferences even though they scored poorly in both DPT measurements. So for people with dominant System 2, who also meet normative criteria of rationality, content doesn't affect their rational way of decision-making. Witteman et al. (2009) obtained similar results, i.e., they found correlation between the performance in thematic and abstract Wason tasks and the score on the REI-R.

Another interesting result is the confirmation that the three selected strategies—i.e., LEX, CON, and MAU—are good representations of three kinds of information processing: simple heuristics, bounded rationality and normative models. As might be expected, salient differences were observed between MAU and CON-users and the others, in both the index of transitivity and the score on the REI-R. MAU-users, in contrast to CON-users, also scored highly in the CRT. This may reflect the difference in numeracy skills between these two groups rather than a difference in rationality measured as consistency with basic logical principles. The higher transitivity and the higher DPT scores of respondents who used strategies based on global evaluation is additional support for the claim that the REI-R and CRT are good measurements of individual differences in information processing in terms of rational preferences.

In light of the above conclusion, the high score on the REI-R and in the CRT found for respondents who didn't consistently use the same strategy in tasks with specific content, requires additional explanation. In these tasks, respondents had to face undesirable trade-offs that might cause problems with the weighting of attributes and therefore with the avoiding of conflict. This favors use of lexicographic rules (Beattie and Barlas, 2001) that lead to intransitivity if JND varies across attributes and more than one attribute is used (Tversky, 1969). They also might switch between CON and LEX strategies. Indeed, these respondents scored the lowest in the transitivity index. However, the intransitivity of specific choices might also result from sensitivity to configurations of values on attributes which are in disagreement with the independence axiom. These problems do not follow from processing information with the aid of System 1 and so are not measured by the REI-R or the CRT.

Even though most authors consider simple heuristics as belonging to the class of Bounded Rationality models, they do not test a conjunctive rule that fully reflects Herbert Simon's Principle of Satisficing. Note that a majority of research is focused on comparison of linear models with simple heuristics, whereas CON rule is only rarely investigated. In our research, an interesting finding was that the most differentiated results were obtained for CON-users. They scored as high on the REI-R as MAU-users, but in the CRT they scored as poorly as LEX-users. This might point to the willingness of CON-users to be rational, which is reflected in self-declarative measurements. However, this willingness is not the same as numeracy skills. On the other hand, CON-users had an equally high index of transitivity of preferences as MAU-users. This supports the thesis that in every-day decisions, making satisficing choices is as rational as optimization. In contrast, selective and partial information processing does not guarantee transitivity. Only 40% of LEX-users respected the transitivity axiom. They also had low scores on the REI-R and in the CRT.

As mentioned in the Introduction, the fundamental assumption in decision-making is that rational choice requires a global evaluation of each option and the additive integration of information. The alternative perspective suggested here might be that choices based on global evaluation and the Satisficing Principle, instead of averaging, are also rational. Linear models lead to the optimization for the prize of trade-offs, whereas a conjunctive rule that doesn't require trade-offs leads only to satisficing decisions. So both have advantages and disadvantages in terms of accuracy. Thus, there are no reasons to treat linear models as the single criterion of rational choice.

Our results support this view. Respondents who had transitive preferences used either averaging (31%) or the CON rule (19.8%), so they met the normative criterion of rationality. Moreover, they also scored highly on the REI-R, i.e., declared a willingness to solve problems in an analytical way. Both findings suggest that users of the CON rule met both objective and subjective criteria of rationality.

However, the higher score in the CRT found for MAU-users compared to CON-users is not in agreement with this conclusion. This may have two explanations. First, the CRT measures not only the dominant style of information processing but also numeracy skills-CON-users had lower such skills than MAU-users. Second, the CRT may be a stronger test of analytical thinking than a self-declarative measurement such as REI-R, as suggested by Toplak et al. (2011). Therefore, the findings that users of CON had transitive preferences and scored highly on the REI-R but not in the CRT might be interpreted as the difference between the concepts of rationality and Bounded Rationality. To check this hypothesis, one should investigate which cognitive abilities are related to the use of averaging vs. the Satisficing Principle as the criterion for choice. In particular, previous research was limited to a comparison between simple heuristics and linear models, forgetting Bounded Rationality idea to which they refer often.

Finally, since there is a relation between transitivity and System 2 it would be interesting to investigate whether people consider either averaging or satisficing as an effective tool for reaching accurate decisions and if so, what situational factors reinforce the tendency to use either strategy.

This study was carried out in accordance with the recommendations of the Ethics Committee of University of Social Sciences and Humanities with informed consent from all subjects. The study was conducted online and all subjects gave informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Ethics Committee of University of Social Sciences and Humanities.

PS and JS developed the experimental design, collected, analyzed and interpreted the data. PS and JS wrote the first draft of the manuscript. Both authors participated in drafting the article and made critical revisions. Both authors approved the final version of the paper.