Mind Mach (2006) 16:365 380
DOI 10.1007/s11023-006-9035-1
How causal knowledge simplifies decision-making
Rocio Garcia-Retamero Ć Ulrich Hoffrage
Received: 23 February 2005 / Accepted: 14 November 2005 /
Published online: 11 August 2006
Ó Springer Science+Business Media B.V. 2006
Abstract Making decisions can be hard, but it can also be facilitated. Simple
heuristics are fast and frugal but nevertheless fairly accurate decision rules that
people can use to compensate for their limitations in computational capacity, time,
and knowledge when they make decisions [Gigerenzer, G., Todd, P. M., & the ABC
Research Group (1999). Simple Heuristics That Make Us Smart. New York: Oxford
University Press.]. These heuristics are effective to the extent that they can exploit
the structure of information in the environment in which they operate. Specifically,
they require knowledge about the predictive value of probabilistic cues. However, it
is often difficult to keep track of all the available cues in the environment and how
they relate to any relevant criterion. This problem becomes even more critical if
compound cues are considered. We submit that knowledge about the causal struc-
ture of the environment helps decision makers focus on a manageable subset of cues,
thus effectively reducing the potential computational complexity inherent in even
relatively simple decision-making tasks. We review experimental evidence that
tested this hypothesis and report the results of a simulation study. We conclude that
causal knowledge can act as a meta-cue for identifying highly valid cues, either
individual or compound, and helps in the estimation of their validities.
Keywords Causal knowledge Ć Compound cue Ć Cue selection Ć Fast and frugal
heuristics Ć Search processes Ć Take the Best Ć Take the Best Configural Ć
Validity estimation
R. Garcia-Retamero (&)
Max Planck Institute for Human Development, Lentzeallee 94, D-14195 Berlin, Germany
e-mail: [e-mail]
U. Hoffrage
Ecole des Hautes Etudes Commerciales, Université de Lausanne, CH-1015 Lausanne-
Dorigny, Switzerland
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Introduction
When we are faced with a decision, for example, which restaurant to go to or which
meal to order, it is often impossible to consider all the available alternatives and to
gather and process all the information regarding these options. For instance, we
generally do not consider every restaurant in the city, and when we do select one, we
often do not have much detail about the entrees on the menu (e.g., the amount of
cholesterol, fat, or preservatives in the dishes, the cooking methods used, or how
they taste) to help us infer which one we would like most. In fact, in real-life
situations such as this, we often make fast decisions based on little information.
Recently, Gigerenzer, Todd, and the ABC Research Group (1999) have suggested
that we use simple heuristics in these situations, that is, fast and frugal but never-
theless fairly accurate strategies for making decisions with a minimum of informa-
tion (see also Todd & Gigerenzer, 2000). These rules are fast because they do not
involve much computation, and they are frugal because they search for only some of
the available information in the environment.
One of the fast and frugal heuristics proposed by the ABC research group is
Take The Best (TTB; Gigerenzer & Goldstein, 1996, 1999). This heuristic is de-
signed for so-called two-alternative forced-choice tasks and can be used to infer
which of two alternatives has a higher value on a quantitative criterion, such as
which of two university professors earns more money. The alternatives are de-
scribed on several dichotomous cues such as gender or whether the professor is on
the faculty of a state or a private university. These cues allow to make probabilistic
inferences about the criterion. Like each of the fast and frugal heuristics that has
been proposed in the context of this research program, TTB is constructed from
building blocks, which are the precise steps of information gathering and pro-
cessing involved in making a decision. Specifically, this heuristic has a search rule,
which defines the order in which to search for information (TTB looks up cues in
the order of their validity, i.e., the probability that a cue will point to the correct
decision given that it discriminates between the alternatives); a stopping rule,
which specifies when the search is to be stopped (TTB stops after the first
discriminating cue); and a decision rule, which specifies how to use the information
that has been looked up when it comes to making a decision (TTB chooses the
alternative favored by the first discriminating cue).
The TTB heuristic and an extension of TTB for comparisons among more than
two alternatives have been subjected to empirical tests in a number of studies (e.g.,
Bröder, 2000, 2003; Bröder & Schiffer, 2003a; Newell, Rakow, Weston, & Shanks,
2004; Newell & Shanks, 2003; Rieskamp & Hoffrage, 1999). There is accumulating
experimental evidence for the use of this heuristic, particularly when there are
search costs for accessing cues (see Bröder, 2000, 2003; Bröder & Schiffer, 2003b), or
when decisions have to be made under time pressure (e.g., Rieskamp & Hoffrage,
1999). In addition, Newell, Weston, and Shanks (2003) tested the building blocks of
TTB separately and reported that 75% of participants followed TTB s search rule by
validity. Furthermore its stopping and decision rules were obeyed in 80% and 89%
of the trials, respectively (see also Newell & Shanks, 2003).
