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A New and Unique Prediction for Cue-Search in a Parallel-Constraint Satisfaction Network Model: The Attraction Search Effect

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A common assumption of many established models for decision making is that information is searched according to some prespecified search rule. While the content of the information influences the termination of search, usually specified as a stopping rule, the direction of search is viewed as being independent of the valence of the retrieved information. We propose an extension to the parallel constraint satisfaction network model (iCodes: integrated coherence-based decision and search), which assumes—in contrast to prespecified search rules—that the valence of available information influences search of concealed information. Specifically, the model predicts an attraction search effect in that information search is directed toward the more attractive alternative given the available information. In 3 studies with participants choosing between two options based on partially revealed probabilistic information, the attraction search effect was consistently observed for environments with varying costs for information search although the magnitude of the effect decreased with decreasing monetary search costs. We also find the effect in reanalyses of 5 published studies. With iCodes, we propose a fully specified formal model and discuss implications for theory development within competing modeling frameworks.
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Running head: THE ATTRACTION SEARCH EFFECT 1
A New and Unique Prediction for Cue-search in a Parallel-constraint Satisfaction Network
Model: The Attraction Search Effect
Marc Jekel
FernUniversität in Hagen
Andreas Glöckner
FernUniversität in Hagen and MPI Collective Goods, Bonn, Germany
Arndt Bröder
University of Mannheim
c
2018, American Psychological Association. This paper is not the copy of record and
may not exactly replicate the final, authoritative version of the article. Please do not copy
or cite without authors’ permission. The final article will be available, upon publication,
via its DOI: 10.1037/rev0000107
Author Note
Marc Jekel, Department of Psychology, FernUniversität in Hagen; Andreas Glöckner, Department of Psychol-
ogy, FernUniversität in Hagen, and MPI Collective Goods, Bonn, Germany; Arndt Bröder, School of Social
Sciences, University of Mannheim. This research was supported by a grant of the German Science Foundation
(Deutsche Forschungsgemeinschaft, DFG) awarded to Andreas Glöckner (GL 632/5-1) and Arndt Bröder
(BR 2130/13-1). Part of the data and ideas were presented at SPUDM (Haifa, Israel, 2017), Kongress der
Deutschen Gesellschaft für Psychologie (Leipzig, Germany, 2016), Meeting of the European Group of Process
Tracing Studies (Bonn, Germany, 2016), and Tagung experimentell arbeitender Psychologen (Hildesheim,
2015, Germany; Heidelberg, 2016, Germany). The manuscript has not been made available on any online
depository or website previously. Correspondence concerning this article should be addressed to Marc Jekel,
FernUniversität in Hagen, Institut für Psychologie, LG Allgemeine Psychologie UEH & LME, 58084 Hagen.
E-mail: marc.jekel@fernuni-hagen.de
THE ATTRACTION SEARCH EFFECT 2
Abstract
A common assumption of many established models for decision making is that information
is searched according to some pre-specified search rule. While the content of the
information influences the termination of search, usually specified as a stopping rule, the
direction of search is viewed as being independent of the valence of the retrieved
information. We propose an extension to the parallel constraint satisfaction network model
(iCodes: integrated coherence-based decision and search), which assumes—in contrast to
pre-specified search rules—that the valence of available information influences search of
concealed information. Specifically, the model predicts an attraction search effect in that
information search is directed towards the more attractive alternative given the available
information. In three studies with participants choosing between two options based on
partially revealed probabilistic information, the attraction search effect was consistently
observed for environments with varying costs for information search although the
magnitude of the effect decreased with decreasing monetary search costs. We also find the
effect in reanalyses of five published studies. With iCodes, we propose a fully specified
formal model and discuss implications for theory development within competing modeling
frameworks.
Keywords: Search in probabilistic decision making, attraction search effect,
parallel-constraint satisfaction network model, fast-and-frugal heuristics
THE ATTRACTION SEARCH EFFECT 3
A New and Unique Prediction for Cue-search in a Parallel-constraint Satisfaction Network
Model: The Attraction Search Effect
The accuracy of inferences clearly depends on the quality of available information. If
valid information is not conveniently presented at a glance—as it is often the case in
real-world environments—people need to search for information before making a decision.
Doctors need to look for symptoms, educated consumers need to retrieve
product-information, police needs to search for evidence, etc. While there exist many
accounts on how people integrate probabilistic information, a “puzzling preference for
theories that ignore search and stopping” (Gigerenzer, Dieckmann, & Gaissmaier, 2012,
p. 243; Todd, Hills, & Robbins, 2012) has been lamented recently. In the current article, we
compare fixed search rules as formulated in the research-program on the adaptive toolbox
(Gigerenzer et al., 2012) or the adaptive decision maker (Payne, Bettman, & Johnson,
1988) to a new theory of coherence-based search that emerges from parallel-constraint
satisfaction processes (Glöckner & Betsch, 2008a; Glöckner, Hilbig, & Jekel, 2014;
McClelland, Mirman, Bolger, & Khaitan, 2014).
Fixed Search Rules
Formalized heuristics include search-, stop-, and decision-rules (Payne et al., 1988;
Todd, Hills, & Robbins, 2012): According to the non-compensatory heuristic Take-the-best
(TTB), for example, people search cues in the order of their predictive validity, stop when
the first cue discriminates between choice-options, and decide in line with this first
discriminating cue (Gigerenzer & Goldstein, 1996). As a consequence, information is
searched and compared within each cue, which is referred to as cue-wise search and
constitutes a typical property of the class of non-compensatory strategies (Payne et al.,
1988). In contrast, people applying a compensatory strategy (in which less valid cues can
compensate more valid cues) such as the Weighted Additive Rule (WADD) are often
assumed to tend to search all cues option-wise, that is by searching and integrating
THE ATTRACTION SEARCH EFFECT 4
information mainly within options.
More recent refinements of heuristic search assume that the order of cue-values
inspected is not exclusively dependent on cue-validities but also driven by other properties
of cues such as cue-discrimination (Lee & Newell, 2011; Lee, Newell, & Vandekerckhove,
2014; Martignon & Hoffrage, 1999; Newell, Rakow, Weston, & Shanks, 2004; Ravenzwaaij,
Moore, Lee, & Newell, 2014), the gain in the probability of a correct decision (Nelson,
2005; Nelson, McKenzie, Cottrell, & Sejnowski, 2010), or cue-outcome correlation (Rakow,
Newell, Fayers, & Hersby, 2005). Furthermore, strategies for search have been formulated
that involve learning in that they are contingent on the experienced accuracy of decisions
resulting from search-orders (Todd & Dieckmann, 2004; Dieckmann & Todd, 2012) or the
expected reward from search (McNamara & Fawcett, 2012).
There is a solid body of evidence supporting the view that information search
(cue-wise vs. option-wise) changes adaptively contingent on the structure of the
environment (e.g., Bröder, 2003; Payne et al., 1988; Rieskamp, 2006; Rieskamp & Otto,
2006) and many other factors such as task-complexity (Payne, 1976; Böckenholt, Albert,
Aschenbrenner, & Schmalhofer, 1991), information-costs (Bröder & Schiffer, 2006), time
pressure (Rieskamp & Hoffrage, 1999, 2008; Payne et al., 1988; Edland, 1994; Edland &
Svenson, 1993), stress (Glöckner & Moritz, 2008), and age (Mata, Schooler, & Rieskamp,
2007; Mata, von Helversen, & Rieskamp, 2011). These adaptive changes have mainly been
interpreted as resulting from the selection of different strategies that are composed of
search-, stopping-, and decision rules.
However, other evidence puts into question whether modeling information search as
fixed search rules within heuristics is appropriate. Many studies show that people search by
default more information than would be necessary to apply the respective heuristics (e.g.,
Bröder, 2000, 2003; Hausmann & Läge, 2008; Newell & Shanks, 2003; Newell, Weston, &
Shanks, 2003) leading to the conclusion that “[o]nly if search costs are explicit are stricter
stopping (and decision) rules employed” (Newell & Bröder, 2008, p. 211). Further research
THE ATTRACTION SEARCH EFFECT 5
shows that the stopping rule for information search is not fixed but dependent on already
revealed evidence (Söllner & Bröder, 2016; Söllner, Bröder, Glöckner, & Betsch, 2014).
These findings concerning search and stopping are difficult to reconcile within a simple
heuristics framework and indicate that there is a need for alternative conceptualizations.
Coherence-based Search
An alternative view of information-processing assumes that a fundamental property
of the cognitive system includes forming coherent interpretations by interactive neuronal
activation (Clark, 2013; Rumelhart, McClelland, & The PDP Research Group, 1986, see
also Wertheimer, 1938; Festinger, 1957; Pennington & Hastie, 1981). This approach has
also been applied to decision making (Thagard & Millgram, 1995; Glöckner & Betsch,
2008a; Betsch & Glöckner, 2010; Kunda & Thagard, 1996), which has led to the
development of the parallel constraint satisfaction model for decision making (PCS-DM;
Glöckner et al., 2014), a fully specified decision model with one free person parameter that
captures inter-individual differences in sensitivity to differences in cue validities. According
to PCS-DM, decisions are achieved by automatically integrating decision-relevant
information through spreading activation in a network. As one core limitation, PCS-DM
does not model search for new information (Marewski, 2010). Previous empirical
investigations of PCS-DM therefore intentionally simplified the decision situation in that
participants did not need to acquire information.
Rather, all pieces of information were presented in an open information-board and
could be directly inspected (cf. Glöckner & Betsch, 2008b). Although this setup simplifies
the decision situation (and thus also modeling of this situation), it also neglects search as a
crucial aspect for making good decisions. In the current article, we propose a
straightforward extension of the PCS-DM model that includes modeling of search for
information. To avoid cumbersome acronym extensions of PCS-DM with additional letters,
we refer to the new model by the name “iCodes” meaning “integrated coherence-based
THE ATTRACTION SEARCH EFFECT 6
decision and search”. In the first part of the article, we introduce iCodes conceptually: We
derive a qualitative prediction from the model capturing a critical property that diverges
from competing models—the attraction search effect.
We present three empirical studies testing this prediction. First, we analyze the first
information acquisition in each trial, testing the qualitative prediction of the model under
varying conditions in two studies. Second, we conduct overall analyses for the first two
studies in which we compare differences in the restriction of search and information costs
between conditions and extend the test to quantitative predictions for choice and
information search. Third, we extend the joint analyses to investigate further aspects such
as whether the hypothesized effect also holds for whole sequences of search and whether it
results from deliberate or intuitive processes. Fourth, we discuss the “rationality” of the
attraction search effect and present a third empirical study showing that it depends on the
environmental structure, although it can be found regardless whether it is beneficial or
detrimental. Fifth, we present a comprehensive re-analysis of previously published studies
to test the generality of our findings. In the concluding section, we discuss our findings and
their implications for decision theory.
