2.1 What is intuition?

Intuition has remained a hot topic, both in the field and in the popular press (Baron, Reference Baron1998; Gigerenzer, Reference Gigerenzer2007; Glöckner & Witteman, Reference Glöckner and Witteman2010; Hogarth, Reference Hogarth2001; Plessner, Betsch, & Betsch, Reference Plessner, Betsch and Betsch2007). The standard view of intuition is captured in dual-process approaches pitting intuition and emotion against logic and deliberation: the old reptilian brain and limbic system (intuition) versus the neocortex (rationality; e.g., De Martino, Kumaran, Seymour, & Dolan, Reference De Martino, Kumaran, Seymour and Dolan2006). This familiar dualism harkens back to Descartes and to Freud’s primary and secondary processes (Reyna, Nelson, Han, & Dieckmann, Reference Hogarth and Einhorn2009). In this standard view, intuition is the old system of animal impulses and low-level decision making (the experiential system “1” to reflect its primacy in evolution) as contrasted with conscious cognition and high-level decision making (the rational system “2” to reflect its recency in evolution; Epstein, Reference Epstein1994; Stanovich & West, Reference Stanovich and West2008).

The problem with this familiar dualism is that the data do not consistently support it. People higher in self-reported rational, as opposed to intuitive, thinking do not consistently show fewer biases and heuristics; in fact, they are more prone to certain biases (Peters et al., Reference Peters, Vastfjall, Slovic, Mertz, Mazzocco and Dickert2006; Reyna & Brainerd, Reference Reyna and Brainerd2008; Reyna et al., Reference Hogarth and Einhorn2009). These results are a problem for dual-process models because they directly contradict explicit predictions of those models (e.g., Epstein’s rational-experiential inventory, REI, is supposed to explain and predict biases; see Reyna & Brainerd, Reference Reyna and Brainerd2008). Indeed, a major motivation for dual-process theories has been to account for both logical or rational thinking and violations of logic and probability theory as manifested in heuristics and biases; the latter were said to originate chiefly through intuition (e.g., Epstein, Reference Epstein1994; Kahneman, Reference Brainerd and Reyna2003; Peters et al., Reference Peters, Vastfjall, Slovic, Mertz, Mazzocco and Dickert2006). (Again, the question is not whether standard intuition theorists can provide post hoc rationalizations of results that run counter to their core mechanisms, but, rather, the question is what the mechanisms of those theories actually predict.) Not all intuition theorists are standard dualists, however (e.g., Betsch & Glöckner, Reference Betsch and Glöckner2010).

As fuzzy-trace theory predicts, unconscious gist-based intuition often produces superior reasoning (when there is a gist to uncover) compared to conscious analytical thought that focuses on superficial details (Dijksterhuis, Bos, van der Leij, & van Baaren, Reference Dijksterhuis, Bos, van der Leij and van Baaren2009). The overall developmental shift, according to fuzzy-trace theory, is from greater reliance on verbatim-based analysis to greater reliance on gist-based intuition in reasoning, judgment, and decision making (e.g., Reyna & Brainerd, Reference Reyna and Brainerd1995a, 2011). Rather than facilitating reasoning (or being neutral) as classic decision theories assume, verbatim memory can interfere with reasoning. To take one example of a counterintuitive effect of verbatim memory on reasoning, experiments on fuzzy-trace theory showed that removing numbers and other background information (so that verbatim memory faded) systematically improved reasoning involving those numbers, especially in reasoners likely to focus on superficial details. In these problems, quantitative information suggested the wrong answer, but the qualitative gist supported the right answer (Brainerd & Reyna, Reference Brainerd, Reyna and Brandse1995). Therefore, worse memory for numbers was associated with better reasoning performance (this effect was not about a few data points; rather, there was a negative dependency, an inverse correlation, between memory accuracy and reasoning performance across the range of data points; Reyna & Brainerd, Reference Reyna and Brainerd1995a). Conversely, increasing cognitive load to high levels has been shown to leave gist-based reasoning unimpaired (e.g., see Brainerd & Reyna, Reference Brainerd and Reyna1992; Reyna, Reference Reyna and Kiernan1995; Reyna & Brainerd, Reference Reyna and Brainerd1990).

Rather than discard the classic distinction between intuition and analysis entirely, fuzzy-trace theory refined and augmented it. (For a review of how the theory handles conflicts between emotion and inhibition, see Rivers et al., Reference Rivers, Reyna and Mills2008.) Two kinds of reasoning—verbatim-based analysis and gist-based intuition—were retained in the theory, accompanied by developmental and individual differences in impulsivity (or lack of inhibition; Reyna, Estrada, et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011; Reyna & Rivers, Reference Reyna and Rivers2008). Note that there is a role for rote stimulus-response (or stimulus-stimulus) associations in fuzzy-trace theory. These kinds of mindless associations or rote computations would fall under verbatim-based processes, as opposed to gist-based processes (e.g., matching bias, Evans, Reference Brainerd and Reyna2011; see also Liberali et al., Reference Liberali, Reyna, Furlan, Stein and Pardo2011; Wolfe, Reyna, & Brainerd, Reference Wolfe, Reyna, Brainerd and Mestre2005). Association, as in stimulus-response driven choice, is an example of rote processing, and, thus, are verbatim-based processes, as opposed to intuition as defined in fuzzy-trace theory (see Glöckner & Witteman, Reference Glöckner and Witteman2010). These fuzzy-trace theory distinctions are not simply opinions, but, instead, are justified by specific findings (e.g., see Brainerd et al., Reference Brainerd, Reyna and Mojardin1999; Reference Reyna and BrainerdReyna & Brainerd, 1995a, Reference Reyna and Brainerd1995b).

Intuition in fuzzy-trace theory is similar to the old ideas about intuition in some ways: It is fuzzy rather than precise, operates in parallel rather than being serial, and typically is unconscious and automatic (a conclusion resting on evidence from mathematical models and experiments). However, intuition is not necessarily primitive and it is not a result of rote stimulus-response (or stimulus-stimulus) associations, in contrast to Sloman’s (Reference Sloman1996, 2002) and others’ conceptions (e.g., Gilovich, Griffin, & Kahneman, Reference Baron2002; Glöckner & Witteman, Reference Glöckner and Witteman2010). Rather than being mindless and low-level, the core construct of cognition in fuzzy-trace theory (the fuzzy trace, also called gist) is based on meaning—on extracting the essential, bottom-line meaning of information.