However, these experimental results on the use of TTB need to be qualified. In
most of these studies, participants were encouraged to use cues in the order of their
validity by being informed about cue validities or the validity order (see Bröder,
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2000, 2003; Bröder & Schiffer, 2003b; Newell et al., 2003). In two studies that tested
search by validity against alternative search orders, validity was not the search cri-
terion that predicted participants searches best (Läge, Hausmann, Christen, &
Daub, 2005; Newell et al., 2004) because participants were instead making use of
simple rules for ordering cues based on trial-by-trial learning (Dieckmann & Todd,
2004; see also Garcia-Retamero, Takezawa, & Gigerenzer, 2006). The cue orderings
established through such rules do not necessarily converge toward the ordering
established by validity. Therefore, participants might have had difficulties computing
cue validities and then ordering cues accordingly even though they were dealing in
those experiments with relatively few cues (i.e., four to six).
The problem of finding a good cue ordering appears even more severe if one
considers that in most situations, there are myriad potential cues that could be used
to make a decision, and it is practically impossible to keep track of them all and to
compute their validities for any potentially relevant criterion (Juslin & Persson,
2002). Cue selection is further complicated if potential combinations of cues (i.e.,
compound cues) are taken into account. Yet sometimes an accurate decision re-
quires us to do so. For example, some medications might have side effects, such as
nausea, if ingested together with alcohol, whereas neither the drug nor the alcohol
would cause any problems if ingested alone (of course, this would also depend on the
amount of alcohol that is consumed). Thus, the relationship between one cue (the
ingestion of a medication) and the criterion (nausea) depends on the presence of
another cue (the ingestion of alcohol). The problem is that in real-world environ-
ments, there exist a multitude of potential combinations of cues to form compounds,
rendering it nearly impossible to keep track of them all. As a consequence, a strategy
that processes all possible compound cues as configurations would be too compu-
tationally demanding. Nor is it plausible to assume that the brain comes   prewired 
with a representation for each of the combinations of elementary stimulus inputs
(Kehoe & Graham, 1988).
Bearing these comments in mind, the interesting question is whether there is a way
in which the relevant cues, individual or compounded, can be selected from the
abundance of possibilities in the environment. We hypothesize that people do not
process all possible cues in their natural environments but rather use their causal
knowledge, that is, their knowledge about causal relationships between events in the
environment, to focus on a small and manageable subset of relevant cues. We further
assume that causal knowledge might also aid learning of cue validities. In sum, causal
knowledge might allow decision makers to deal adaptively with the huge number of
individual and compound cues that appear in the environment by directing them to
those that are potentially relevant. In the remainder of this paper, we offer more
precise predictions about how causal knowledge can influence decision-making
processes and review several experiments and a simulation study, all conducted within
the fast-and-frugal heuristic framework, in which these predictions were tested.
The adaptive value of knowledge about the causal texture of the environment
The adaptive importance of causal processing has been stressed by many authors in a
wide range of disciplines (see Gopnik & Schulz, in press, for a review), including
computer science (e.g., Pearl, 2000), philosophy (Glymour, 1998; Harre & Madden,
1975; Hume, 1987; Kant, 1965; Mackie, 1974; White, 1995), developmental
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psychology (Gopnik et al., 2004; Koslowski & Masnick, 2002; Schlottmann, 1999),
and cognitive psychology (Ahn & Kalish, 2000; Cheng, 1997; Garcia-Retamero, in
press; Waldmann, Holyoak, & Fratianne, 1995). We have a general tendency to
consider connections between events in terms of causal relationships, and we
understand, predict, and control our environment by positing underlying causal
mechanisms that generate our sensory experience (Lagnado & Sloman, 2004).
When it is said that a cause brings about an effect, the implication is that there is a
stable causal link between the cause and the effect and an underlying causal
mechanism that is an essential property of this link (Ahn & Kalish, 2000; Glymour &
Cheng, 1999). Such a link between a cause and an effect goes beyond the mere
covariation between them as the cause produces the effect (Cheng, 1997; Novick &
Cheng, 2004). Having causal knowledge about the cues in the environment is
adaptive for individuals because it allows them to make predictions about future
events and to intervene in the ecology to bring about new events (Gopnik et al.,
2004; Lagnado & Sloman, 2004; Steyvers, Tenenbaum, Wagenmaker, & Blum, 2003;
Waldmann & Hagmayer, 2005). Therefore, it is quite conceivable that natural
selective pressures have, over the course of evolution, established some genetic basis
for causal thinking (Shultz, 1982). Causal beliefs are not isolated but are tightly
connected with other causal beliefs in a broad base of knowledge that represents the
causal structure of the environment, henceforth referred to as a causal mental model.