Modeling Heuristic and Coherence-based Search for Cues
Consider, for illustration, the example that a person decides between two stocks in a
hypothetical stock-market game (Bröder, 2000) in which information from two binary
probabilistic experts (i.e., cues) can be retrieved. The first expert (cue 1) has a higher
predictive validity than the second expert (cue 2). Both provide information whether
investing in stock A or stock B would be recommendable (+) or not (–). Now let us
assume that one piece of information—the prediction of cue 1 for stock A—is already
available but all other information is still concealed (Figure 1, upper left display). Which
predictions concerning the next step of information search can be derived from standard
heuristic models? A user of the non-compensatory TTB heuristic would search for the
THE ATTRACTION SEARCH EFFECT 7
second cue-value of the most valid cue 1 next. In contrast, a user of a compensatory
WADD strategy is expected to open the cue-value of cue 2 for stock A next. Importantly,
both predictions are independent of the valence of the available cue-value. That is, the
direction of search is independent of whether the already available piece of information
from cue 1 speaks for or against stock A (Figure 1, upper left display, value in parenthesis).
This prediction concerning the independence of the direction of search from the specific
valence of already available information results from the more general assumption of fixed
search rules, which is typical for strategies suggested in the tradition of the adaptive
decision maker and shared by all of them.
In contrast to this prediction, in iCodes cue-search is dependent on the current
evidence of already revealed cue-values. iCodes assumes that people form an initial
preference for one of the options based on the available cue-value(s), as already described
by PCS-DM (Glöckner et al., 2014). As the pivotal extension, we propose that the
resulting preliminary impression then influences which cue-value is opened next such that
concealed cue-values of currently preferred options are more likely opened next than cue
information concerning less preferred options. In line with the general idea of interactive
activation models, this important property of the iCodes model developed in this paper
proposes that the more highly activated (attractive) option receives more attention which
governs cue search in addition to the validities of cues. Specifically, for allowing to model
cue-search we extend the original PCS-DM model (Glöckner & Betsch, 2008a; Glöckner et
al., 2014) in two respects: (1) each cue-value (+ or –) is represented by a separate node in
the network that is connected to a cue-node for modeling interdependence between
cue-values from the same cue and (2) the original PCS-DM network consisting of options
and open cue-values is extended by a subnet consisting of concealed cue-values.
Open cue-value(s; unshaded rectangle C1A for cue 1 concerning stock A; Figure 1,
upper right panel) are connected to cue-nodes and to option-node(s) (i.e., positive
connection as indicated by the black line from C1A to A). Connections between options are
THE ATTRACTION SEARCH EFFECT 8
inhibitory—as indicated by a dashed line between A and B—because participants can only
choose one of the options. The strength of connections between source node and cue-nodes
is proportional to the cue-validities as indicated by thicker lines for the more valid cue 1 as
compared to cue 2. The process of forming an initial preference for one of the options is
simulated as activation spreading from the source-node to the cues and single cue-value(s)
and to the options in an iterative process of updating activations of cues. In the example
provided in the upper right part of Figure 1 involving a positive value of Cue 1 for option
A (i.e., C1A), option A receives high activation. The positively activated option A inhibits
option B, which results in a highly activated option A and a less activated option B as
indicated by differences in box-sizes.
Concealed cue-values form a subnet: Activation flows from the cue-nodes and the
option-nodes (Figure 1, lower left display) to the concealed cue-values. Note that
connections between option-nodes and cue-nodes to concealed cue-value nodes are only
uni-directional (as indicated by grey single-arrowed connections), since we assume that yet
unknown cue-values cannot influence the activation of options. Activation flowing from the
source node to the cue-nodes is proportional to cue-validities as in the original PCS-DM
model.
For information search, this leads to two core predictions: First, the probability of
opening a cue-value increases with its validity (keeping everything else constant). This
prediction has already received ample support (e.g., Glöckner & Betsch, 2008b; Glöckner et
al., 2014, Exp. 4) but since it is shared with several alternative models (e.g., evidence
accumulation models: Busemeyer & Townsend, 1993; Krajbich & Rangel, 2011; adaptive
strategy selection models: Payne et al., 1988; Payne, Bettman, & Johnson, 1993;
Gigerenzer & Goldstein, 1996; Todd, Gigerenzer, & The ABC Research Group, 2012), it is
not particularly useful for testing models comparatively. Second, activation flowing from
the options to the nodes representing concealed cue-values leads to the prediction of an
increased tendency to search cue-values of the currently preferred option (i.e., higher
THE ATTRACTION SEARCH EFFECT 9
activated option-node). This should lead to an attraction search effect, which is not
predicted by alternative models (heuristics as well as diffusion/evidence accumulation
models). According to this model-inherent prediction, information will be mainly searched
within an option if it is attractive but that the direction of information search tends to
switch to the other option if the searched alternative appears to be unattractive.
In line with the well supported concept of interactive activation and parallel
constraint satisfaction (McClelland et al., 2014), iCodes predicts that both sources of
activation (i.e., validity of the cue and attractiveness of the option) are additive (as also
encoded in the activation function, see section on the formalization of the model below)
and jointly determine the activation of concealed cue-value nodes and thereby the
likelihood of opening it derived from those activations. Specifically, iCodes predicts that
the likelihood for each cue-value to be opened increases with the activation of the
respective cue-value node (as compared to the overall activation of all concealed cue-value
nodes). In case the initial evidence is positive for option A and the difference in validities
between cues is small, iCodes predicts that it is more likely that participants inspect the
cue-value of cue 2 for option A instead of the more valid cue-value of cue 1 for option B. In
case the initial evidence is negative for option A, participants are predicted to search
evidence for option B more likely instead.
In sum, based on its core property of interactive activation, iCodes predicts an
attraction search effect in that the next step of information search should tend to be more
option-wise in case there is a current tendency to prefer option A and more cue-wise in
case there is a current tendency to prefer option B.1This effect allows for a critical
property testing against the most prominent classes of competing models. Adaptive
strategy selection models (Gigerenzer, Todd, & The ABC Research Group, 1999; Payne et
al., 1993) assume as a core property that people use fixed rules for information search. For
such rules, the valence of the information cannot influence the direction of search. Also, the
class of evidence accumulation models (Busemeyer & Townsend, 1993; Krajbich & Rangel,
THE ATTRACTION SEARCH EFFECT 10
2011; Lee & Cummins, 2004) does not predict such an effect. These models assume that
attention switches probabilistically between cues (or attributes) and evidence is
accumulated until a decision threshold for one of the options is reached. The random
distribution of attention to cues is influenced by validity or other factors (e.g., perceptual
salience) of cues and the decision environment but is independent of the initial evidence
resulting from the interplay of already available cues. The crucial difference to PCS models
is that backward activation processes from options to search are precluded. Hence,
evidence accumulation models do not predict the attraction search effect either.
Studies that directly compare the adequacy of heuristic search-rules to alternative
accounts are still largely missing mainly because alternative models (such as PCS-DM)
were so far underspecified with respect to information search (but see Glöckner & Herbold,
2011, for describing first steps towards a network model of attention and integration in
risky choice). We aim to close this gap by comparing the predictions from an extended
PCS model for search against predictions from heuristic search-rules and evidence
accumulation models using a critical property testing account with a focus on the
attraction search effect in three experimental studies.
Related Evidence: Pseudodiagnosticity in Hypothesis Testing
In research on information search for conditional probabilities in reasoning and
hypothesis testing, a phenomenon similar to the attraction search effect has been
demonstrated, which is referred to as pseudodiagnostic search (Doherty, Mynatt, Tweney,
& Schiavo, 1979; Kern & Doherty, 1982; Mynatt, Doherty, & Dragan, 1993). It is shown
that individuals do not look up both relevant conditional probabilities for considering
whether a piece of information (e.g., the patient has fever) speaks for a hypothesis (e.g., the
patient has flu) or an alternative (e.g., the patient has a sepsis). This is usually explained
by peoples’ inability “to think about one datum in relation to two hypotheses” (Mynatt et
al., 1993, p. 119) and a default attentional shift in focus on the information about a single
THE ATTRACTION SEARCH EFFECT 11
hypothesis (Evans, Venn, & Feeney, 2002). Since only the comparison of both conditional
probabilities between hypotheses (e.g., is the probability of fever given a flu higher than
the probability of fever given sepsis?) allows to evaluate whether this piece of information
speaks for one of the hypotheses (i.e., by calculating the ratio of likelihoods), not looking
up the other relevant information has to be considered suboptimal.2
In hypothesis testing, pseudodiagnostic search is consistently observed. Providing an
initial information (e.g., conditional probability of fever given flu = .80) that seems to
speak for the hypothesis due to a probability larger than .50 leads to an increased search
for a next piece of information that relates to the same hypothesis (e.g., the conditional
probability of headache given flu), whereas the relevant other piece of information (e.g.,
conditional probability of fever given sepsis) is ignored. If—in contrast—the first
information seems to speak against the hypothesis (e.g., conditional probability of fever
given flu = .20), search switches to information concerning the other option (Mynatt et al.,
1993). Hence, pseudodiagnostic information search in hypothesis testing describes a
phenomenon similar to the attraction search effect predicted by iCodes for multiple-cue
decision making in that information search is dependent on the valence of the already
revealed information. Given the differences between the pseudodiagnosticity paradigm and
typical multi-attribute decision tasks, it is, however, unclear whether the effect generalizes,
which we investigated in the current research. Furthermore, while explanations of the
phenomenon in pseudodiagnosticity research include mainly broad framework models
(Evans, 2007, 2008; Evans et al., 2002), iCodes provides a fully specified computational
formal model for predicting the magnitude of the attraction search effect.
Study 1
In Study 1, we test for the existence of an attraction search effect that is uniquely
predicted by iCodes but not predicted by competitors such as adaptive decision making and
evidence accumulation models. Instead of comparative model fitting, we thereby rely on a
THE ATTRACTION SEARCH EFFECT 12
critical property when testing a qualitative hypothesis that can only be accounted for by
one model but not by the others. This approach avoids the problem of potential over-fitting
(Gigerenzer & Brighton, 2009; Marewski & Olsson, 2009; Roberts & Pashler, 2000) since
the prediction of the attraction search effect does not depend on parametric constellations.
Methods
Participants. Thirty-three participants (17 male; mean age = 25 years, SD = 4,
mainly students from the University of Göttingen) were recruited using the database
ORSEE (Greiner, 2004). Participants received a show-up fee of 2e(2.2USD) and
performance-contingent payment for each correct choice of up to 3.20e(3.6USD).
Material. Participants played a hypothetical stock-market game in which they
were asked to choose the more profitable of two stocks (Figure 2). They could use the
advice from four experts that varied in predictive power with cue validities v = {.90, .80,
.70, .60}, which was introduced as the number of correct predictions of the respective
cue/expert in the past one-hundred rounds prior to the study. Participants were also made
aware of the fact that cues with fifty out of one-hundred predictions correct are no better
than chance. Each expert made a binary prediction (“+” = good, “–” = bad) concerning
the performance of each stock. Some of these cue-values were directly available, other
cue-values were concealed. From the concealed cue-values, some were potentially available,
as indicated by “?”, or unavailable as indicated by “x” (Figure 2).