Hence, fuzzy-trace theory differs from standard views of intuition, which is what is new about this new intuitionism. On the one hand, there is the classical view of intuition as an unconscious, fuzzy, parallel process, and then, on the other hand, there are notions of meaning, and usually meaning and intuition do not go together. However, in this theory, gist—the central construct—is at the intersection between intuition and meaning (Figure 3). In real life, in natural decision making, people are meaning makers. They look for meaning (e.g., for patterns that can be interpreted), and they base their judgments and decisions on that essential meaning (e.g., Gaissmaier & Schooler, Reference Gaissmaier and Schooler2008; Proulx & Heine, Reference Proulx and Heine2009; Reyna, Reference Reyna, Chapman, Dougherty and Confrey2012; Wolford, Newman, Miller, & Wig, Reference Wolford, Newman, Miller and Wig2004). What is the meaning of the event or the information, in the broad sense? Typically, people encode multiple meanings for a given stimulus. The gist representations of a stimulus encompass the meaning to us as individuals, the meaning to us based on our life history, and the meaning in our culture (Reyna, Reference Reyna2004, 2008; Reyna & Adam, Reference Reyna and Adam2003; Reyna et al., Reference Reyna, Nelson, Han and Dieckmann2009). In the following section, I discuss how this concept of gist representations of information plays out in specific psychological phenomena, and how representations are combined with retrieval of social values and moral principles, which are then applied to those representations to produce judgments and decisions.

Figure 3:

A new intuitionism: Fuzzy meaning

3.1 Risk-taking: Framing effects in adults

In this section, I discuss examples of phenomena studied under the rubric of fuzzy-trace theory. As noted, the early work on framing was aimed at the question, “Do judgment and decision making process memory in the narrow sense?”, and the answer was, surprisingly, no. As an example, precise verbatim information (e.g., exact numbers) was neither necessary nor sufficient to observe framing effects (e.g., Kühberger & Tanner, Reference Kühberger and Tanner2010; Reyna & Brainerd, Reference Reyna and Brainerd1991, Reference Reyna and Brainerd1995a). I first discuss psychophysical predictions of traditional approaches, such as prospect theory, followed by predictions from fuzzy-trace theory for these same manipulations (see Figure 2). The main point of these comparisons is not whether prospect theory might accommodate some of these results after the fact, but whether the psychophysics of numbers is both necessary and sufficient to observe the range of observed framing effects.

Framing effects describe shifts in risk preferences, for instance, from risk aversion when prospects are described in terms of gains (e.g., money won or number of people saved) to risk seeking when the same prospects are described in terms of losses (e.g., money lost or number of people who died; Tversky & Kahneman, Reference Tversky and Kahneman1986; cumulative prospect theory predicts risk seeking for gains with small probabilities and risk aversion for losses with small probabilities, but the decisions in Figures 4 and 5 do not involve small probabilities). Most theories of framing effects rely on the psychophysics of quantities, exemplified in perceived diminishing returns as quantities, such as money, increase. (Technically, the concept is diminishing marginal utility.) Expected utility theory, subjective expected utility theory, prospect theory, cumulative prospect theory and so on rely on the general psychophysical account of diminishing returns for outcomes, and that outcomes trade off with probabilities (i.e., are combined multiplicatively); in some accounts probabilities are processed nonlinearly, too (Tversky & Kahneman, Reference Tversky and Kahneman1986; Reference Tversky and Kahneman1992). Experiments show that adults process both outcomes and probabilities (so failing to encode or process probability does not account for results presented below), and that they combine numerical outcomes and probabilities multiplicatively (see Reyna & Brainerd, Reference Reyna, Brainerd, Wright and Ayton1994; Figures 1 & 2). Although adults process outcomes and probabilities multiplicatively (i.e., they compute something like expected value), the issue is whether framing effects arise from this numerical processing.

Early research on fuzzy-trace theory challenged the predictions of psychophysical theories (e.g., Reyna & Brainerd, Reference Reyna and Brainerd1991; Reyna & Ellis, Reference Reyna and Ellis1994). For example, how could framing effects derive from the psychophysics of quantities if numbers could be removed from the problems and framing effects increased? This effect is called the nonnumerical framing effect (see Reference Reyna and BrainerdReyna & Brainerd, 1995a). If one ignores the psychophysical mechanisms through which framing effects are produced in prospect theory, non-numerical loss-versus-gain differences can be explained by invoking evaluation from a reference point and loss aversion. However, it is difficult, to explain larger framing effects under some deletion conditions compared to when numbers are present. The issue at hand, nonetheless, is whether the psychophysics of numerical quantities (e.g., dollars, probabilities) is necessary to observe framing effects.

Figure 4 shows results from three different conditions in which numerical information was deleted. In some problems, we took outcomes out and put vague phrases in (e.g., a 1/3 probability of saving many people and 2/3 probability of saving no one); in some problems, we only took the probabilities out and put in vague phrases (e.g., some probability of saving 600 people and a higher probability of saving no one); and in some problems, we took them both out and put in vague phrases (Reyna & Brainerd, Reference Reyna and Brainerd1991, Reference Reyna and Brainerd1995a). As is evident from Figure 4, framing effects were preserved in all conditions, and were largest when both numerical outcomes and probabilities were deleted. If all of the numbers are taken out of these problems, and replaced with vague phrases, the necessary ingredients according to expected utility theory, prospect theory, and so on, have been deleted. The nonlinear perception of the numbers is supposed to cause the framing effect. However, nonnumerical framing effects demonstrate that numbers are not necessary to observe the effect. These results cannot be explained by ambiguity aversion because a) in some conditions, subjects preferred the ambiguous option, but moreover b) preference ratings remained high even when both options were ambiguous.

Figure 4:

Nonnumerical framing effects. Deleting numbers from framing problems and replacing them with vague words, “some” and “none” (probabilities deleted = 200 saved vs. some probability of saving 600 and a higher probability of saving none; outcomes deleted = some saved vs. 1/3 probability of saving many and 2/3 probability of saving none; both deleted = some saved vs. some probability of some saved and some probability none saved); Reyna & Brainerd, Reference Reyna and Brainerd1991, 1995

But, are these numbers sufficient to cause framing effects? Again, the most popular and enduring theories of decision making have assumed that the psychophysics of these numbers was sufficient to cause framing effects. To test the sufficiency hypothesis, another class of manipulations was implemented called selective attention effects (e.g., Reyna & Brainerd, Reference Reyna and Brainerd1995a, 2011). It is not obvious how to explain all of the critical selective attention results using prospect theory or any of the other expected utility variants (Table 2; see also Kühberger & Tanner, Reference Kühberger and Tanner2010): For example, how could deleting zero make framing effects disappear? Deleting zero focuses attention on the specific numbers critical to either to prospect theory or to utility theory; yet, it eliminates framing effects.