There are two main approaches in the psychological literature to explain how
causal links between events can be inferred. The bottom-up approach assumes that
observing or experiencing correlations among events could help in the generation of
these causal links or in the adjustment of existing ones (Cheng, 1997; Glymour &
Cheng, 1999; Gopnik et al., 2004; Koslowski & Masnick, 2002; Novick & Cheng,
2004; Shanks & Dickinson, 1987; Spellman, 1996). The top down approach was
advanced by Waldmann (Waldmann & Holyoak, 1992; Waldmann et al., 1995; see
also Ahn & Kalish, 2000; Harre & Madden, 1975; White, 1995), who argued that
people s abstract knowledge about causality (such as causal directionality) shapes
how data are interpreted.
When it comes to decision-making, we posit that causal knowledge is advanta-
geous for three reasons. First, causal knowledge might act as a meta-cue for iden-
tifying valid cues in the environment. Second, causal knowledge might help us focus
on certain cues, which, in turn, facilitates learning of cue validities. Third, causal
knowledge might guide people in the selection of the relevant compound cues in the
environment. We now elaborate on each of these three advantages in more detail.
Considering the first advantage, we hypothesize that cues that are causally linked
to a criterion tend to be more valid than other cues lacking such a connection to the
criterion (Garcia-Retamero, Wallin, & Dieckmann, 2006; see also Ahn & Kalish,
2000; Wallin & Gärdenfors, 2000). For instance, lung cancer (here, an effect) is more
likely to be predicted from a well-established smoking habit (i.e., a cause) than from
yellowed fingers (i.e., a second effect of the common cause; see Boyle, 1997). Fur-
thermore, correlations between events that are causally linked are likely to be more
robust across environments, that is, less sensitive to contextual changes, than those
without such a connection (Pearl, 2000; Reichenbach, 1956). Following our example,
the correlation between smoking and lung cancer would be more robust across
different series of patients than the correlation between lung cancer and yellowed
fingers would be. We could expect this to be the case even if we control for other
alternative causes that could bring about yellowed fingers (e.g., being a painter) that
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might reduce their predictability for lung cancer. We hypothesize that this asym-
metry between causal and non-causal cues that holds in the physical world would be
reflected in human cognitive processes. We therefore expect decision makers to use
their causal knowledge as a meta-cue for selecting highly valid and robust cues in the
environment.
Besides facilitating the selection of valid cues in the environment, causal
knowledge might reduce the number of cue criterion correlations to keep track of
when computing cue validities (Garcia-Retamero et al., 2006). This hypothesis is
supported by research using multiple cue probability learning (MCPL) tasks. In this
paradigm, participants have to predict the criterion of a given object from multiple
cues that are probabilistically related to this criterion. Previous empirical studies
using this paradigm (see Kruschke & Johansen, 1999, for a review) suggest that there
exists interference effects when multiple cues are available and, consequently, cue
validities have to be learned concurrently. For instance, if irrelevant cues are present
in such a task, the utilization of valid cues is reduced and, consequently, the accuracy
of people s judgments is lower as compared to a condition in which these irrelevant
cues are not included (Castellan, 1973; Edgell & Hennessey, 1980). One can explain
this finding, which can be observed even after a large number of learning trials,
by assuming that in the condition with the irrelevant cues it is harder for participants
to identify and focus on the valid cues. In contrast, when participants can learn
cue criterion relationships sequentially, that is, for one cue after another, their
judgments more closely correspond to the ecological correlations (Brehmer, 1973).
Based on this finding we suggest that in multiple-cue settings people equipped with
causal knowledge might be able to use this knowledge to focus on certain cues,
which, in turn, might facilitate learning of cue validities.
Note, however, that causal knowledge about the cues in the environment also has
to be learned. Therefore, our argument holds only if the acquisition of causal
knowledge is simpler than the learning of cue validities. We think that this is, in fact,
the case. Consider, for instance, learning of causal Bayes nets. Such learning is
certainly not necessarily simple, but it could be simplified if prior specific or abstract
domain knowledge about the structure of the environment (e.g., causal direction-
ality) constrains the number of potential causal relations that need to be considered
(see Tenenbaum, Griffiths, & Niyogi, in press; Waldmann, 1996; Waldmann &
Martignon, 1998).1
The third advantage of causal knowledge is that it can guide people in the
selection of the relevant compound cues in the environment that should be repre-
sented as configurations (see Garcia-Retamero, Hoffrage, Dieckmann, & Ramos, in
press b). Specifically, we hypothesize that when people perceive several cues to act
through a common causal mechanism in bringing about an effect, they will consider
the possibility that these cues might also interact with each other in bringing about
that effect. This possibility may lead them to check whether the accuracy of their
predictions would be increased through representing these cues as a configuration.