Participants were asked to open one additional available information only (i.e., “?”)
before deciding which option to choose. The cue-value they opened before making a
decision was the dependent variable. The more likely option according to naïve Bayes
(Jekel, Glöckner, Fiedler, & Bröder, 2012; Lee & Cummins, 2004) given validities and all
cue-values (i.e., open and concealed) of a trial was reinforced with 2.5 Cents for each
correct decision and participants were informed about their performance (i.e., number of
correct decisions) at the end of the study.
THE ATTRACTION SEARCH EFFECT 13
Participants were told that experts generated their predictions independently and
that the resulting recommendations were thus independent from each other. Names of the
stocks and experts changed for each new trial to further stress that trials were independent
of each other and no information of prior trials could be used to infer concealed cue-values
in subsequent trials (Jekel, Glöckner, Bröder, & Maydych, 2014). Overall, eight
cue-patterns (i.e., all cue-values concerning option A and B) with two different versions
each were presented. Each of them was repeated eight times resulting in 8 (cue-patterns) ×
2 (versions: stock A attractive vs. stock B attractive) ×8 (repetitions) = 128 rounds in
total (Table 1). The factor “version” contained the critical within-subjects manipulation of
options’ attractiveness that should induce differences in information search according to
the attractive search effect. For manipulating version, the cue-pattern was held constant
except for one or two directly available cue-values that were varied so that option A was
more attractive in the first version and option B was more attractive in the second version
according to iCodes.
It was expected that the manipulation of attractiveness implemented in the factor
version leads to respective changes in information search, that is, increased search for
cue-values from stock A than stock B in version 1 and vice versa for version 2. For each
cue-pattern, we calculated an attraction search score as the dependent variable that equals
1 if all participants search for stock A in version 1 and for stock B in version 2 and that
equals 0 if no switches in search are induced by the manipulation of attractiveness (i.e.,
score = p(search stock A|version 1) - p(search stock A|version 2)). The factors cue-patterns
and repetitions test the generality and robustness of the effect. For each cue-pattern,
evidence of concealed cue-values was randomly set positive or negative.3The order of
patterns was randomized between participants.
Procedure. Participants received a paper-and-pencil instruction of the
stock-market game. After clarifying potential questions individually to assure
understanding, they completed 64 trials of the game. After a short self-paced break, they
THE ATTRACTION SEARCH EFFECT 14
then completed the second half of the trials and indicated demographic data. Finally,
participants were debriefed, and paid according to their performance.
Results
R-scripts and data from Study 1, Study 2, and Study 3 can be downloaded from the
Open Science Framework at http://doi.org/10.17605/OSF.IO/Q6C5Y. Participants made
on average 78% (SD = 3%) correct decisions according to naïve Bayes standards, which is
significantly higher than the 50% chance-level (t(32) = 46.23, p < .001). This indicates that
people made informed decisions, taking into account the information provided. More
importantly, we descriptively found the predicted attraction search effect for all
cue-patterns (Figure 3). The average attraction search score is M=.30 (SD = .14) and
significantly larger than zero (t(32) = 12.37, p < .001). This means that participants
searched in 30% of all trials more often cues of option A when option A was more
attractive than option B than vice versa (i.e., version 1 vs. version 2) according to iCodes.
See Appendix A for a complete display of the observed proportions of cue-values opened
first. The attraction search effect is also consistently found in separate analyses for all
cue-patterns (all paired ts(32) >2.39, p < .05) and thus does not seem to depend on
specifics of the cue-patterns (Wells & Windschitl, 1999; Westfall, Judd, & Kenny, 2015)
although its size varies across patterns.
The overall effect size of the attraction search effect is Cohen’s d= 2.15 and the effect
sizes per pattern range from d= 0.42 (cue-pattern 3) to d= 2.66 (cue-pattern 7).
Importantly, differences in the size of the effect are in line with model predictions: iCodes
predicts the strongest attraction search effect ceteris paribus for cue-patterns 6 and 7.
Specifically, the model predicts that search is determined both by validity and top-down
activation generated by the attractiveness of options. Hence, the attraction search effect
should be weaker (but still present) in patterns where top-down activation by the
attractive option is in conflict with tendencies generated by validity, such as in cue-patterns
THE ATTRACTION SEARCH EFFECT 15
1, 2, 3, 4 and 5, but not 6, 7, and 8.
Analyses at the level of individuals revealed that 76% of the participants showed a
significant attraction search score (all ts(7) >2.00,ps< .05;t-tests based on eight
attraction search scores) and nearly all participants (i.e., 97%) showed a positive attraction
search score, indicating that the effect is not only driven by a small subset of participants.
Discussion
We find strong support for the attraction search effect predicted by iCodes. The
effect is consistently found for all cue-patterns and for the majority of participants
supporting the critical property prediction of the model. Neither fixed strategies, as
formulated in the adaptive toolbox program, nor standard evidence accumulation models
can account for this effect that follows from interactive activation.
One limitation of Study 1 is that the decision task was restricted by the fact that
participants were only allowed to open one additional cue-value before making a decision.
This might reduce the generality of our findings since information search in natural
environments is rarely restricted in this way. We address this issue in Study 2 by
investigating the prevalence of the attraction search effect in a less restricted and thus
potentially more natural environment.
Study 2
Study 2 tested whether the attraction search effect generalizes to situations where
participants could search for more than one additional cue-value. Furthermore, we
investigated the effect of monetary costs of search, which has been shown to crucially
influence information search in previous studies (Bröder & Schiffer, 2006).
Methods
Participants and Design. One-hundred-eleven new participants (73 female; mean
age = 25 years, SD = 5, two participants did not indicate their age) were recruited from
THE ATTRACTION SEARCH EFFECT 16
the same database used in Study 1. Participants again received a show-up fee of
2e(2.2USD) and performance contingent payment for each correct choice of up to
3.20e(3.6USD). We manipulated information costs between participants who were
randomly assigned to either a condition with or without monetary costs for information
search.
Materials and Procedure. We used the same materials and procedure as in
Study 1 except for that people were free to choose how many cue-values to open before
making a choice. In the information cost condition, participants could open one cue-value
for free. For every additional cue, participants were told that a fee of .25 Cents was applied
(i.e., 10% of the potential reward). In the condition without information costs, participants
were asked to open one cue-value and could open as many additional values as they wanted
without any costs.
Results
Participants made on average 87% (SD = 4%) correct decisions in the condition with
information search costs but only 81% (SD= 7%) in the condition without information
search costs. Both are significantly different from chance-level (both ts>33,p<.001) and
they are different from each other (t(109) = 5.49,p<.001). In the information cost
condition, participants inspected on average only freq = 0.25 costly cues (i.e., cues beyond
the first cue opened) per decision, whereas freq = 2.1 additional cue-values were inspected
in the condition without information cost (t(109) = 19.43,p<.001). Less inspection thus
led to more correct decisions. This is likely due to the non-compensatory structure of the
decision environment given validities and the naïve Bayesian incentive scheme4and
participants who tended to integrate information in a more compensatory fashion as
suggested by fits of the P-Parameter in iCodes (i.e. P < 1.9, see below for details).
In accordance with Study 1, we calculated the attraction search score based on the
first cue-value opened for both conditions by comparing search between versions of
THE ATTRACTION SEARCH EFFECT 17
cue-patterns. We observe the predicted attraction search effect in both conditions
(Figure 3). For the information cost condition, the average attraction search score is
M=.32 (SD = .22). The attraction search effect is significantly smaller for the condition
without costs M=.11 (SD = .14) (t(109) = 5.91,p<.001), but both are again
significantly larger than zero (both ts>6.38,p<.001).
The overall effect size of the attraction search effect is Cohen’s d= 1.50 for the
information-cost condition and Cohen’s d= 0.86 for the no-cost condition. Overall, we find
that the attraction search effect is present in both conditions but letting participants
search for cues without monetary costs reduces the size of the effect considerably. On the
individual level, 75% of the participants show a significant attraction search effect (all
ts(7) >1.97,p<.05;t-tests based on eight attraction search scores) and nearly all
participants (i.e., 91%) show a positive attraction search score in the information cost
condition. In the no-cost condition, a considerably lower 25% of participants (all
ts(7) >2.00,p<.05) show a significant attraction search effect but the majority of
participants (i.e., 82%) shows at least a positive attraction search score overall.
Discussion
We find again strong support for the attraction search effect predicted by iCodes
under more realistic conditions of unrestricted search. The size of the effect appears to
depend on the type of search as analyzed next.
Comparison of Studies and Analysis of Psychometric Properties
Comparison between Studies
In the first study, participants were only allowed to search for one additional cue. In
the second study, participants could either search additional cues with or without any
monetary costs. All other aspects (i.e., cue-patterns and procedure) were identical in both
studies.
THE ATTRACTION SEARCH EFFECT 18
A comparison within and between studies reveals that the attraction search effect is
similar for restricted search and unrestricted search with costs and lower for all
cue-patterns in the condition with unrestricted search without costs as shown in Figure 3.
A multi-level regression (Table 2) predicting the attraction search score with random
intercepts and random slopes for participants and two Helmert contrasts comparing
conditions confirmed this impression (unrestricted search without costs < restricted search
& unrestricted search with costs; t(133.31) = 7.27,p<.001; restricted search vs.
unrestricted search with costs; t(86.05) = 0.56,p=.58).
There are various factors that could cause the attraction search effect to be lower in
the unrestricted search condition without costs. One factor is that participants in the
condition might search information less systematically. Furthermore, they might be less
likely to form a preliminary assessment of the options concerning their attractiveness
before searching, which is required for the attraction search effect to evolve. Both potential
explanations are indirectly supported by the fact that search time (i.e. time before an
information is opened) is lower in the unrestricted search condition (i.e., 4506ms for
restricted search versus 3153ms and 2140ms for unrestricted search with or without costs;
see section on the automaticity of the attraction search effect below for details).
A third further factor that is likely to reduce the attraction search effect in the
unrestricted search condition without information costs is the effect of reading direction,
which is more likely to overwrite the systematic attraction search effect in the unrestricted
search condition without costs. Specifically, in decision tasks without restrictions of search
(and particularly in open displays), individuals tend to focus initially more on the
information provided on the upper left side of the screen (e.g., Fiedler & Glöckner, 2012).
In line with this explanation, there are strong reading biases in the unrestricted search
condition without costs as compared to the other conditions. For cue-patterns in which the
most valid cue-values for both options are the same (i.e., patterns 6 to 8; Table 1), for
example, participants looked up a piece of information displayed on the left in 73% of the
THE ATTRACTION SEARCH EFFECT 19
trials, whereas this bias was much weaker (58% of the trials) in the two other conditions,
t(142) = 6.10, p < .001, Cohens’s d= 1.05. Similarly, for remaining cue-patterns 1 to 5, in
which the most valid cue is different for both options, there is a stronger top/bottom
reading bias for unrestricted search without costs than in the other two search conditions.