Table 2:Predictions of prospect theory and fuzzy-trace theory for three selective attention conditions (one example shown, but effects have been replicated for many problems).

Figure 5 shows effects of selectively focusing attention on parts of the gamble; two variations on selective attention effects are displayed. (Note that missing parts of the gamble were presented in the preamble to eliminate ambiguity; thus, when all three groups had the same information, the pattern shown in Figure 5 is observed; Reference Reyna and BrainerdReyna & Brainerd, 1995a; 2011.) These experiments address the question of whether supposedly key numbers are sufficient to observe framing effects. For example, in the gain frame of the Asian disease problem, the key numbers, according to expected utility and prospect theory, are 200 saved versus a 1/3 probability of 600 saved. In the loss frame, the key numbers according to these theories are 400 die versus 2/3 probability that 600 die. These numbers are supposed to provide everything needed to show framing effects. (The zero complement of the gamble literally multiplies out to equal zero.) Thus, focusing attention on these numbers should produce identical framing effects (compared to full-complement, traditional versions of the problem), according to psychophysical theories.

Figure 5:

Selective attention effects. Framing problems with variations in gambles—focusing on nonzero complement shown at the left, both complements (traditional presentation) shown in the middle, or zero complements shown at the right. Labels are shown for the Asian disease problem, but the data are from multiple problems (each of which shows the effect).

In contrast, according to fuzzy trace theory, an attenuation of framing should be observed under this condition of focusing on “key” numbers because the decision maker does not focus on the categorical contrast between some and none, a simple gist (discussed below). As you can see in Figure 5, there is little or no framing effect when attention is focused on the supposedly critical numbers, an effect that has been replicated in different languages and cultures (e.g., Betsch & Kraus, Reference Betsch and Kraus1999; Kühberger, Reference Kühberger1995; Kühberger & Tanner, Reference Kühberger and Tanner2010; Mandel, Reference Mandel2001; Stocké, Reference Stocké, Druwe and Kunz1998). When the categorical contrast is put in the background, the decision becomes about “six of one versus half a dozen of another” (as the aphorism goes), and no framing effect is observed.

What happens if the opposite truncation of the gamble is performed, another selective attention manipulation (Table 2)? In this variation of the gain frame, for example, the 1/3 probability of 600 saved is put in the background information, and the focus is on the contrast between 200 saved and none saved. According to fuzzy trace theory, this variation highlights the some-none contrast: some people are saved or there is a categorical possibility that no one is saved. Therefore, an increase in the framing effect should be observed, and, in fact, this is what the studies showed (Figure 5). As noted earlier, this categorical gist is encoded in parallel with verbatim analysis of something like expected value; so the claim is not that people are insensitive to expected value, on the contrary (see Reference Reyna and BrainerdReyna & Brainerd, 1995a; Figures 1 & 2). When the expected values of the options are equal (or close to it), however, focusing attention on categorical contrasts between options produces sharp preferences, in spite of the equivalence in expected value.

This series of experiments on selective attention effects pits predictions characterizing decision making in terms of psychophysical transformations of probabilities and outcomes, which trade off, against predictions that decision making boils down to essential meaning: simple categorical or ordinal distinctions (e.g., better to save some lives than to save none; for a recent summary of these effects and a model, see Reyna & Brainerd, Reference Reyna and Brainerd2011). The effects shown in Figures 4 and 5—making framing effects disappear and making these effects larger—fall out of the assumptions of fuzzy-trace theory. It is possible to explain some of these findings with prospect theory (or cumulative prospect theory) by going beyond its psychophysical mechanisms, but it is not obvious how all of the effects in Figures 4 and 5 can be accommodated by that approach.

Fuzzy-trace theory’s assumptions built directly on those of prospect theory, not only about gain-loss distinctions, but also about editing and cancellation (Tversky & Kahneman, Reference Tversky and Kahneman1986; Reference Tversky and Kahneman1992). Prospect theory seems to capture what people do when they process numbers, but more often than not, people make decisions based on crude qualitative contrasts (some-none or low-high) rather than on numerical details (Reyna, Reference Reyna and Rivers2008). How people mentally represent quantities in judgments and decisions, along with the social and moral values that they retrieve and apply to their representations, determine behaviors, such as choices.

Moreover, the level of representation is not arbitrary, but, rather, begins at the lowest or simplest level of gist (the nominal, or categorical, level) and proceeds up the hierarchy of gist (increasing in precision) until a choice can be made (e.g., Hans & Reyna, Reference Hans and Reyna2011). Applying this principle, the representation of the gamble “1/3 probability of saving 600 lives and 2/3 probability of saving no one” in the Asian disease problem is most simply characterized in categorical terms: save some people or save none. Similarly, the simplest representation of the sure option of “200 saved” in the Asian disease problem is some saved. The fuzzy-processing principle stipulates that the lowest level of gist, the categorical or some-none distinction, is attempted first because it is the simplest gist (e.g., Reyna & Brainerd, Reference Reyna and Brainerd1995a). That is, if one thinks of any kind of numerical quantity, the simplest distinction that can be made is at the nominal (some vs. none) level, corresponding to the lowest scale of measurement. This level is sufficient to discriminate options, so the decision maker does not proceed to more precise representations (as would be required to discriminate between two gambles; see Reyna & Brainerd, Reference Reyna and Brainerd1995a; 2011). Thus, the gist of the Asian disease problem boils down to a choice between saving some people versus saving some people or saving none, favoring the selection of the sure option in the gain frame; the same simple dichotomization favors selection of the gamble option in the loss frame (Reyna, Reference Reyna and Rivers2008).

However, implicit in these preferences is a principle of valuing human life (Reyna & Casillas, Reference Reyna, Casillas, Bartels, Bauman, Skitka and Medin2009). (Other decisions cue other values, such as valuing money or health, which are then applied to representations of the decision options in order to generate a preference.) Retrieving and applying a value for human life (e.g., for the Asian disease problem) is required in order to generate a preference between the sure option (save some people) and the gamble (save some people or save none). If decision makers had this some-none representation, but did not have this human-life value, they would not necessarily have a preference, even though the representation was simple. It is this value, retrieved in the context of choice, that allows someone to decide between the sure option versus the gamble option. Stored in long-term memory is a qualitative social value for human life—a moral value—that saving some people is better than saving none (Reyna & Casillas, Reference Reyna, Casillas, Bartels, Bauman, Skitka and Medin2009; see also Mills et al., Reference Mills, Reyna and Estrada2008; Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011).