1
Along these lines, research in the field of artificial intelligence has recently proposed a number of
algorithms capable of easily inferring causal relations from covariation patterns (e.g., the TETRAD
II program; Spirtes, Glymour, & Scheines, 1993, 2000). These algorithms use causal models to
generate a certain pattern of statistical dependencies and then search for certain clues that reveal
fragments of the underlying structure. These fragments are pieced together to form a coherent causal
model. Obviously, these systems do not provide information about how humans learn causal links,
but they do tell us how such a task might be solved.
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370 R. Garcia-Retamero, U. Hoffrage
This might be the case in the medicine/alcohol example mentioned above. Specifi-
cally, the effect of a medicine would be expected to be modulated by the ingestion of
alcohol with both agents being taken up in the blood, and only the presence of both
might cause nausea. Therefore, processing a compound cue as a configuration is an
emergent property of a causal mental model of the environment when the compound
cue s components are perceived to act jointly through the same underlying causal
mechanism. As configural processing requires extra cognitive effort, we expect that
when cues are perceived to act through different causal mechanisms, they will be
represented as several individual elements. This might be the case if we have to
predict the speed of a cyclist while taking tailwind and physical strength into ac-
count. These cues would be expected to affect the criterion independently.
In short, we hypothesize that causal knowledge might allow decision makers to
constrain the countless number of combinations of cues that appear in a particular
environment to a subset for which it is more likely that configurations have a high
predictive value. In the following sections, we review some experiments conducted
to test whether causal knowledge helps people to select a subset of reliable (indi-
vidual or compound) cues and aids learning of cue validities.
Causal knowledge helps us select cues in the environment
In two experiments, Garcia-Retamero et al. (2006) examined the impact of pro-
viding causal information about cue criterion relationships on decision-making
processes. More specifically, these authors analyzed whether causal knowledge
about the cues in the environment had an effect on the selection of a subset of cues
that were used to make decisions, and whether that knowledge made the compu-
tation of cue validities easier. Specifically, we tested the following predictions.
Based on our assumption that causal knowledge can help us identify highly valid
cues in the environment, we hypothesized that participants would look up cues that
were causally connected to the criterion (in short, causal cues) earlier than non-
causal cues, even when they had the same validity.2 They would also rely more on
causal cues than on non-causal cues in their decisions, and they would be more
confident and faster in their decisions when causal cues were available than when no
causal cues were available. On the other hand, given that causal knowledge reduces
the number of cue criterion relationships to keep track of to compute validity, we
hypothesized that participants would be more exact in their validity estimates for
causal than for non-causal cues and consequently would also be more accurate in
their inferences.
The two experiments tested these hypotheses. The first addressed the basic
assumption that causal cues are preferred over non-causal cues. The second repre-
sented a stronger test by allowing participants to learn the validities of the cues after
they had received information about which cues were causally related to the crite-
rion. The experiments were computer based and used two-alternative forced-choice
tasks. On each trial, participants were presented with two alternatives (i.e., two
species of insects) and had to decide which would show a higher criterion value (i.e.,
2
For the sake of brevity, we just distinguished between causal and non-causal cues in these
experiments, thereby ignoring alternatives such as indirect causal relationships (e.g., causal chains;
see Waldmann & Hagmayer, 2001).
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which would do more damage to a crop). To make this decision, they could look up
information on up to four cues (i.e., properties of the insects, such as the presence or
absence of a particular metabolic factor), represented by little boxes on the screen
that could be clicked to retrieve information (see Bröder, 2000, 2003; Newell &
Shanks, 2003; Rieskamp & Hoffrage, 1999, for a similar experimental procedure).
Two of these cues had, counterbalanced across participants, a high validity (.85) and
the other two a low validity (.65). All four cues had a discrimination rate of .56.3
Causal knowledge was manipulated in a between-subjects design. In the causal
group, participants were provided with information that causally related two of the
cues to the criterion via the experimental instructions (e.g.,   the metabolic factor
makes the insects hungry and aggressive  ). For these two cues, the instructions
suggested an underlying causal mechanism that went beyond the possible covaria-
tion between the cue and the criterion. The remaining two cues were neutral. Here,
participants received information that did not link the cue causally to the criterion
(e.g.,   the metabolic factor leads to green and blue coloration of the insects body  ).
Which cues were causally linked to the criterion and which were neutral was
counterbalanced across participants. In the control group, information about all four
cues was neutral. A pre-test confirmed that the causal cues, but not the neutral cues,
were indeed perceived as having a strong causal effect on the criterion.
In Experiment 1, participants went through a decision phase in which information
about whether the cues were present or absent was not automatically displayed;
instead they had to look up information for one cue after another. When a cue was
looked up (at the cost of 1 cent) the cue values of both alternatives were shown.