Participants in the unrestricted search condition without costs focus more on the
information presented on the top as compared to participants in the other conditions
(average ranks: unrestricted without costs = 2.86 vs. other = 3.20,
t(142) = 4.70, p < .001, Cohen’s d= 0.81). Note, however, that this analysis has to be
interpreted cautiously since presentation order is confounded with cue validity in our
paradigm.
In summary, there is evidence from multiple process measures that the observed lower
attraction search scores in the condition with unrestricted search without costs as
compared to the other conditions might be driven by the fact that under unrestricted
search without costs (i) participants look up information less systematically, (ii) they might
be less likely to take the time to generate a required preliminary attractiveness rating
before search, and (iii) they show stronger reading biases by preferring information on the
left and on the top of the display that overwrite effects of attraction search.
Inter- and Intraindividual Stability of the Attraction Search Effect
Next, we investigated whether the attraction search effect is stable within each
person. This seems to be the case since individuals’ search across eight cue-patterns is
reliably affected by the attractiveness of choice-options (Cronbach’s α=.80; eight items;
144 participants). To further investigate the stability of attraction search over time, we
analyzed how consistently participants looked up information from the more (=1) or less
(=0) attractive option over eight repetitions of sixteen cue-patterns. Overall, individuals
show very stable search strategies in that for 32% of the cases (i.e., 16 cue-patterns ×144
persons) behavior was perfectly consistent (i.e. variance of zero). That is, participants
THE ATTRACTION SEARCH EFFECT 20
inspect consistently over eight repetitions cue-values from the same option.
To counter a possible objection that repeating the patterns artificially inflated the
effect, we also calculated the attraction search score for the first occurrence of each
cue-pattern per person only. The magnitude of the effect does not differ from the
attraction search effect calculated for all repetitions: The average difference between scores
for each cue-pattern averaged over all participants per condition and for each participant
averaged over all cue-patterns is low (diffpattern = 0.001,t(23) = 0.048,p=.96;
diffparticipant =0.01,t(143) =0.53,p=.59). Correlations between scores are also high
for cue-patterns (r=.89,p<.001; Figure 4, left display) and participants (r=.63,
p<.001; right display). Hence, the size of the attraction search effect is stable within
persons and independent of the number of repetitions of cue-patterns.
Quantitative Predictions of Choice and Search with a Fully Specified iCodes
Model
In this section, we introduce a fully specified iCodes model and test how accurately
the model can predict choice of options in comparison to the noncompensatory strategy
TTB and the compensatory strategy WADD. We further analyze if the new model can
predict which concealed cue-value participants first opened in both studies.
Formalization of iCodes
The decision situation is encoded in a symbolic network (Figure 5) with nodes
representing elements of the decision situation (cues and options) and links between nodes
representing constraints between elements. The new model iCodes retains all core aspects
of the former version PCS-DM (Glöckner et al., 2014; Glöckner & Betsch, 2008a; Glöckner
& Betsch, 2012) including a layer of option nodes (opt1and opt2), a layer of cue nodes
(cue1,cue2,cue3,cue4) and a general validity node. Note that an extension of the model to
more options and more or less cues is, however, of course straightforward. The network
structure depicted illustrates the representation of the decision situation of cue-pattern 2
THE ATTRACTION SEARCH EFFECT 21
version 1, in which the first most valid cue favors option 1 and all other cues are concealed
(Table 1).
The original model is extended in two important respects. First, an additional layer
of cue-value nodes is included (cue1,1,cue2,1,. . . , cue4,2)that allows the model to take into
account single cue-values by individual nodes that are connected to a shared cue-node.
Hence, each prediction of a cue for an option is now represented by a separate node (i.e.,
cue1makes a positive prediction for option 1, represented by node cue1,1which is
connected by a facilitating link to option 1). This new layer contains nodes that represent
cue-values that are already available (unshaded rectangles) and nodes that represent
cue-values that have not been inspected (shaded rectangles) by the decision maker yet.
Thus, single nodes for cue-values (e.g., cue1,1and cue1,2) represent the pieces of open or
concealed information in the decision situation while nodes for cues (i.e., cue1) model the
interdependence of cue-values that stem from the same cue. Second, activations of cues
and the activation of options impact the activation of concealed cue-values. Thus,
activations of cue-values is driven by cue-validity and the current attractiveness of options.
In the model, concealed cue-values do not impact the decision situation of already available
cues (i.e., cue1,1in the example) and thus links to concealed cue-values are uni-directional
only (i.e., concealed cue-values form a subnet).
The impact of open positive cue-values on options and from options to cue-values is
encoded as bi-directional positive links with a weight of .01 (e.g., link between cue-value
cue1,1and first option opt1) whereas open negative cue-values are encoded as bi-directional
negative links (i.e., .01). The impact of options on concealed cue-values (i.e., modeling of
the attraction search effect) is encoded as positive links of size .01 (e.g., link between
option opt1and concealed cue-value cue2,1). The impact of cues on cue-values is encoded as
positive links of size .1. Thus, the impact of cue-validities versus attractiveness of options
on search was set to a ratio of 10 to 1 in the simulations.5
Like in the original PCS-DM model, cue-validities v={.90, .80, .70, .60}are
THE ATTRACTION SEARCH EFFECT 22
transformed into net weights for validities between the validity-node and cues according to
the function Wv(i)= (vi.5)P(Glöckner et al., 2014). Pis a free parameter fitted
individually to participants. A high Presults in high ratios between cues which leads to
non-compensatory decision making. A low Presults in compensatory decision making.
Thus Prepresents the participant’s sensitivity to differences in validities.
The decision-making process is simulated as weighted activation flowing iteratively
between nodes. At each iteration i={1,2, . . . , I}, constant activation flows from the
validity node into the network at avalidity = 1. Each node receives input from all connected
nodes according to a simple linear weighted additive rule inputi=Pw×a. Input is
transformed into activation aaccording to a sigmoid function with
at+1 = (1 decay)×at+input ×(1 at)if inputi0or
at+1 = (1 decay)×at+input ×(at+ 1) if inputi<0. In accordance with prior studies,
the parameter decay was set to .1. The overall coherence is defined as the negative
Hopfield energy over all qnodes with energy =PQ
q=1 PR
r=1,r6=qwq,r ×aq×ar(Glöckner
& Betsch, 2008a; Read, Vanman, & Miller, 1997). Iterative updating is stopped when the
change in negative energy per iteration does not supersede an arbitrary low threshold at
106for ten iterations.
For transforming node-activations into choice probabilities, we used the
node-activations of the option aO
ppreferred by participants and options aO
np not preferred
by participants and calculated choice-probabilities for trials t={1, . . . , T }according to a
softmax choice rule with p(Op|P, λc, t) = eλc×aO
p(t)/Pk={p(t),np(t)}eλc×aO
k(cf. Glöckner et al.,
2014, p. 662, equation B2). The individually fitted parameter λcdetermines the steepness
of the choice-function: A participant with a high versus low λcis more or less sensitive to
the differences in activations of options. For modeling search, activations for concealed
cue-values Zare similarly transformed into probabilities of inspecting a concealed
cue-value iof option jaccording to the same softmax choice rule with
p(cuei,j |P, λs, t) = eλs×ai,j (t)/PZ
z=1 eλs×az(t). As before, the individually fitted parameter λs
THE ATTRACTION SEARCH EFFECT 23
determines the steepness of the choice-function. Thus, in total the model consists of one
individual parameter Pfor modeling sensitivity to differences in validities and two
individual parameters λcand λsfor transforming activations of options or concealed
cue-values into choice probabilities and probabilities for inspecting a cue value, respectively.
Predicting Choices
Model Fitting. To test whether iCodes can describe participants’ choices of
options better than the strategies TTB and WADD and to test how search relates to
decision making, we fitted all three models to participants’ choices taking cue-patterns into
account after participants had searched for information.
For iCodes, we used a maximum-likelihood method to identify individual level
parameters Pand λc(both in the range [0,5]) that maximize the sum of the log-likelihoods
of the choices of all trials Taccording to PT
t=1 ln(p[Op|P, λc, t]).
For the single strategies WADD and TTB, participants are assumed to apply the
strategy with a trembling-hand application error in the range of [0, .5] (i.e., from perfect
strategy application to chance-application). Based on the number of strategy consistent
choices c, strategy inconsistent choices nc and the number of predicted guesses g(i.e.,
probability of .5 for choices between two options), the maximum sum of log-likelihoods of
participant’s choices is calculated by finding the parameter that maximizes
ln[(1 )c×nc ×.5g]. From the maximum sum of log-likelihoods, the Bayesian
information criterion BIC is calculated for each model m∈ {iCodes,WADD,TTB}and all
trials Taccording to 2×ln(Lm) + ln(T)×pm(Glöckner et al., 2014, equation B10). The
number of parameters pmis set to 2 for iCodes (i.e., Pand λc) and 1 for strategies (i.e., )
to adjust fit for model-flexibility.
The estimated best-fitting parameters for participants (Figure 6, two upper left
displays) show a similar mean of 1.66 for the iCodes-parameter Pand a slightly lower
mean of 2.34 for sensitivity λcin comparison to previous studies from our lab (cf., Glöckner
THE ATTRACTION SEARCH EFFECT 24
et al., 2014, p. 663, Table B 1). Strategy application errors are considerably higher with
means .15 and .18 for TTB and WADD than in prior studies (cf., Glöckner et al., 2014, p.
663, Table B 1; between .03 and .09).
Adherence with Choice Predictions. Considering all participants in both
studies, iCodes can account for 89% of all decisions correctly (Figure 7). The proportion of
choices in line with the theory predictions was considerably and significantly lower for the
alternative strategies with WADD reaching 84% (t(143) = -12.80, p<.001) and TTB 77%
(t(143) = -22.77, p<.001). iCodes could account better for the data in the condition with
unrestricted search without information costs (Study 2) than in the condition with
information costs in the same study (t(109) = 2.99, p<.01) and in Study 1 with restricted
search (t(86) = 5.87, p<.001). The overall Bayesian Information Criterion for all I= 144
participants in Study 1 and Study 2 (i.e., 2×PI=144
i=1 ln(Lm(i)) + 144 ×ln(144 ×T)×pm)
indicates strong support for iCodes in comparison to WADD and TTB (both Bayes factors
for iCodes at least e1250 >10308). Classifying each participant according to individual BICs
results in 79.8% of participants best described by iCodes, 14.6% best described by WADD,
and 5.6% by TTB.
Cross-prediction. To test how well models are able to predict choices, we did a
cross-prediction analysis where we fitted individual model-parameters to odd numbered
cue-patterns (i.e., pattern 1 versions 1 and 2, pattern 3 versions 1 and 2, etc.) and
predicted choices with fixed parameters for even numbered cue-patterns (i.e., pattern 2
versions 1 and 2, pattern 4 versions 1 and 2, etc.). Results are overall similar to fitting
choices: iCodes makes 88% correct predictions for choices whereas WADD and TTB make
84% and 77% correct predictions, respectively (both paired ts(143) >7.38,p<.001). The
percentage of participants best described by iCodes based on the individual sum of
maximum log-likelihood scores is slightly lower in cross-prediction than in fitting: iCodes
predicts 59.0% of participants best, whereas WADD and TTB account best for 27.8% and
13.2% of participants, respectively. Overall, iCodes is at least e320 >10138 more likely the
THE ATTRACTION SEARCH EFFECT 25
data-generating model than TTB or WADD.