Therefore, in the gain frame, because saving some people is better than saving none, one prefers the sure option. In the loss frame, the mental processes are analogous to those in the gain frame, but the resulting preference is exactly the opposite. If some people die for sure, and none dying is preferred over some dying, now one chooses the gamble option. Algorithmically applying the same representation and retrieval processes (e.g., retrieval of social/moral values) to the loss frame produces the framing effect—and accounts for its variations. Additional variations include that framing effects increase, rather than disappear, with repeated choices presented within subjects (e.g., in contrast to decision field theory’s predictions; see Reyna & Brainerd, Reference Reyna and Brainerd1995a). Also, framing effects disappear if people are told that whatever they choose will be re-enacted many times, effectively removing the zero outcome of the gamble, and, hence, removing the categorical contrast between some and none (Reyna, Reference Reyna and Rivers2008; Reference Reyna and BrainerdReyna & Brainerd, 1995a). These effects, as well as the nonnumerical and selective attention effects discussed earlier, are predicted by the representational and retrieval assumptions of fuzzy-trace theory.

3.2 Risk-taking: Framing effects in children and adolescents

After the initial demonstrations of nonnumerical framing and selective attention effects, Ellis and I conducted the first study on framing in children—showing that framing effects developed with age (Reyna & Ellis, Reference Reyna and Ellis1994). This result mirrored other emerging developmental results for similar reasons. Reyna and Ellis argued that the representativeness heuristic and other biases increased with age, too, because of an increased reliance on gist-based intuition (e.g., Davidson, Reference Davidson1995; Jacobs & Potenza, Reference Jacobs and Potenza1991). Young children were found to be loss averse, as adults are (Reyna, Reference Reyna1996a), but they roughly calculated and responded similarly to gain and loss frames in true framing (as opposed to reflection) problems: when net gains are the same for gains and for so-called “losses” problems (for reflection problems, gains are compared to actual losses). In particular, young children did not show framing effects for true framing problems when “losses” were explicitly displayed in front of them, eliminating the need to subtract or to remember outcomes (for discussion, see Reyna, Estrada, et al., Reference Estrada and Reyna2011). Rather than show gist-based framing effects, young children appear to roughly calculate expected value, and they modulate their choices based on the magnitudes of risks and rewards (e.g., Figner et al., Reference Figner, Weber, Mackinlay and Wilkening2009; Reyna & Farley, Reference Reyna and Farley2006; Schlottmann & Anderson, Reference Schlottmann and Anderson1994).

However, fuzzy-trace theory does not assume that verbatim-based analysis (e.g., of risk and reward) is replaced by gist-based intuition in development. Instead, fuzzy-trace theory incorporates a duality: numerical calculation (verbatim-based analysis) and gist-based intuition both develop from childhood to adulthood. When instructions are simplified and tasks are clear, young children (four to six years of age, depending on the study) behave rationally, in the sense that they traded off risks and rewards (for a review, see Reyna & Farley, Reference Reyna and Farley2006). Their ability to calculate—to multiply magnitudes of risks and rewards—improved during roughly the same period that framing biases and other numerical fallacies also emerged (Reyna & Brainerd, Reference Reyna, Brainerd, Wright and Ayton1994).

Therefore, cuing and context elicited mathematically astute judgments early in development (e.g., Acredolo et al., Reference Acredolo, O’Connor, Banks and Horobin1989; Rakow & Rahim, Reference Rakow and Rahim2009; Siegler, Reference Siegler1981) followed by heuristics and biases later in development that, thus, coexisted with mathematical competence. Furthermore, mathematical performance improved during the same period in which heuristics and biases emerged for seemingly mathematical tasks, such as probability judgment and decision making (i.e., framing problems in which expected value, as a function of numerical probabilities and numerical outcomes, varied; Figner et al., Reference Figner, Weber, Mackinlay and Wilkening2009; Levin, Hart, Weller, & Harshman, Reference Levin, Hart, Weller and Harshman2007; Levin, Weller, Pederson, & Harshman, Reference Levin, Weller, Pederson and Harshman2007; Reyna & Brainerd, Reference Reyna, Brainerd, Davies and Logie1993, 1994, 2008). In sum, framing and other judgment-and-decision-making biases grew with age during childhood, consistent with fuzzy-processing preferences being present in adulthood (see also Markovits & Dumas, Reference Markovits and Dumas1999 and Morsanyi & Handley, Reference Morsanyi and Handley2008, but see Klaczynski, Reference Klaczynski, Jacobs and Klaczynski2005).

3.3 Gist-based intuition increases with age and experience

More generally, the emergence of framing effects is an example of how reliance on gist-based intuition increases with age and experience. If one considers theories of the development of reasoning from childhood to adulthood, there are many reasons to expect that reasoning should only get better (in the traditional sense of being more quantitatively sophisticated and less biased). Working memory capacity increases, inhibition and cognitive control improve, and metacognition develops during that age period (e.g., Bjorklund, Reference Bjorklund2012). A person becomes a better computer all the way around, from childhood, to adolescence, to adulthood. In all standard developmental and dual process theories — if an age difference is observed — it should generally reflect improvement in reasoning and judgment-and-decision-making performance. However, there are many demonstrations of the opposite developmental trend–the framing example is only one of them–of increases in biases with age (Reyna & Brainerd, Reference Reyna and Brainerd2011; Reyna & Farley, Reference Reyna and Farley2006). Increases in biases or distortions are called developmental reversals because they reverse the usual expectation of developmental progress (e.g., Brainerd, Reyna, & Ceci, Reference Brainerd, Reyna and Ceci2008; Reyna & Ellis, Reference Reyna and Ellis1994; Reyna & Farley, Reference Reyna and Farley2006).