After looking up one cue, participants could stop and decide on one of the alter-
natives at any time. After each decision, participants received feedback about
whether the decision was correct (if so, they earned 7 cents). At the end of the
experiment, participants made an estimation of cue validities. In Experiment 2,
before they entered the decision phase, participants went through a learning phase in
which the values of the four cues were automatically provided to allow participants
to learn cue validities. Note that the actual cue validities were not provided.
Otherwise, Experiment 2 was identical to Experiment 1.
In line with our hypothesis, the results of Experiment 1 show that when causal
information about some of the cues was available, without a separate phase for
learning cue validities before decision making, participants preferred to start
searching with a causal cue, regardless of its validity. They also followed the causal
cues more often than the neutral ones and were faster and more confident in their
decisions than when they did not have causal cues to rely on. Finally, participants
were also more precise in estimating the validities of the causal cues than those of
the neutral ones. Note that, in this experiment, they could check which cues were
reliable predictors of the criterion throughout the decision-making phase of the
experiment, but they still preferred to rely just on causal cues.
When participants had the opportunity to learn about cue validities before the
actual decision-making phase (i.e., in Experiment 2), their search processes were
influenced by both causal information and validity. Specifically, participants in the
causal group preferred to start by looking up the causal high-validity cue over the
rest of the cues. Furthermore, these participants became more accurate in their
3
The discrimination rate of a cue is the proportion of pair comparisons in which the value of that
cue in the two decision alternatives differs (Gigerenzer & Goldstein, 1996).
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decisions. They also achieved, on average (i.e., across all cues), a higher precision in
estimating cue validities. Overall, the higher frugality and accuracy in the causal
group led to a higher final payoff than in the control group.
These results could be interpreted as evidence that participants perceived causal
information as indicative of highly valid cues in the environment, as they gave
priority to causal cues in both the search and the decision processes. Furthermore,
causal knowledge seems to facilitate cue validity learning, as participants in the
causal group were more precise in their validity estimations. In sum, our experi-
mental results show that information about the causal relations between cues and
criterion could be used as a meta-cue for identifying and selecting relevant cues in
the environment, helping participants target a manageable subset of cues and,
consequently, leading to more accurate learning of cue validities.
Causal knowledge helps us process cues as configurations
Garcia-Retamero et al. (in press b; see also Garcia-Retamero, Hoffrage, & Dieck-
mann, in press a) went one step further and analyzed whether causal knowledge
might also guide people in the selection of the relevant compound cues in the
environment in order to improve the accuracy of their inferences. Note that fast and
frugal heuristics do not take compound cues into account to predict a criterion.
However, as we said above, this is sometimes required to make accurate predictions.
For example, according to the diathesis-stress model, hereditary predisposition and a
current stressor (e.g., a traumatic experience) are assumed to be necessary for the
onset of certain diseases such as schizophrenia (Walker & Diforio, 1997) or
depression (Abela & Seligman, 2000). Previous studies have shown that people can
and do process compound cues in some problems (Edgell, 1993; Shanks, Charles,
Darby, & Azmi, 1998; Williams & Braker, 1999). However, none of the fast and
frugal heuristics proposed so far by Gigerenzer et al. (1999) can adequately deal with
such problems.
With this in mind, Garcia-Retamero et al. (in press b) raised the question of
whether the repertoire of fast and frugal heuristics could include a strategy that
processes compound cues. In particular, they proposed the Take The Best Configural
heuristic (TTB Configural for short). Like TTB, TTB Configural is a heuristic in
which cue search is ordered according to the cues validities. In contrast to TTB,
however, TTB Configural also includes compound cues in the cue search ordering
under some conditions. TTB Configural begins searching with the cue that has the
highest validity be it an elemental or a compound cue. If the cue search ordering
requires that a compound cue be looked up, TTB Configural looks up the cues that
jointly constitute that compound. Correspondingly, the stopping rule entails that as
soon as a cue (either individual or compound) discriminates, search for further
information is stopped. As far as the decision rule is concerned, TTB Configural
decides in favor of the alternative to which the cue (be it an individual or a com-
pound cue) points.
We posit that the use of TTB Configural is supported by causal knowledge be-
cause such knowledge may help to identify the relevant compound cues in the
environment. Specifically, when the decision maker expects that several cues act
through a common causal mechanism in bringing about the criterion, such cues will
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Causal knowledge and simple heuristics 373
be represented as a compound and subsequently included in the cue search order of
cues according to validity.4
Gigerenzer et al. (1999) pointed out that the specific decision-making strategy
that is selected to be used should be contingent on the structure of the environment
(see also Rieskamp & Otto, 2006). One issue in the literature on configural strategy
use that has generated special interest is whether linearly separable environments
are easier to learn than non-linearly separable ones, which indeed seems to be the
case (see Kimmel & Lachnit, 1991; Lachnit & Kimmel, 1993; Smith, Murray,
& Minda, 1997; but see Shanks et al., 1998). Bearing these findings in mind, Garcia-
Retamero et al. (in press a, in press b) hypothesized that the type of environment
that participants receive in the experimental task (i.e., linearly versus non-linearly
separable) would have an impact on the probability that TTB Configural is used.