Impact of Search on Choices. Although we cannot measure the impact of
searching cues on the final choice directly since we did not assess participants’ preference
for choices prior to cue-search, we can proxy the impact of search on choice indirectly. If
additional search does not have any impact on choice, iCodes-predictions based on the
initially concealed cue-patterns should be equally accurate in accounting for choices as
iCodes-predictions based on observed cue-patterns after search. To allow such a
comparison, we fitted iCodes to choices for all participants based on concealed cue-patterns:
iCodes fitted to initial available cue-values only accounts for 79.8% of choices, which is
significantly lower than 89.1% overlap for iCodes-predictions based on available cue-values
after search (t(143) = -19.52, p<.001). When considering only the trials in which the two
versions of iCodes make distinct predictions (approx. 20% of the trials), the advantage of
iCodes taking into account all available pieces of information after search becomes
considerably more pronounced: 75% of choices in these trials are in line with iCodes.
Finally, the data indicated that participants who can be best described by iCodes
based on choices for options show a tendency, although not statistically significant
(t(142) = 1.89,p=.06), for a higher attraction-search effect (.26 versus .18 overall
attraction search score) than participants classified as users of the strategies WADD or
TTB. In summary, we find that iCodes can account for participants’ choices best and we
show that choices can be related to cue-search in a meaningful way providing some
converging evidence for the choice-based model-classification.
Predicting Search of Cue-values
Model Fitting. To investigate how well iCodes can account for search, we
correlated the mean predicted probability of inspecting a concealed cue-value with the
observed proportion of participants indeed inspecting this cue-value. For doing so, we ran
simulations of iCodes with individual parameters for participants and all cue-patterns as
THE ATTRACTION SEARCH EFFECT 26
exemplified in Figure 5. For each participant, we re-used sensitivity parameter Pfrom
fitting choices and fitted λsfor transforming activations of concealed cue-values into
probabilities for inspecting cue-values in the range [0, 1000] by maximizing the sum of
log-likelihoods of concealed cue-values inspected (see Figure 6 upper right panel for
distribution of λs).6From these simulations, we derived for each participant and concealed
cue-value the probability of opening the cue-value according to iCodes. We then averaged
predicted probabilities over participants per concealed cue-value and correlated those with
the observed proportions of search.
Adherence with Search Predictions. For the 55 concealed cue-values included
in all studies, the predicted probabilities and observed proportions of inspecting them
correlate almost perfectly with r=.95 (p<.001) (Figure 8, left display). Since proportions
of the same trial are dependent (i.e., predicted probabilities and observed proportions of
opening cue-values add up to 1 in each trial), we also compared the predicted probabilities
and the observed proportions for the most likely cue-value opened first for each cue-pattern
according to the model (black dots in Figure 8, left display). Predicted probabilities and
observed proportions correlate with rblack =.81 (p<.001). We also assessed how often
participants chose the cue-value with the highest probability predicted by the model (i.e.,
overlap between choice and prediction of cue-value opened first). Overall, predictions by
the model and participants’ choices of first cue-value opened overlap in 67% of all trials. As
a lower benchmark, note that random prediction (i.e., choosing a cue-value to be opened
next randomly) would lead to 37% correct predictions on average only.
One notable difference to fixed search rules is the proposed attraction search effect.
In iCodes, the effect results from the connections between option-nodes and cue-values. To
test whether this aspect of the model adds to its accuracy in predicting search, we re-ran
all simulations using a reduced version of iCodes with all connections between options and
concealed cue-values removed (i.e., no direct impact of options on concealed cue-values).7
The correlation between predicted probabilities and observed mean rates of the first
THE ATTRACTION SEARCH EFFECT 27
cue-value opened is lower for the reduced model with r=.87 and rblack =.51 (both
ps< .01).8
We also assessed the overall model fit as a comprehensive measure for comparison by
calculating the log-likelihoods from the predicted search-probabilities of cue-values
participants actually uncovered first for both versions of the iCodes model. According to
the maximum log-likelihood values of the models, the overall observed data is e186 >1080
more likely under iCodes than under the reduced iCodes model thus supporting the use of
coherence-based principles in modeling search. Comparing model-fits for single
participants, 55% of all participants can be accounted better by iCodes than the reduced
iCodes model. Percentage of participants best described by iCodes by condition matches
the strength of the attraction search score reported before: In the first study with
restricted information search, 85% of participants can be best described by iCodes. In the
second study with unrestricted search with costs, the percentage decreases to 54%. In the
condition with unrestricted search without information costs, the percentage further
decreases to 38%. Thus, for unrestrictive search without search costs, the majority of
participants’ search can be better described without assuming coherence-effects in search.
Cross-prediction. To test how accurately models predict search, we did a
cross-prediction analysis where we again fitted the free model-parameter λsto odd
numbered cue-patterns (i.e., pattern 1 versions 1 and 2, pattern 3 versions 1 and 2, etc.)
and predicted search with λsfixed for even numbered cue-patterns (i.e., pattern 2 versions
1 and 2, pattern 4 versions 1 and 2, etc.). Overall, results replicate when applying
cross-prediction and are therefore only briefly summarized: iCodes is e590 >10256 more
likely than the reduced iCodes-model and 63% of all participants can be best described by
iCodes (separated for conditions: 91%, 59%, 49% of participants when search is restricted,
unrestricted with costs, or unrestricted without costs, respectively). Overall correlations
between predicted mean probabilities of cue values searched and observed proportions of
cue-values for cross-prediction trials with fixed parameter λsdiffer by a value less or equal
THE ATTRACTION SEARCH EFFECT 28
to .01 in comparison to correlations reported above. Correlations between predicted
probabilities and observed proportions for cue-values per cue-pattern that are most likely
opened next according to the model are lower with rblack =.77 for iCodes and rblack =.33
for iCodes with no impact of options on concealed cue-values (cf. Figure 8).
Joint Analyses of Properties of Attraction Search
Generalizability of the Attraction-search Effect beyond the First Cue-value
Opened
The aforementioned analyses examined the predicted attraction search effect relative
to the experimental design comparing different cue information patterns. In the upcoming
section, we test whether the attraction search effect also shows in absolute terms (and not
only when comparing two versions of cue-patterns) and whether the effect generalizes to
search beyond the first cue-value opened. For each acquisition of a cue-value, we simulated
iCodes’s search prediction with sensitivity parameter Pfitted from choices for each
participant. We then assessed whether the cue-value of the more attractive option
according to iCodes (i.e., a cue-value of the option with the highest activation) was also
opened by the participant. The mean overlap of trials in which a participant behaved
according to the model, p(agree), was subtracted from the complementary mean number of
trials in which a participant behaved in disagreement to the model (i.e., searching a
cue-value of the less attractive option), p(disagree)=1p(agree). Hence, we can define an
absolute attraction search score ASSc =p(agree)p(disagree)with the same properties as
the score above: The minimum is -1, the maximum is +1. A value of 1 signifies a perfect
attraction search effect. The index is zero if there is no correlation between search direction
and the content of revealed information.9
Figure 9 shows the mean values of the absolute ASSc for the first to sixth cue-value
opened together with the 95% confidence intervals and Cohen’s deffect size measures. The
attraction search effect as predicted by iCodes was observed for the first, second, third and
THE ATTRACTION SEARCH EFFECT 29
fifth cue-value opened with all Cohen’s d > 0.28 and all ps< .05 as evaluated by t-tests.
Overall, results suggest that the attraction search effect also shows in absolute terms and
generalizes to up to at least three cues searched.
Automaticity of the Attraction Search Process
The Parallel Constraint Satisfaction Model of Decision Making has been proposed as
a dual process model for intuitive (i.e., effortless and automatic) and deliberate decision
making (Glöckner & Betsch, 2008a; see also Glöckner & Witteman, 2010). The core
process of cue integration is assumed to be based on intuitive-automatic processing. This
assumption has been supported by studies showing that participants are able to integrate
multiple pieces of information in a compensatory fashion rapidly and in much less time
than would be required for deliberate calculations (e.g., Glöckner & Betsch, 2008b, 2012).
To explore whether information search and in particular the attraction search effect rests
mainly on deliberate or intuitive processes, we analyzed individuals’ average time for
deciding which information to search first (search-decision time) and its correlation with
interindividual differences in the magnitude of the attraction search effects. If attraction
search would result mainly from slow and time-consuming deliberation, a positive
correlation would be expected and slower participants should show larger attraction search
effects. If (more) careful deliberation concerning search reduces the effect, a negative
correlation would be expected.
Search-decision time was measured as the time participants took to open the first
concealed cue-value for the first occurrence of each of the 16 cue-patterns, to rule out
learning effects due to pattern repetition. The overall median search-decision time is 3134
milliseconds, which indicates that some deliberation might be involved, considering that
the overall decision time including search and integration in previous studies was in a
similar range (cf. Glöckner & Betsch, 2008b). In a similar vein, there is an overall positive
correlation between individuals’ median search time and their attraction search score,
THE ATTRACTION SEARCH EFFECT 30
Pearson’s r=.18 (t(142) = 2.13,p<.05).10 This correlation is, however, mainly driven by
differences between studies and conditions, and disappears when controlling for conditions
(partial correlation r=.08,p=.36). Specifically, median search-decision times were longer
for restricted search (Md = 4506ms) than for unrestricted search with costs (Md =
3153ms) and unrestricted search without costs (Md= 2140ms) and corresponding
differences were found for effect sizes of the attraction search score (see Figure 3). Hence,
scarcity and costs for information search seem to increase the degree of deliberation about
search and this is associated with an increasing attraction search score. Overall, this
indicates that attraction search effects are driven by more time-consuming top-down
activation processes that might involve increased deliberation. If this hint to rather
deliberative processes extends to information integration in tasks involving search is an
interesting question for further research.
Study 3: Search Bias and Accuracy
Search for cue-values of the more attractive option may lead to better or worse
decisions depending on the decision environment. For the cue-patterns used in studies 1
and 2, search according to the attraction search effect did not relate to choice accuracy (see
Appendix B for details). In the third study, we tested cue-patterns that are—according to
iCodes—predicted to either mislead or support participants showing the attraction effect in
finding the better option. If choice depends on search, participants’ tendency to search for
cue-values of the more attractive option is predicted to correlate negatively or positively
with accuracy depending on the specific pattern of cue values that are hidden and yet to be
uncovered.