Developmental reversals were predicted by fuzzy-trace theory, but they have been found serendipitously, too. According to the theory, these increases are predicted because they reflect gist-based meaning biases. Shown in false memory as well as in reasoning, meaning-based processing increases with age from childhood to adulthood. (For a review of studies on developmental increases in memory distortion, see Brainerd, Reyna, & Zember, Reference Brainerd, Reyna and Zember2011.) A study conducted by Markovits and Dumas (Reference Markovits and Dumas1999) is instructive for understanding increases in reasoning biases. They presented transitive inference problems to young children (transitive inference questions are on IQ tests—A is bigger than B, B is bigger than C, therefore A is bigger than C). Young children generally get these problems right (Reyna & Brainerd, Reference Reyna and Brainerd1990; Reyna & Kiernan, Reference Reyna and Kiernan1994). For example, “Paul is taller than Harry, and Harry is taller than Sam; is Paul is taller than Sam?” Young children get that problem right. What if Paul is a friend of Harry, and Harry is a friend of Sam, is Paul necessarily a friend of Sam? Young children say, “No! That’s not logical,” which is correct.

As children get older, systematic errors go up in the friendship version of the problems. Older children are more likely to conclude erroneously that Paul is a friend of Sam. That erroneous inference increases with pragmatic knowledge, social knowledge, and so on, because knowledge supports the processing of meaning (e.g., Reyna, Reference Reyna1996a). However, as the emergence of framing effects shows, knowledge differences are not essential to observing increases in gist-based intuition. Older theories acknowledge the possibility of meaning-based distortions, but they claim either that reasoning is inherently biased or that such biases are artifacts (e.g., Liben, Reference Liben, Kail and Hagen1977). Both verbatim analysis (e.g., calculating expected value) and gist-based intuition (e.g., belief bias as illustrated in inferences about friendship) coexist in the adult mind, according to fuzzy-trace theory. The interplay of these two kinds of processing has been used most recently to explain adult biases in conjunction and disjunction judgments (e.g., Brainerd & Reyna, Reference Brainerd, Yang, Reyna, Howe and Mills2008; Brainerd, Reyna, & Aydin, Reference Brainerd, Reyna and Aydin2010; Brainerd, Reyna, Holliday, & Nakamura, Reference Brainerd, Reyna, Holliday and Nakamura2012; Reyna & Brainerd, Reference Reyna and Brainerd2008; Wolfe & Reyna, Reference Wolfe and Reyna2010).

To summarize, during childhood, despite increasing skill in calculation, including in calculating probabilities and expected value, the tendency to use the bottom-line meaning in many situations goes up faster than the tendency to rely on computational ability. Mathematical models are useful in testing such predictions involving opposing processes, in this instance, verbatim-based analysis versus gist-based intuition (e.g., Reyna & Brainerd, Reference Reyna and Brainerd2011). Models incorporating simple assumptions from fuzzy-trace theory have been tested for goodness-of-fit to real data and evaluated against alternative models (e.g., see Brainerd, Reyna, & Howe, Reference Brainerd, Reyna and Howe2009; Brainerd et al., Reference Brainerd, Reyna and Mojardin1999). The heart of a mathematical model of a psychological process, such as decision making, is not the mathematics, but, rather, the interpretation of the mathematics in terms of core constructs. The core constructs in fuzzy-trace theory are verbatim and gist representations that are encoded and processed in parallel, and which support analysis versus intuition, respectively. Verbatim and gist representations compete against each other for control of task performance; the winner depends on which memory is more accessible and the constraints of the task (see Figure 1). In general, gist is more accessible and more useful than verbatim representations—especially when gist is informed by age and experience.

3.4 Risk-taking from lab to life: Adolescents and young adults

As noted earlier, gist-based “false” memory has been a research theme, explained by the same processes discussed hitherto for judgment and decision making. False memory, occurring when people remember things that never happened as though they did happen, typically derives from unconscious meaning-based inferences (e.g., Brainerd & Reyna, Reference Brainerd and Reyna2005; Reyna, Holliday, & Marche, Reference Reyna, Holliday and Marche2002). A lesson learned from the false-memory literature is that seemingly “artificial” laboratory tasks explain real-world forensic situations—when those tasks tap causal mechanisms (Brainerd, Reyna, & Estrada, Reference Brainerd, Reyna and Estrada2006; Reyna, Mills, Estrada, & Brainerd, Reference Reyna, Mills, Estrada, Brainerd, Toglia, Read, Ross and Lindsay2006). Indeed, the conclusions discussed below are drawn from an extensive review of the literature on real-life risk taking as well as from laboratory data from behavioral and brain studies (Reyna & Farley, Reference Reyna and Farley2006; Reyna, Chapman et al., Reference Reyna, Chapman, Dougherty and Confrey2012). Popular myths, such as that adolescents underestimate risks, have been studied extensively and ruled out by multiple investigators. Therefore, underestimation of risk, changes in beliefs, and other conventional wisdom do not account for the effects I now discuss.

Applying the lesson that laboratory findings bear on real life to the problem of risk taking, I have more recently examined risky decision making of adolescents, portrayed in the literature as paradigmatic examples of irrational decision makers (Reyna, et al., Reference Reyna, Adam, Poirier, LeCroy, Brainerd, Jacobs and Klaczynski2005; Steinberg, Reference Steinberg2008). Extrapolating decision-making mechanisms from laboratory to life, is it possible to explain adolescent risk taking? Laboratory tasks reveal that overall risk taking (collapsing gains and losses) declines from childhood to adulthood, a robust pattern across studies (Boyer, 2008; Reyna & Farley, Reference Reyna and Farley2006). (Tasks that add the experience of actual outcomes—children experience wins and losses—cloud assessment of risk preferences per se: Figner et al., Reference Figner, Weber, Mackinlay and Wilkening2009; Reyna & Brainerd, Reference Reyna, Brainerd, Wright and Ayton1994).

As noted earlier, around preschool age, there is no consistent difference between risk preferences for gains (e.g., win 2 prizes) and for identical net gains (e.g., have 4 prizes, then lose 2 prizes) phrased in terms of losses (in contrast, aversion to actual losses is present early in childhood, Reyna, Reference Reyna1996a). The biasing effect of context, that net gains were achieved as a result of losses, emerges in childhood (Galvan, Reference Galvan, Reyna, Chapman, Dougherty and Confrey2012). Although risk preferences for gains versus gains framed as losses are similar in preschoolers, such preferences begin to diverge for elementary schoolers.