One non-linearly separable problem that has generated special interest is the
eXclusive-OR (or XOR, for short) problem (Medin & Schwanenflugel, 1981;
Rumelhart, Hinton, & Williams, 1986). In an environment in which two cues, A and
B, are amalgamated into a compound that obeys the XOR logical rule, an object for
which one (and only one) of these cues is present is more likely to have a higher
criterion value than an object for which either both or neither of these cues is present
(i.e., A1B0, A0B1 > A1B1, A0B0, where 1 denotes that the cue is present, 0 denotes
that the cue is absent, and > denotes the expectation of a higher criterion value).
This problem is non-linearly separable as it cannot be solved by a strategy that
predicts an outcome based on a linear function of the weighted cues without an
interaction term (Zurada, 1992). In contrast, the AND problem has a linearly sep-
arable structure. In an environment in which two cues are amalgamated into a
compound that obeys an AND logical rule, an object for which these cues are
present is more likely to have a higher criterion value than an object for which only
one or neither of these cues is present (i.e., A1B1 > A1B0, A0B1, A0B0).
Garcia-Retamero et al. (in press a, in press b) were interested in what effect the
type of environment that participants encountered had on participants strategy
selection, and how the causal mental model with which they approached these
environments influenced the type of strategy they used. In these experiments, the
two-alternative forced-choice tasks were framed as a medical diagnostic task. Spe-
cifically, participants were presented with information about two patients and had to
choose the one with the higher body temperature. The information provided about
the patients was whether they had ingested three different substances (referred to as
A, B, and C, respectively). In the first phase of the experiment, participants were
provided with information about all three cues in a given comparison at no cost.
They then had to make a decision. Outcome feedback about the correct option was
given in this phase to enable participants to learn the cues validities. Subsequently,
they went through a decision-making phase in which the information was no longer
automatically displayed; instead they had to look it up sequentially by clicking boxes
on the computer screen to retrieve the information. The acquisition of cue infor-
mation was costly. Again, outcome feedback was provided.
In these experiments, Garcia-Retamero et al. (in press a, in press b) used both
simple and complex environments, that is, environments that are best handled
through TTB and TTB Configural, respectively. Two complex environments were
4
Note that, in this case, both the components and the compound cue would be included in the
hierarchy of cues ordered according to their validity.
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generated in which two of the three cues (i.e., A and B) were amalgamated into a
highly valid compound cue that obeyed either the XOR or the AND logical rule. In
these environments, the validity of the critical compound, AB, was 1.00, but the
validity of each of its component cues, A and B, was .50, thus corresponding to pure
guessing. The third cue, C, which was not included in the compound, had a validity of
.75. Consequently, these environments allowed high separability between the
strategies being studied. Whereas participants using TTB should start by looking up
cue C (the only individual highly valid cue in these environments) and should decide
on the basis of this cue whenever it discriminates, participants using TTB Configural
should start by looking up cues A and B first and should decide on the basis of the
compound AB whenever it discriminates. A simple environment was also generated.
In this environment, the validity of the compound AB was .50, as was the validity of
each of its component cues. Just as in the complex environments, the validity of cue
C was .75. That is, this was the only individual valid cue in this environment. Thus,
the difference between the complex and simple environments resided in the validity
of the critical compound cue, AB.
Garcia-Retamero et al. (in press a, in press b) also manipulated, in a between-
subjects design, participants causal mental model of the environment through
instructions. Particularly, we induced either a configural, an elemental, or a neutral
causal model. In the configural causal model, the instructions emphasized that cues
act through the same causal mechanism in bringing about the criterion. We assumed
that these instructions would then lead participants to search for valid compound
cues in the environment. In the elemental causal model condition, the instructions
emphasized that the cues acted through different causal mechanisms to bring about
the criterion. We assumed that these instructions would lead participants to process
cues as individual elements in the environment. In the third condition, the neutral
causal model, participants did not receive any information about the possible causal
mechanisms through which the cues acted. Therefore, this condition would show
how participants searched for information and how they decided spontaneously. In
short, having in mind a configural, an elemental, or a neutral causal model, partic-
ipants received an XOR, an AND, or a simple environment (see Table 1).