Methods
We replicated the same methodology from Study 2 for the condition with
unrestricted search with costs. 44 participants (26 female, mean age = 25, SD = 6, mainly
students from the University of Bonn) were recruited and received a fixed amount of
THE ATTRACTION SEARCH EFFECT 31
4e(4.8USD) and 2.5 Cents for each correct decision using the same 128 trials as in
studies 1 and 2 (Table 1). In each trial, participants had to open one additional cue-value
for free and were allowed to open as many additional cue-values as desired with a cost of
0.25 Cents for each uncovered cue-value, replicating the condition unrestricted search with
costs from Study 2. In difference to prior studies, we included four repetitions of four new
cue-patterns (i.e., 16 additional trials in total). For two beneficial cue-patterns, search for
cue-values of the more attractive option is predicted to result in more correct decisions
(Table 3, top row). For the other two detrimental cue-patterns, search for cue-values of the
more attractive option is predicted to result in fewer correct decisions (Table 3, bottom
row). For example, for the detrimental cue-pattern 1, a positive cue-value speaks for option
B with all other cue-values concealed before search. Following the attraction search effect
would lead to search for cue 2 of option B. Opening this positive cue-value renders option
B even more positive. Doing this, however, is detrimental because option A dominates
option B when considering all cues. Not following the attractions search effect would lead
to search of cue 1 of option A showing indifference of cue 1 between options. Thus, in case
participants do not search cue-values of the more attractive option, they are more likely to
make a correct decision for option A.
Results
Concerning the attraction search effect, results are very similar to the condition with
unrestricted search with costs in Study 2. The overall attraction search score based on 128
trials is of almost identical size and significantly different from zero (mean of ASSc =.34;
t(43) = 11.98,p<.001). Attraction search scores for single cue-patterns are all
significantly different from zero (t(43) >2.80). The size of the attraction search scores for
single cue-patterns is almost perfectly correlated between studies (r=.99,t(6) = 25.10,
p<.001) indicating a high reliability of the findings.
For the beneficial cue-patterns (Table 3, top row), almost all participants chose the
THE ATTRACTION SEARCH EFFECT 32
better option after search (mean performance M=.97, SD =.05). For the detrimental
cue-patterns (Table 3, bottom row), mean performance was low with M=.30 (SD =.32)
for cue-pattern 1 and M=.18 (SD =.22) for cue-pattern 2. Mean performances for
beneficial and for detrimental cue-patterns are significantly different from each other
(t(43) = 26.92,p<.001) and different from chance performance of .50 (detrimental:
t(43) = 10.32,p<.001; beneficial: t(43) = 61.70,p<.001).
We calculated individual attraction search scores based on 128 trials as a measure of
participants’ individual tendency to search cue-values of the more attractive option to
predict average performance for the sixteen additional trials. As predicted, we found a
negative correlation between the individual attraction search score and average
performance in the detrimental cue-patterns (r=.44,t(42) = 3.14,p<.01). That is,
participants showing the attraction search effect in the 128 trials more strongly are also
more likely to choose the inferior option for the detrimental cue-patterns. Almost all
participants answered the beneficial cue-patterns correctly which probably generated a
ceiling effect. For the beneficial cue-patterns, we therefore find a positive although
statistically insignificant correlation between the individual attraction search score and
average performance (r=.15,t(42) = 0.99,p=.33).
Discussion
Overall, results of Study 3 show that search for cue-values of the more attractive
option can lead to lower or higher accuracy in choices dependent on the type of
cue-patterns available in the environment. Thus, bias in search can be linked to accuracy
in choices in a meaningful way as predicted by iCodes.
Re-analyses of Published Data Sets
The unique iCodes prediction of the attraction search effect was confirmed in three
experimental studies, and it turned out surprisingly large. However, all studies reported so
far were designed in a restrictive fashion to demonstrate this effect, and hence, one might
THE ATTRACTION SEARCH EFFECT 33
suspect that its size might be exaggerated (Wells & Windschitl, 1999; Westfall et al., 2015).
If the tendency to prefer information search about the currently most attractive option is a
general feature of information search as predicted by iCodes, it should also show in typical
MouseLab studies without these artificial restrictions. Therefore, we re-analyzed five
published studies by one of the authors (AB) that had been conducted for different
purposes. The studies are described in Bröder and Schiffer (2003, here: Study 1), Bröder
(2003, Exp. 2, here: Study 2), Bröder (2005, Exp. 4a, here: Study 3), and Bröder and
Schiffer (2006, both experiments, here: Studies 4 and 5). The sample sizes in the five
studies were 60, 120, 60, 120, and 120, respectively, resulting in 480 participants altogether.
Methods
All experiments also employed hypothetical stock market games with three options
described by four cues. For half of the participants in Study 5, the stock market game
changed to a structurally equivalent real estate investment game in the second half of the
trials. Cue-values were concealed, and participants had the opportunity to learn the cue
validities through feedback. In each of 80 trials (160 trials in Studies 4 and 5), participants
saw an empty cue-by-option matrix, and they could acquire new information by clicking on
the respective fields. All experiments used binary cues like the experiments described
above. We refer the reader to the original sources for details of the experiments that varied
payoff structures and other independent variables that are not of interest in the current
context.
Second Information Purchase
The simplest analysis in order to test for the existence of an attraction search effect is
to examine the second information acquisition after one of the 12 information boxes had
been opened. If the first cue revealed is positive, then the respective option would become
the most attractive one relative to the other two. If the cue-value was negative, however,
then the respective option would be the currently least attractive option. Hence, according
THE ATTRACTION SEARCH EFFECT 34
to the attraction search effect, the probability of switching search to another option when
the revealed cue-value is negative p(switch option|negative value)should exceed the
tendency p(switch option|positive value)to switch the option if the revealed information is
positive. Hence, we can define an attraction search score as
p(switch option|negative value)p(switch option|positive value)which is identical to the
absolute attraction search score ASSc introduced above. This index is independent of any
general tendency to search more option-wise or more cue-wise: Any general tendency to
show a certain search direction would not be influenced by the content of the information
opened in the first search step. This index was computed for each participant across all
trials of the experiment. Figure 10 shows the mean values of the ASSc for the five
reanalyzed studies together with the 95% confidence intervals and Cohen’s deffect size
measures. The attraction search effect predicted by iCodes was observed in all experiments
with all Cohen’s ds>1.00 and all ps< .001 as evaluated by one-sample t-tests.
Information Purchases Beyond the Second Purchase
Analyzing the second purchase after one piece of information was revealed gives the
most unequivocal evidence of an attraction search effect as demonstrated above. However,
it is also of interest if the attraction search effect can be found in later purchases. Since the
re-analyzed studies had three options, a different scoring had to be used in order to deal
with the fact that options’ attractiveness values may be tied occasionally. For example,
after opening the most valid cue for options A and B, they might both have positive
cue-values. Hence, they have the same current attractiveness which is higher than option
C’s. In these cases, continuing search on either option A or B was scored “+0.5” whereas
continuing with option C was scored “-1”. If both cue values were negative, the scoring
would have been “-0.5”, “-0.5”, and “+1” for options A, B, and C, respectively.
Attractiveness of all options in each trial was approximated by a strictly
compensatory linear rule integrating the hitherto revealed cue-values. Note that this
THE ATTRACTION SEARCH EFFECT 35
modified index has similar properties to the indices above: Its expected value is zero if
there is no dependency of search on the attractiveness of options, and it is positive
(negative) if the choice conforms to (contradicts) the attraction search effect prediction.
Note, however, that it may not reach the “+/- 1” boundaries. Also, the later the
purchasing step analyzed, the smaller is the number of trials on which its calculation is
based since in many trials, participants stopped search quite early. Hence, we only
analyzed the 3rd up to the 6th information purchase in each trial. The score was computed
for each participant in each trial, and Figure 11 reports the overall means of these
individual means together with 95% confidence intervals and effect sizes.
Figure 11 indicates that the prediction of an attraction search effect was corroborated
for 17 of the 20 analyses. In the three remaining cases (all in Studies 1 and 2), the score
did not significantly deviate from zero. Note, however, that the modified score for later
information purchases beyond the second purchase need not provide unequivocal support
for iCodes since the predictions are not completely unique for the model. The effect for the
fourth information purchase, for example, would also be predicted by an elimination by
aspects heuristic (EBA, Tversky, 1972) when people exclude the least attractive option
from consideration after they have inspected the most valid cue for all options.
Discussion
Whereas the experiments reported in the first part of this article were explicitly
intended to test for the new prediction of the extended model, the re-analyzed data sets
were collected before iCodes was even formulated. They comprise usual MouseLab studies
on information search that were originally analyzed with the standard parameters
characterizing search introduced by Payne et al. (1988). However, this general
characterization of the search process obviously obscured the powerful attraction search
effect that could be revealed now by a second look at the same data. The second
information purchase after opening one cue-value provides unequivocal evidence: if the
THE ATTRACTION SEARCH EFFECT 36
cue-value opened is negative, participants are more likely to switch to another option than
if it is positive. This is clearly in line with the predicted attraction search effect, but it
cannot be explained by fixed search strategies as assumed by heuristics. The prediction of
an attraction search effect was also confirmed by analyzing the purchases beyond the
second acquisition, but note that this evidence is weaker since the predictions for positive
scores may not be unique to iCodes.
These overall large effects in the data had been overlooked by the former analyses that
aimed at describing general characteristics of the search process, such as Payne’s (1976)
strategy index that quantifies whether search is more cue-wise or option-wise without
considering the content of the revealed information. Given these surprising confirmations of
the attraction search effect in our re-analyses, we encourage researches to scrutinize their
old MouseLab studies to test for a potential attraction search effect in their data.
Overall Discussion
In this article, we propose a model of integrated coherence-based decision and search
(iCodes) as a comprehensive process model for decision making. Furthermore, we tested
the attraction search effect as a new qualitative prediction derived from the model as well
as the model’s overall capability to predict choices and search in decision making.
We showed that participants tend to increasingly search for cue-values of attractive
as compared to less attractive options in three studies. The effect was present when search
was restricted (Study 1), unrestricted with costs (Study 2), or unrestricted without costs
(Study 2). Unrestricted search with costs and restricted search doubled the size of the
effect relative to unrestricted search without costs. We showed (Study 3) that biased search
can result in higher or lower choice accuracy depending on the cue-patterns in the decision
environment.
Participants consistently (over cue-patterns) differed in the extent that they were
affected by the initial attraction for options suggesting that size of the attraction search
THE ATTRACTION SEARCH EFFECT 37
effect depends on individual properties of participants. The attraction search effect could
be demonstrated for the first, second and third cue-value searched. iCodes, a fully specified
coherence-based network-model of decision making and search, could explain the data very
well and better than a network model that did not involve interactive activation of
concealed cue-values and options. Extensive reanalyses of data from five published studies
could also demonstrate the attraction search effect showing that the effect is not restricted
to the cue-patterns and settings used in the three studies of the article.