Specifically, a pattern of preferences begins to emerge around second grade that my colleagues and I have called reverse framing (Estrada & Reyna, Reference Estrada and Reyna2011; Reyna & Ellis, Reference Reyna and Ellis1994; Reyna, Estrada, et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011; these problems do not involve small probabilities, and so results are not predicted by cumulative prospect theory). Reverse framing is the opposite of standard framing: It is a preference for the gamble option in the gain frame, but the sure option in the loss frame. Recall that, when expected value is equal, risk and reward trade off in these problems. Thus, in reverse framing, second graders choose the gamble more in the gain frame; they go for the larger rewards (i.e., the greater gains in the gamble; see also Reyna & Farley, Reference Reyna and Farley2006). Apparently, second graders compare numerical outcomes in the loss frame, too; they go for the smaller losses in the sure thing, relative to the losses in the gamble (focusing on probabilities would have produced opposite preferences). So, unlike younger children who process both risk and reward—two dimensions—older children mainly focus on the one dimension of reward outcomes. (To clarify, younger children are capable of processing both dimensions under carefully simplified conditions, but their preferences shift during this period to a focus on outcomes; and each of these developmental differences should be distinguished from the additional complexities of strategy selection as information value varies; see Mata, Helversen, & Rieskamp, Reference Mata, von Helversen and Rieskamp2011).

In early adolescence, the emergence of standard framing can be detected (e.g., Chien et al., Reference Chien, Lin and Worthley1996; Reyna & Ellis,1994; Reyna, Estada, et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). As the studies discussed in an earlier section show, standard framing is evidence for a qualitative processing strategy—the assimilation of different numerical outcomes into a categorical gist of “some,” as opposed to none (and assimilation of probabilities into sure vs. variable). (Standard framing is evidence for qualitative processing because that hypothesis accounts for all of the effects reviewed earlier, as opposed to alternative hypotheses that do not account for all of the effects.) Consistent with this hypothesis, younger adolescents who are just beginning to exhibit standard framing, are more likely to assimilate outcomes when the outcomes are similar to one another than when they differ: Therefore, it makes sense that standard framing emerges first for smaller outcomes (e.g., 1 prize for sure vs. 50% chance of 2 prizes or nothing), but reverse framing remains for larger outcomes (e.g., 30 prizes for sure vs. a 50% chance of 60 prizes or nothing). In other words, the difference in outcomes is greater for larger (e.g., 60 – 30 = 30) than for smaller outcomes (e.g., 2 – 1 = 1). High school students also show reverse framing for larger outcomes (e.g., Estrada & Reyna, Reference Estrada and Reyna2011; Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011).

Thus, children and adolescents are sensitive to quantitative differences between outcomes, manifest in a reverse framing pattern, whereas adults rarely exhibit reverse framing (e.g., DeMartino et al., 2006; Levin, Gaeth, Schreiber, & Lauriola, Reference Levin, Gaeth, Schreiber and Lauriola2002; Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). This developmental trend from a focus on quantitative differences to qualitative categories is consistent with fuzzy-trace theory’s assumption of increases in gist-based intuition with age. Intriguingly, deviation from consistency across frames grows with age until the adult pattern of standard framing is evident. By traditional yardsticks (e.g., Tversky & Kahneman, Reference Tversky and Kahneman1986), then, irrationality grows from childhood to adulthood. Yet, youth are assumed to be more irrational in their risk taking in real life, compared to adults (Committee on the Science of Adolescence, 2011; Reyna & Farley, Reference Reyna and Farley2006; Steinberg, Reference Steinberg2008). How can the risk preferences of lab and life be reconciled?

For gains, the downward trend across age in preference for risk, as measured objectively in the laboratory, is fairly stable. Most real-life risk taking in developed countries involves gains rather than losses, and thus preferences in the lab and in life can be somewhat reconciled (Reyna & Rivers, Reference Reyna and Rivers2008). In addition, real-life increases in risk taking, such as in drunk driving and unprotected sex, are associated empirically with increased freedom and, hence, greater “risk opportunity” in older adolescence and young adulthood, compared to younger ages (Gerrard et al., Reference Gerrard, Gibbons, Houlihan, Stock and Pomery2008). However, as illustrated by reverse framing, adolescents also differ cognitively and motivationally from adults (e.g., see also Chick & Reyna, Reference Chick, Reyna, Reyna, Chapman, Dougherty and Confrey2012; Galvan, Reference Galvan, Reyna, Chapman, Dougherty and Confrey2012). Youth are more likely to compare reward magnitudes, and to take risks to achieve more positive outcomes. According to fuzzy-trace theory, their greater reliance on verbatim-based analysis (e.g., quantitative differences) aids and abets the motivational shifts in adolescence that support risk taking. The cognitive shift from greater reliance on verbatim-based analysis (e.g., quantitative differences) to gist-based intuition (qualitative contrasts) in adults discourages risk taking because it allows adults to avoid unhealthy outcomes–even when unhealthy outcomes are unlikely, such as HIV infection (Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011; Rivers et al., Reference Rivers, Reyna and Mills2008).

In 2006, based on a review of the literature in many domains of adolescent risk taking, Reyna and Farley concluded that precise, hair-splitting calculation of risks and rewards promotes risk taking among adolescents, whereas simple, all-or-none gist protects against unhealthy risk taking—the opposite of most theories of risk taking (e.g., Fischhoff, Reference Fischhoff2008). This prediction was also borne out in subsequent studies (e.g., Mills, Reyna, & Estrada, Reference Mills, Reyna and Estrada2008; Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). Moreover, cognitive measures of verbatim-based analysis versus gist-based intuition (i.e., verbatim hairsplitting vs. simple categorical gist) predicted larger variance, and unique variance, in real-life self-reported risk taking, compared to motivational factors such as reward sensitivity (e.g., sensation seeking; Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011).

Reverse framing, in particular, loaded with other measures of verbatim-based analysis in principal component analyses, and these verbatim measures predicted greater vulnerability to real-life risk taking. In contrast, gist-based intuition was consistently associated with lower levels of unhealthy risk taking. For example, agreement with simple gist principles such as “Avoid risk” and with categorical gist statements such as “It only takes once to get pregnant” was associated with lower levels of sexual initiation, lower intentions to have sex, and fewer sexual partners (Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). Consistent with fuzzy-trace theory, gist-based intuition was more “advanced” in the sense that it was associated with better outcomes (for discussion of coherence and correspondence criteria of rationality in fuzzy-trace theory, see Adam & Reyna, Reference Adam and Reyna2005; Reyna, Reference Reyna and Rivers2008; Reyna & Adam, Reference Reyna and Adam2003; Reyna & Brainerd, Reference Reyna, Brainerd, Wright and Ayton1994; Reyna, Lloyd & Brainerd, Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003; Reyna & Farley, Reference Reyna and Farley2006; Reyna & Lloyd, Reference Reyna and Lloyd2006).