Garcia-Retamero et al. (in press a, in press b) hypothesized that the configural
causal model would facilitate the detection of the highly valid compound cue in the
environment. Therefore, we expected that a high percentage of participants would
use the TTB Configural heuristic when there was a valid compound cue in the
environment and their causal knowledge about the cues hinted toward a common
causal mechanism. However, for the elemental causal model condition (i.e., when
participants were told that cues acted through different causal mechanisms), we
hypothesized that most of the participants would behave elementally using the TTB
heuristic. We expected this to be the case even if there was a perfectly valid
Table 1 Design and experimental hypotheses of the experiment conducted by Garcia-Retamero
et al. (in press a, in press b). TTB denotes Take The Best; TTB Configural denotes Take The Best
Configural
Configural causal model Elemental causal model Neutral causal model
XOR environment TTB Configural TTB TTB
AND environment TTB Configural TTB TTB Configural
Simple environment TTB TTB TTB
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Causal knowledge and simple heuristics 375
compound cue in the environment. For the neutral causal model condition, we
wondered whether we would find evidence for spontaneous TTB Configural use
(however, this applies only to the linearly separable environment, because a linearly
separable structure is easier to learn than a non-linearly separable one; Lachnit &
Kimmel, 1993; Smith et al., 1997). Finally, when there were no highly valid com-
pound cues in the environment, we expected that a high percentage of participants
would behave elementally using TTB, regardless of their causal mental model. To
classify participants according to a particular strategy in our experiments, we used
the Bayesian method for multiple-attribute decision-making proposed by Bröder
and Schiffer (2003a).
In accordance with our hypotheses, results in the experiment show that a high
percentage of participants decided according to the highly valid compound cue,
using the TTB Configural heuristic, when they had a configural causal mental model
of the environment, that is, when causal knowledge suggested that the component
cues acted through a common causal mechanism (see Table 2). Interestingly, this
result was found regardless of whether the component cues were amalgamated into a
compound by applying a non-linearly or a linearly separable logical rule. However,
we found more evidence of TTB Configural use in the linearly separable structures
than in the non-linearly separable ones.
Additionally, even if there was a perfectly valid compound in the environment, a
high percentage of participants represented its component cues as independent
elements and used the elemental TTB heuristic when (1) these cues were said to act
through different causal mechanisms (in the elemental causal model condition),
and also when (2) they had no causal knowledge about the cues in the environment
(in the neutral causal model condition). This result was also found regardless of
whether the component cues were amalgamated into a compound by applying a non-
linearly or a linearly separable logical rule. Finally, when there was no highly valid
compound cue in the environment, that is, in the control condition, the elemental
TTB was also the most frequently used strategy.
In short, results in these experiments suggest that TTB Configural was used only
when the information structure in the environment and in the mind fit together, that
is, when the causal knowledge about the cues induced participants to search for
highly valid compound cues in the environment and a highly valid compound cue
existed. When either of these requirements was not met, the elemental TTB was the
best behavioral model. Consequently, these results support the hypothesis that
causal knowledge could also act as a meta-cue for identifying highly valid compound
cues in the environment. These results are in line with research in the categorization
arena showing that providing participants with a hint that encouraged the additive
integration of features greatly facilitated learning of linearly separable categories
Table 2 Results of the experiments conducted by Garcia-Retamero et al. (in press a, in press b).
The numbers in the cells denote the percentage of participants who were classified according to TTB
Configural versus TTB using the Bayesian method for multiple-attribute decision-making suggested
by Bröder and Schiffer (2003a)
Configural causal model Elemental causal model Neutral causal model
XOR environment 50% vs. 17% 8% vs. 58% 8% vs. 67%
AND environment 67% vs. 25% 8% vs. 50% 17% vs. 42%
Simple environment 0% vs. 67% 0% vs. 100% 0% vs. 83%
123
376 R. Garcia-Retamero, U. Hoffrage
compared to non-linearly separable categories. When, in contrast, a hint induced
encoding compatible with non-linearly separable categories, then these categories
were easier to learn than linearly separable ones (Wattenmaker, Dewey, Murphy, &
Medin, 1986; see also Waldmann et al., 1995; Wisniewski, 1995).
Furthermore, in a simulation study, Hoffrage, Garcia-Retamero, and Cziens-
kowski (2005) evaluated the performance of three decision-making strategies in
several environments: TTB, TTB Configural, and TTB-All (i.e., a strategy that
processes all possible compound cues in the environment). Interestingly, results in
these simulations show that TTB-All was not competitive in cross-validation.5 TTB-
Configural was the most robust strategy, even though TTB-All also processes all the
relevant compounds in the environment.