Attraction Search Effect in Prior Studies
One may wonder why this strong attraction search effect was not observed in prior
studies on cue-search in probabilistic decision making. There are at least two reasons:
First, since theories did not predict an effect of already revealed cue values on search
direction, standard analyses did not include respective conditional analyses and the effect
was considered to be part of a largely noisy information search process. Second, some
research paradigms precluded the effect by artificially restricting information search. A
closer inspection of the literature on search for cues in probabilistic decision making reveals
that our task differed in one crucial aspect from the task used in many key-studies on
cue-search (Bröder, 2000; Dieckmann & Todd, 2012; Lee et al., 2014; Mata, von Helversen,
& Rieskamp, 2010; Newell & Lee, 2011; Newell et al., 2004; Newell & Shanks, 2003; Newell
et al., 2003; Rakow et al., 2005; Rieskamp, 2006; Rieskamp & Otto, 2006; Ravenzwaaij et
al., 2014; Söllner & Bröder, 2016): The task used in those former studies allowed
participants to uncover all values of a cue at once and not single cue-values for options
separately.11 This artificial restriction of information-search in the lab may not be
representative of the real-world (Brunswik, 1955): By gathering a cue-value about one
decision-option, one does not automatically receive all cue-values from this cue for all other
options. More importantly for our research question, this restriction leads to a
non-diagnostic task for the attraction search effect (Jekel, Fiedler, & Glöckner, 2011). This
THE ATTRACTION SEARCH EFFECT 38
is problematic insofar that these studies thereby lent unjustified support for theories of
search based on properties of cues such as validities only.
Alternative Theoretical Accounts
At first glance, the newly predicted attraction search effect shares similarities with
both confirmatory search as well as the win stay/lose shift heuristic. However, the
phenomenon is conceptually different, and these two accounts cannot readily explain our
experimental results.
Confirmatory Search. The attraction search effect is distinct from confirmatory
search (also known as selective exposure), which describes people’s tendency to “avoid
information likely to challenge them and seeking information likely to support them” (Hart
et al., 2009, p. 556). While confirmatory search effects require a priori information of
whether the cue-value is in line with the preferred hypothesis or require a type of search
that makes confirmatory evidence more likely, the attraction search effect follows merely
from interactive activation of available evidence and a piece of concealed information
belonging to an option. Since we did not provide a hint on the valence of the concealed
information in the studies reported in this paper, confirmatory search was by design
precluded.
One might, however, argue that participants infer the valence of concealed cue-values
from the values of available cues. For example, if the two most valid cues are positive for
option A and all other cue-values are concealed (i.e., version 1 of cue-pattern 5; Table 1),
the third most valid cue is also likely to speak for option A since all cues probabilistically
reveal the same true state.12 Thus, confirmatory search and the attraction search effect do
not differ in their prediction of search for cue-values of option A for this trial.
Note, however, that even with this additional assumption confirmatory search and
the attraction search effect differ in predictions for some of the cue-patterns included in our
studies. If the initial choice tendency (or hypothesis) favors an option, confirmatory search
THE ATTRACTION SEARCH EFFECT 39
predicts search of additional positive information for this option. If, instead, the initial
hypothesis disfavors an option, confirmatory search—in a strict interpretation—predicts
search of additional negative information for this option. Thus, confirmatory search for the
task used in our study predicts that the valence of the information of an option searched
matches the initial valence of the option. In contrast, iCodes predicts that search is always
directed towards the favored option. Thus, for example, confirmatory search also predicts
inspection of a further cue-value of option A in case the first two cue-values are of negative
valence for option A as it is for example the case in version 2 of pattern 5 (Table 1). Our
data show that this prediction does not hold empirically, since individuals tend to look up
information for the other option. To account for this finding, it is possible to relax the
predictions of confirmatory search further by also allowing the possibility for looking up
information from the other option that might support the hypothesis that the currently
considered option is inferior. This is problematic since predictions of confirmatory search
then become rather unspecific: Both search for option A and option B are in line with the
theory. Hence, nothing is forbidden, the theory loses its ability to predict behavior and its
empirical content by becoming overly flexible (Roberts & Pashler, 2000; Glöckner &
Betsch, 2011). Therefore, iCodes has the comparative advantage to provide a fully specified
alternative model for the same behavior that makes more precise predictions.
One potential further alternative explanation for the attraction search effect related
to confirmatory search is that people might use the information that cue-values more often
are different between both options than not (i.e., the discrimination rate of cues, see also
footnote 3) to infer the value of a cue without opening it (Jekel et al., 2014). This would
mean that, for example, after seeing a negative cue value for option A, participants would
not look up the value of the same cue for option B but infer it and look up the information
of other less valid cues instead. If this tendency for inferring cues would be related to the
value (positive / negative) of a cue due to confirmatory search, this could potentially lead
to observing behavior in line with the attraction search effect as well. Inspection of the
THE ATTRACTION SEARCH EFFECT 40
data, however, speaks against the hypothesis that participants infer cues based on such a
strategy (see Tables A1 to A3 in Appendix A). For cue-pattern 2, for example, for the
majority of trials (i.e., 60%, 64%, and 80% for the three conditions) participants search the
first cue-value of option B when the initial evidence of the first cue for option A is negative
instead of inferring it. Switching to one of the other less valid cues is only rarely selected
(aggregated probability for searching cues 2 to 4 for option B: 12%, 12%, 5%). Similar
results are observed for other cue patterns (e.g., cue-pattern 5).
Win-Stay/Lose-shift Heuristic. The attraction search effect has conceptual
similarities with the win-stay/lose-shift heuristic in reinforcement learning (Nowak &
Sigmund, 1993; Worthy & Maddox, 2014). The heuristic describes participants’ tendency
to repeat an action if rewarded and to switch to an alternative action if punished.
Participants in our study did not receive feedback on their accuracy of decisions for options
and therefore also did not receive feedback on the efficiency of their search. Therefore, the
win-stay/lose-shift heuristic does not apply to the search task of the studies. Nonetheless,
participants might have experienced uncovering a positive cue-value as “reward” and
uncovering a negative cue-value as “punishment”. If this was true, uncovering a positive
cue-value might have pushed participants continuing search for additional information of
the same option whereas uncovering a negative cue-value might have pushed participants
towards shifting search to the information of the alternative option. Note, however, that we
presented partially uncovered cue-patterns at the beginning of each trial (Table 1) and
participants tended to search cue-values of the more attractive option in accordance to a
compensatory integration of available cue-values such as described by iCodes. Thus, since
opening the first cue-value does not involve prior experience of search in the trial, the
win-stay/lose-shift heuristic cannot explain the strong effect of attraction on search for the
first cue-value opened (Figure 3) but might add to the observed effect for search beyond
the first cue-value opened.
THE ATTRACTION SEARCH EFFECT 41
Stable Individual Differences of the Attraction Search Effect
Since participants differed consistently over cue-patterns in the size of the attraction
search effect, an individual parameter modeling the relative impact of the initial preference
of an option and other influences of the decision situation (i.e., cue-validity or cue-salience)
might add to the modeling of information search in iCodes. Additionally, modeling
stopping of cue-search (Lee et al., 2014) is still missing in the current implementation of
the model. Recent evidence shows that stopping can be best modelled with a flexible
evidence-threshold that needs to be surpassed by evidence from available cues before search
is terminated (Söllner & Bröder, 2016; Hausmann & Läge, 2008; Lee et al., 2014). In a
similar vein, one potential implementation of a flexible threshold in iCodes is to let
activation of nodes representing concealed cue-values surpass a threshold before being
considered.
Situational and Individual Moderators and Generalizations of the Attraction
Search Effect
In the current research we show that the magnitude of the attraction search effect is
moderated by situational factors (e.g., information costs) and that it is likely that it is
moderated by individual factors as well due to the observed reliable interindividual
differences. Promising factors for future investigations might be whether feedback on the
accuracy of decisions is provided (cf. Rieskamp, 2006; Rieskamp & Otto, 2006) that might
be used to correct search as well, or differences in cognitive development between age
groups (cf. Betsch, Lang, Lehmann, & Axmann, 2014). Although we show that the effect is
strong and can be found in various studies, it is an open question to what extent the effect
also applies to more natural representations of information in a search task. It is
furthermore an open question whether the attraction search effect also generalizes to search
for cue-values inside the memory of the decision maker (Gigerenzer et al., 2012). The
attraction search effect predicts that participants are more likely to recall cue-values for
THE ATTRACTION SEARCH EFFECT 42
options that are favored when making decisions from memory. This hypothesis could be
easily tested in a modified standard paradigm for decision making from memory (e.g.,
Bröder, Newell, & Platzer, 2010; Platzer & Bröder, 2012; Persson & Rieskamp, 2009).
Conclusion
With the attraction search effect we have demonstrated a new empirical phenomenon
that is not predicted by current toolbox or evidence accumulation models, but follows
naturally from an interactive coherence maximizing view. A precise computational
instantiation of the latter approach has been provided with iCodes. We conjecture that the
attraction search effect offers a wealth of possibilities for testing its individual and
situational moderators that will eventually advance theoretical development targeting at an
integrative theory of information search and information integration in decision making.
THE ATTRACTION SEARCH EFFECT 43
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Notes
1. Note that the exact sizes of boxes—i.e., the distribution of likelihoods for opening cue-values—is dependent
on the relative impact of cue-validities and the attraction search effect that might differ individually.
2. Note, however, that a recently proposed alternative expected utility framework questions the validity of
this normative evaluation (Crupi, Tentori, & Lombardi, 2009; but see response from Tweney, Doherty, &
Kleiter, 2010).
3. Given the constraint for the entire set of trials that cue-validities—when recalculated for the naïve
Bayesian incentive scheme—were above .5 and in the ordering told to participants. The Bayesian incentive
scheme led to noncompensatory environment with validities of .86, .69. .59, and .56 for cue 1 to 4.
Specifically, after chance correction (subtracting .5) the first cue was more valid than the sum of the
remaining (chance corrected) cues. Note that differences in validities cannot influence choice behavior
because participants did not receive feedback about their choice accuracy before the end of the study. The
discrimination rate for cues 1 to 4 was .74, .50, .71, and .63, respectively.
4. That is, the two least valid cues cannot overrule the first or the second cue since log(.7/.3) + log(.6/.4) is
below log(.9/.1) or log(.8/.2).
5. We fixed this ratio for all participants to keep the model simple. The impact of the attraction of options on
search varied consistently for cue-patterns between participants in the studies. Thus, the ratio could
potentially be implemented as a free parameter in the model.
6. Note that specific values of parameters Pand λcthat were fitted using choices do not necessarily imply a
specific search behavior; both parameters can be independent of search. To test this, we correlated
individual model-parameters with the individual attraction search score and find correlations close to zero
(r=.05 for Pand r=.05 for λc) that are statistically non-significant (all ps> .55).
7. Note that weights for links between options and concealed cue-nodes are fixed with a value of .01 in iCodes
and thus a model with zero weights is not a submodel of iCodes. Thus, the model without connections
from options to concealed cue-values does not necessarily lead to a worse account of the data.