Most theories of adolescent risk taking recognize that something like inhibition or cognitive control (which includes the ability to regulate emotions) also develops during this period. This assumption is shared by fuzzy-trace theory (e.g., Reyna, in press; Reyna & Mills, Reference Reyna, Mills, Gorfein and MacLeod2007b). However, fuzzy-trace theory parts company with traditional theories by assuming that such inhibition is a third factor, beyond the two types of reasoning referred to as verbatim-based analysis and gist-based intuition. Empirical evidence bears this out: behavioral inhibition increases with age during adolescence and young adulthood and accounts for unique variance beyond reasoning styles (Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). The growth of inhibition is consistent with the development of fronto-striatal circuitry during this period (Casey et al., Reference Casey, Getz and Galvan2008; Giedd et al., Reference Giedd, Reyna, Chapman, Dougherty and Confrey2012; see also Roiser et al., Reference Roiser, De Martino, Tan, Kumaran, Seymour, Wood and Dolan2009).

Thus, mature adults differ from immature adolescents in more than the ability to rein in emotional and motivational responses (e.g., to tempting rewards), although such differences are important (Somerville et al., Reference Somerville, Jones and Casey2010). Adolescents also differ in the way in which they think about reward. If offered a million dollars to play Russian roulette, an adult quickly refuses. An adolescent appears to conduct a cost-benefit analysis, which is irrational under these circumstances, according to fuzzy-trace theory (e.g., Reyna et al., Reference Reyna, Adam, Poirier, LeCroy, Brainerd, Jacobs and Klaczynski2005). Compensatory reasoning—is the reward worth the risk—sounds smart and it fits traditional definitions of rationality. Many economists would make the argument that it is rational to play Russian roulette if the reward were large enough (or to smoke if the benefits outweighed the costs for that individual; Reyna & Farley, Reference Reyna and Farley2006). Others would say that the game has infinite disutility, which is another way to say that it seems categorically crazy, a gist-based, all-or-none intuition.

Therefore, investigating rationality through the lens of teenage behavior challenges basic assumptions (e.g., for a recent review of research on adolescent risk taking, see Reyna, Chapman, Dougherty, & Confrey, Reference Reyna, Chapman, Dougherty and Confrey2012; for a review of theory, including the neuroscience of risky decision making, see Reyna & Rivers, Reference Reyna and Rivers2008). Although some theorists have argued that adolescents are more impulsive than adults are—but equivalent to adults cognitively—fuzzy-trace theory implies that there are important cognitive changes from childhood to adulthood. These cognitive changes should produce decreases in risk preference for gains (or rewards) (Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011). After reviewing the literature on children’s and adolescents’ risk taking (see Reyna & Farley, Reference Reyna and Farley2006), it became apparent that many take risks because they analyze and trade off risk and reward. Simple alternative explanations, such as that adolescents lack experience and thus must deliberate (Hogarth, Reference Hogarth2001), are not antithetical to this hypothesis. However, they do not explain the range of results encompassed by the fuzzy-trace theory hypothesis that lacking experience contributes to reliance on a particular kind of processing, verbatim-based analysis of risk and reward, and a lack of fundamental insight into the gist of risky decisions (see Reyna, Estrada et al., Reference Reyna, Estrada, DeMarinis, Myers, Stanisz and Mills2011).

Explicitly, one-time risks (e.g., having unprotected sex one time) are often low and rewards (or benefits) are high; this imbalance promotes risk taking if one analyzes risk and reward. Drawing on results from both the framing task and other risk-taking research inside and outside of the lab, it appears that, as teens become adults, they do less analysis for the decisions that matter (e.g., Lenert, Sherbourne, & Reyna, Reference Lenert, Sherbourne and Reyna2001). They do not engage in compensatory reasoning, despite encoding risk and reward and despite being capable of multiplying them in a compensatory fashion. Rather, decisions are based on the bottom line gist, as adolescents grow up into mature adults (Committee on the Science of Adolescence; Board on Children, Youth, and Families; Institute of Medicine and National Research Council, 2011). A summary paper in Medical Decision Making reviews implications for prevention problems in public health, especially concerning teenagers and infectious diseases, such as HIV (Reyna, Reference Reyna and Rivers2008). A randomized control trial of over 800 adolescents followed for one year found that inculcating gist-based intuitions using fuzzy-trace theory produced significant reductions in risk taking relative to a control curriculum and to another comprehensive risk-reduction curriculum (Reyna, Mills, & Estrada, Reference Reyna, Mills, Estrada, Brainerd, Toglia, Read, Ross and Lindsay2008).

3.5 Risk-taking from lab to life: Experts

At the top of the developmental heap, experts have been a focus of research on fuzzy-trace theory (e.g., Adam & Reyna, Reference Adam and Reyna2005; Reyna, Reference Reyna2004; Reyna & Adam, Reference Reyna and Adam2003; Reyna & Lloyd, Reference Reyna and Lloyd2006; Reyna, Lloyd, & Brainerd, Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003). Experts are entrusted with decisions about health and safety, and, thus, their risk perception and decision processes are important to understand. For example, an emergency-room physician must decide whether a patient is at risk of a heart attack; a meteorologist must decide whether a community is at risk of being struck by a hurricane; and a lawyer must evaluate potential damage awards and decide whether a client should settle or risk going to trial (e.g., Hans & Reyna, Reference Hans and Reyna2011; Reyna, Reference Reyna2004). In addition to domain knowledge, conventional wisdom and many theories suggest that experts apply precise analytical and numerical reasoning skills to achieve the best outcomes, whereas novices are more likely to reason non-analytically and non-numerically (e.g. Epstein, Reference Epstein1994; Peters et al., Reference Peters, Vastfjall, Slovic, Mertz, Mazzocco and Dickert2006; but see Betsch & Haberstroh, Reference Betsch and Haberstroh2005, for alternative views of expertise).

However, recent research on individual differences in analytical and numerical reasoning challenges conventional assumptions about advanced reasoning (e.g., Liberali et al., Reference Liberali, Reyna, Furlan, Stein and Pardo2011; Reyna & Brainerd, Reference Reyna and Brainerd2008; for a review of the literature on numeracy, see Reyna, Nelson, Han, & Dieckmann, Reference Hogarth and Einhorn2009). For example, even experts in quantitative fields struggle with concepts such as risk and probability (e.g., Nelson et al., Reference Nelson, Reyna, Fagerlin, Lipkus and Peters2008; Perneger & Agoritsas, Reference Perneger and Agoritsas2011; Reyna & Brainerd, Reference Reyna and Brainerd2007; Reyna, Lloyd, & Whalen, Reference Reyna, Lloyd and Whalen2001). Furthermore, those high in numeracy are prone to systematic errors when their processing is rote or verbatim (e.g., Peters et al., Reference Peters, Vastfjall, Slovic, Mertz, Mazzocco and Dickert2006; see Reyna et al., Reference Hogarth and Einhorn2009).