General conclusions
The results of the experiments reviewed above (Garcia-Retamero et al., in press a,
in press b). Show that knowledge about the causal structure of the environment
helped people to focus on a small and manageable subset of cues. Specifically, such
knowledge influenced which cues were looked up, in which order these were looked
up, and which of them were used to make decisions. Causal knowledge also facili-
tated the learning of cue validities not an easy task, as Juslin and Persson (2002)
pointed out. Finally, causal knowledge guided participants in the selection of highly
valid compound cues in the environment to improve the accuracy of their decisions.
Taken together, these findings suggest that causal knowledge can effectively reduce
the computational complexity inherent in even relatively simple decision-making
tasks.
Seen through the lens of the fast and frugal heuristics framework, causal
knowledge helps people select valid cues in the environment which might be placed
in a high position in the cue ordering, that is, in the hierarchy of cues that is accessed
by the search process of a decision-making strategy. To the extent that the feedback
about whether a decision was correct or incorrect leads to an updating of cue
validities, the cue ordering might consequently be updated as well. In this sense,
causal beliefs can be perceived as hypotheses to be tested and updated with
empirical data (see also Koslowski, 1996; Koslowski & Masnick, 2002). For instance,
some of the selected causal cues might turn out to be highly valid cues. Such cues
would remain at a high position in the cue ordering. Consequently, the expected
usefulness of the causal beliefs that link those cues to the criterion would be
strengthened. However, other causal cues might turn out to have low validity. The
expected usefulness of the causal belief that links those cues to the criterion would
therefore be reduced, and those cues would end up in a lower position in the cue
ordering. Briefly, causal beliefs might act as hypotheses that constrain the cues that
are selected to make decisions, and these beliefs are subsequently confirmed or
disconfirmed based on the experience with the selected cues in the environment.
From the results of our experiments, we can infer that people sketch an incre-
mentally constructed picture of the environment to make decisions. That is, unless
5
Cross-validation refers to the analysis of the accuracy of a decision strategy when, after fitting it to
one part of a data set (training set), it is applied to the other part (test set).
123
Causal knowledge and simple heuristics 377
the decision maker has causal knowledge indicating she should do otherwise, she
would start with a simple representation of the environment, that is, an elemental
representation where cues are treated as individual elements (see also Cheng, 2000;
Novick & Cheng, 2004; Waldmann & Martignon, 1998). Spontaneously, elemental
strategies such as the TTB heuristic would be used. The specific strategy that is
selected for decision making would be contingent on the environmental structure
(see Gigerenzer et al., 1999; Rieskamp & Otto, 2006; Todd & Gigerenzer, 2000). If
cues in the environment differ in validity, and accurate decisions are crucial, the
decision maker could use her knowledge about the causal structure of that envi-
ronment to focus on the highly valid cues and compute their validities. As the
internal representation of the environment becomes more complicated, a more
complex strategy that processes compound cues would be used to make decisions.
This would occur only when there is a match between the mind and the environment,
that is, when the components of such a compound are perceived to act through a
common causal mechanism to bring about the criterion and the compound is indeed
highly valid in the physical world. In this way, fast and frugal heuristics can also take
causally interacting cues into account and exploit an even wider range of information
structures to make adaptive decisions, thereby allowing more refined and higher-
order knowledge to be used for decision-making.
Are our conclusions about the beneficial effect of causal knowledge restricted to
the family of fast and frugal heuristics? Our intuition is that the present approach
might also be extended to other strategies. Causal knowledge possibly could also
help to reduce the computational complexity inherent in more demanding strategies
for making decisions such as the weighted additive model (WADD) which is a
compensatory strategy that uses cue validities as weights (Martignon & Hoffrage,
2002).
However, contrary to fast and frugal heuristics, WADD and other compensatory
strategies do not model the search process. That is, they strictly assume that all the
relevant and necessary information to make decisions is provided in the task. Yet in
the real world, as we mentioned above, this is not, in fact, the case. We find it difficult
to see how people using such compensatory strategies could use their causal
knowledge to select from the wide range of alternatives in the environment those
cues (individual or compounded) that are highly valid. If the assumption of cue
search and selection is dropped, how would causal knowledge aid learning of cue
validities? Briefly, simplification is not an inherent feature of these decision models.
Consequently, in their present form, they could not benefit from the advantages of
causal knowledge we pointed out above.
Causal knowledge modulates decision-making processes. Not providing such
knowledge in an experiment will make decision makers appear less competent than
they would be in their natural environment in which such information is frequently
available. The presence of causal knowledge is vital as it directs the search for
information, facilitates the learning of cue validities, and improves decision accu-
racy.
Acknowledgements We thank Gerd Gigerenzer and Peter Todd for their helpful discussion of our
results. We are deeply indebted to Chris White for his helpful comments on early drafts of the
present paper. Finally, we also thank Anita Todd for editing the manuscript.
123
378 R. Garcia-Retamero, U. Hoffrage
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