According to fuzzy-trace theory, experts differ developmentally from novices, and should rely more often on gist-based intuition rather than verbatim-based analysis (see also Hogarth & Einhorn, Reference Brainerd and Reyna1992; Shanteau, Reference Shanteau1992). This view is not unlike Hogarth’s (Reference Hogarth2001) idea of educated intuition, which experts acquire as a result of experience that affords insight. As might be expected from our discussion of the gist origins of framing effects, a recent study comparing risk experts (i.e., experienced intelligence officers) to college students and to non-expert adults found that the framing bias was significantly larger among the experts who had extensive real-world experience with risk, even when sensation seeking and other factors were controlled (Reference ReynaReyna, 2011a). Thus, experts focus on the “deep structure” of decisions in their domain of expertise, on gist representations that eschew surface details, despite encoding both gist and verbatim (surface) representations (e.g., Reference Chi and FeltovichChi & Feltovich,1981).

Consistent with this developmental expectation, my colleagues and I have found that experts used less information, and processed it less precisely, to make decisions, compared to novices (e.g., Reyna, Reference Reyna2004; Reyna & Lloyd, Reference Reyna and Lloyd2006; Reyna et al., Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003). For example, we have shown that more-expert physicians have better discrimination than less-expert physicians regarding predictions of medical outcomes, but the former rely on simpler gist-based representations to achieve this discrimination (Lloyd & Reyna, Reference Lloyd and Reyna2009; Reyna & Lloyd, Reference Reyna and Lloyd2006). Hence, precise information processing was not associated with better judgments of patient risks or better emergency-room decisions about patients—on the contrary.

Nevertheless, experts’ risk and probability judgments violated internal coherence (e.g., Adam & Reyna, Reference Adam and Reyna2005; Reyna & Adam, Reference Reyna and Adam2003; Reyna & Lloyd, Reference Reyna and Lloyd2006). In particular, for judgments regarding emergency room admissions, about 1 out of 3 judgments were incoherent among physicians, for real as well as hypothetical patients. These physicians judged the probability that a patient was at risk of a myocardial infarction (heart attack) or had clinically significant coronary artery disease, or both, to be lower than the probability that the same patient had one or the other condition. The three elicited probability judgments were incoherent; the logic of their probabilities just did not make sense (see Reyna et al., Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003, for an overview). Yet, those physicians who displayed this internal incoherence, nevertheless, were able to discriminate low-risk from high-risk patients very effectively. My research team and I followed patient’s actual outcomes after they had been seen in the emergency department and verified that more expert physicians (cardiologists) were better able to discriminate low versus high risk patients (based on practice guidelines and on subsequent cardiac outcomes within a year), but they were still as prone to heuristics and biases as generalist physicians.

More generally, experts show framing biases, conjunction and disjunction fallacies, and so on despite good correspondence (e.g., good discrimination of low vs. high risk; Adam & Reyna, Reference Adam and Reyna2005; Kostopoulo, Reference Kostopoulou and Kattan2009; Perneger & Agoritsas, Reference Perneger and Agoritsas2011; Reyna, Reference Reyna2004; Reyna & Adam, Reference Reyna and Adam2003; Reyna, Lloyd, & Brainerd, Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003; Reyna, Lloyd, & Whalen, Reference Reyna, Lloyd and Whalen2001). For example, physicians exhibit base-rate neglect: Suppose that the base rate of a disease is 10% and a diagnostic test for that disease is 80% accurate (i.e., an 80% chance of a “positive” result if the patient has the disease; an 80% chance of a “negative” result if the patient does not have the disease). If a patient has a positive test result, how likely is it that he or she has the disease; is it closer to 30% or to 70%? As Reyna (Reference Reyna2004) reported for a sample of 82 physicians, only 31% of physicians selected the correct answer (of 30%), well below chance. Despite almost daily feedback about how base rates combine with diagnostic test results (and formal training in Bayes’ theorem as part of medical education), these experts violated coherence. For these and other biases that violate coherence, coherence and correspondence do not appear to converge with experience over time, which makes sense given their explanations derived from fuzzy-trace theory. (See Reyna et al., Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003; for process models, see Reyna, Reference Reyna and Brainerd1991; Reyna & Brainerd, Reference Reyna and Brainerd2008; Reyna & Mills, Reference Reyna and Mills2007a; Wolfe & Reyna, Reference Wolfe and Reyna2010.) As predicted by fuzzy-trace theory, measures of coherence and correspondence are not the same thing. The intension, or gist, of probabilities does not obey the same rules as the extension, or reality, of the outcomes (see Reyna, Reference Reyna and Brainerd1991; Reyna & Brainerd, Reference Reyna and Brainerd2008; Reyna & Farley, Reference Reyna and Farley2006).

In sum, there are people who are logically coherent and those who have good outcomes, and these are not necessarily the same people. Coherence errors (internal inconsistency, such as violations of axioms of preference) are not necessarily related to correspondence errors (external correspondence to reality), such as good vs. bad medical outcomes. Fuzzy-trace theory provides a perspective on rationality that encompasses both coherence and correspondence (see also Reyna & Farley, Reference Reyna and Farley2006). Degrees of rationality are distinguished in fuzzy-trace theory based on process models identifying the cognitive loci of errors in different tasks; some errors are dumber than others and they tend to occur earlier in development (Reyna & Brainerd, Reference Reyna and Brainerd2011; Reyna et al., Reference Reyna, Lloyd, Brainerd, Schneider and Shanteau2003; Reyna & Farley, Reference Reyna and Farley2006). Errors of both coherence and correspondence generally decrease with greater reliance on gist-based intuition. Therefore, the answer to the question, “Does the brain calculate [numerical] value?” is “yes” in fuzzy-trace theory (Vlaev, Chater, Stewart, & Brown, Reference Vlaev, Chater, Stewart and Brown2011), and this valuation sometimes wins out, but the more developmentally advanced brain relies mainly on the results of qualitative, meaning-based processes despite verbatim valuation.