8. The good comparative performance in predicting search of the reduced iCodes model without connections
to options is mainly driven by “easy trials” in which the predicted probability for search is extreme. It
drops to r=.65 (r=.10) for “harder trials” with predicted search probabilities in the range .2 to .8 (.3 to
THE ATTRACTION SEARCH EFFECT 55
.7), respectively. The predictive performance of the full model, in contrast, remains relatively constant also
for harder trials (r=.83 and r=.73).
9. Note that the attraction search score for the second to sixth cue-value opened excludes participants from
Study 1 who could only acquire one additional cue-value and cue-patterns 1, 3, 4, and 6 with only two
concealed cue-values.
10. The pattern of results is stable when including search times of all 128 trials: differences in search time are
statistically significant between Study 1 and Study 2 and statistically not significant between conditions in
Study 2. We also find a statistically significant positive correlation between individual attraction search
scores and search time of similar size (r=.19) when including all 128 trials in all studies. The only
difference are much lower search times with an overall median search time of only 1354ms and a higher,
albeit statistically not significant, partial correlation when controlling for conditions (r=.15,p=.08,
two-sided test).
11. For exceptions see Bröder (2003, 2000); Bröder and Schiffer (2003, 2006); Glöckner and Betsch (2008b);
Mata et al. (2007); Payne et al. (1988); Reisen, Hoffrage, and Mast (2008); Rieskamp and Hoffrage (1999).
Note that studies using the Payne-Index of cue-search (Payne et al., 1988) or similar measures (Böckenholt
& Hynan, 1994) need to allow for search of single cue-values.
12. To give an intuition for this fact: Assume all cues are perfectly reliable, that is, assume cues always give a
correct prediction. Inspecting one cue is sufficient to infer the values of all other cues since cues are
perfectly correlated in this case.
THE ATTRACTION SEARCH EFFECT 56
Table 1
Cue-patterns used in Studies 1, 2, and 3. ? = concealed information, x = unavailable
information, + = positive advice, – = negative advice. For each trial, value/s in
parenthesis/es represent the second versions of cue-patterns. The attraction search effect as
predicted by iCodes states that participants search cue-values for option A for version 1 and
more likely for option B in version 2 in parentheses.
Cues Pattern 1 Pattern 2 Pattern 3 Pattern 4
A B A B A B A B
Cue 1 + + (–) ? x ? – (+)
Cue 2 + (x) + ? ? x – (+) ?
Cue 3 ? + ? ? ? + +
Cue 4 ? ? ? ? +
Pattern 5 Pattern 6 Pattern 7 Pattern 8
A B A B A B A B
Cue 1 + (–) ? + (–) – (+) + (–) – (+) +
Cue 2 + (–) ? ? ? ? ? +
Cue 3 ? ? + – + – ? ?
Cue 4 ? ? + ? + (?) ?
THE ATTRACTION SEARCH EFFECT 57
Table 2
Differences of the attraction search score between study conditions predicted by a multilevel
regression with random intercepts and random slopes for participants.
Variables b se t df p
Intercept 0.25*** 0.01 17.67 121.75 <.001
Unrestricted without costs vs. others -0.19*** 0.03 -7.27 133.31 <.001
Restricted vs. unrestricted with costs -0.02 0.04 -0.56 86.05 .58
Note. Contrast “Unrestricted without costs vs. others” is coded as 2/3 for condition with unre-
stricted information search without costs and -1/3 for the other two conditions. Contrast “Re-
stricted vs. unrestricted with costs” is coded 1/2 for the condition with restricted information
search (i.e., Study 1) and -1/2 for unrestricted information search with costs. ∗∗∗ p<.001.
THE ATTRACTION SEARCH EFFECT 58
Table 3
Four additional cue-patterns in Study 3 (repeated four times) for which attraction search is
predicted to increase (beneficial) vs. decrease (detrimental) the likelihood of accurate choice.
Cues Pattern 1 Pattern 2
A B A B
Beneficial task structure
Cue 1 + +
Cue 2 + +
Cue 3 + +
Cue 4 + +
Detrimental task structure
Cue 1 + + +
Cue 2 + + +
Cue 3 +
Cue 4 + +
Note. All cue-values except for cue-values in rectangles are concealed (i.e., the cue-patterns are
identical to cue-pattern 2 version 1 and 2 in Table 1 in studies 1 and 2). Cue-patterns are sorted
in the table such that option A is the better option (according to naïve Bayes). In the study, the
order of columns of cue-patterns was set randomly and cue-patterns were included in the remaining
128 trials at random positions.
THE ATTRACTION SEARCH EFFECT 59
Exemplary Trial
+(−)
?
?
?
Cue 1
Cue 2
Stock A Stock B
Positive Cue−value
C1A
Source
A B
Cue 1
Positive Cue−value with Subnet
C1A C2A C1B C2B
Source
A B
Cue 1 Cue 2
Negative Cue−value with Subnet
C1A C2A C1B C2B
Source
A B
Cue 1 Cue 2
Figure 1 . Modeling cue-search in a model of integrated coherence-based decision and
search (iCodes). Continuous and dashed lines indicate excitatory and inhibiting
connections, respectively. Black and grey lines indicate bi-directional and uni-directional
links, respectively. The open cue-value (either positive or negative) that is already available
in the decision situation (upper left display) forms a network resulting in an initial
preference for option A as indicated by a larger box-size for option A (upper right display)
in case the cue-value is positive (or an initial preference for option B in case the cue-value
is negative, not shown). Concealed cue-values (shaded rectangles) form a subnet: The
current preference for options (lower left or right display for positive or negative evidence
for option A) as well as cue-validities influence search for cues. Larger box-sizes indicate
the increased likelihood (i.e., preference) for each concealed cue to be opened next (see text
for more explanations).
THE ATTRACTION SEARCH EFFECT 60
Figure 2 . Screenshot of the stock-market game (translated from German) of cue-pattern 3
in version 2 (Table 1). Expert DFMS speaks against stock “uyz” (“-”); information on
stock “cqw” is not available (“X”) for experts DFMS and FJMT. The participant can
either uncover the recommendation of expert KNTV on stock “cqw” or expert CDJP on
stock “uyz” (“?”). After uncovering one concealed recommendation, the participant is
asked to choose between stocks. Names and order of options were randomly generated for
each participant.
THE ATTRACTION SEARCH EFFECT 61
Cue−pattern
Attraction search score
1 2 3 4 5 6 7 8 Overall
−.1
0
.1
.2
.3
.4
.5
.6
.7
.8
Figure 3 . Mean attraction search score with 95%-confidence intervals by cue-pattern and
overall for Study 1 and Study 2. Numbers above upper confidence intervals indicate the
effect size (Cohen’s d) of the attraction search score for each pattern or overall in both
studies. An additional interactive boxplot of the data showing also the distribution of
individual scores can be accessed at
http://coherence-based-reasoning-and-rationality.de/materialASE/interactiveASE.html.
THE ATTRACTION SEARCH EFFECT 62
Attraction search score per cue−pattern
Attraction search score per cue−pattern (first occurrence only)
−0.2 0 0.2 0.4 0.6 0.8 1
−0.2 0 0.2 0.4 0.6 0.8 1
r = .89***
Study 1: Restricted information search
Study 2a: Unrestricted with information costs
Study 2b: Unrestricted without information costs
Attraction search score per participant
Attraction search score per participant (first occurrence only)
−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
r = .63***
Figure 4 . Mean attraction search score for all eight repetitions (cf. Figure 3) plotted
against the mean attraction search score based on the first occurrence of each cue-pattern
per pattern (left display) and per participant (right display). The dotted diagonals indicate
the identity line. ∗∗∗ p<.001
THE ATTRACTION SEARCH EFFECT 63
Options
Cue−
Values
Cues
Validity
opt1opt2
avalidity = 1
wv1 # wv2 # wv3 # wv4
wcue1opt1=.01 wcue2opt1=.01 wcue3opt1=.01 wcue4opt1=.01
acue1,1 acue2,1 acue3,1 acue4,1
wcue1opt2=.01 wcue2opt2=.01 wcue3opt2=.01 wcue4opt2=.01
acue1,2 acue2,2 acue3,2 acue4,2
aopt1
wopt1opt2= −.2
aopt2
wopt2opt1= −.2
wcue1cue1,1 = .1 # wcue1cue1,2 = .1 wcue2cue2,1 = .1 # wcue2cue2,2 = .1 wcue3cue3,1 = .1 # wcue3cue3,2 = .1 wcue4cue4,1 = .1 # wcue4cue4,2 = .1
acue1acue2acue3acue4
Figure 5 . Depiction of the model of integrated coherence-based decision and search
(iCodes) for cue-pattern 2 version 1 (i.e., all cue-values except for the most valid cue-value
of option 1 are concealed, Table 1). Grey shaded rectangles indicate concealed cue-values.
Grey lines indicate uni-directional links, all other links are bi-directional. Within each
rectangle, weights for links (i.e., w) are provided (e.g., strong inhibitory link
wopt1opt2=.2between options). Animations of the process of iterative updating of
node-activations in iCodes can be accessed at
http://coherence-based-reasoning-and-rationality.de/materialASE/pos/iCodes_pos.html in
case the first cue-value speaks for option 1 and
http://coherence-based-reasoning-and-rationality.de/materialASE/neg/iCodes_neg.html in
case the first cue-value speaks against option 1.
THE ATTRACTION SEARCH EFFECT 64
iCodes: Sensitivity P
P
Frequency
0 1 2 3 4 5
0 5 10 15 20
M = 1.66, SD = 0.91
iCodes: λc
λc
Frequency
0 1 2 3 4 5
0 5 10 15
M = 2.34, SD = 0.62
iCodes: λs
λs
Frequency
0 10 20 30 40 50 60 70
0 5 10 15
M = 20.18, SD = 12.97
WADD: ε
εWADD
Frequency
0.0 0.1 0.2 0.3 0.4 0.5
0 5 10 15 20
M = 0.15, SD = 0.06
TTB: ε
εTTB
Frequency
0.0 0.1 0.2 0.3 0.4 0.5
0 5 10 15
M = 0.18, SD = 0.08
Figure 6 . Frequency of fitted parameters P(extent of non-compensatory net-weights), λc
(sensitivity to differences in activations for options A or B), and λs(sensitivity to
differences in activations of concealed cue-values that can be searched) for iCodes and
(strategy application error) for WADD and TTB. Note that 19 participants have a P
parameter close to or exactly 0. When we remove those participants from the analysis, the
overall attraction search score is still statistically significant in all conditions (all ts>6.1,
p<.001) and the effect is still strong with Cohen’s dranging from 0.88 to 2.12.
THE ATTRACTION SEARCH EFFECT 65
% correct predictions
50 60 70 80 90 100
50 60 70 80 90 100
correct: 89.1%, BIC: 14093, part: 79.9% correct: 84.1%, BIC: 16592, part: 14.6% correct: 76.7%, BIC: 19390, part: 5.6%
Study 1, restr
Study 2, unrestr,
with costs
Study 2, unrestr,
without costs Study 1, restr
Study 2, unrestr,
with costs
Study 2, unrestr,
without costs Study 1, restr
Study 2, unrestr,
with costs
Study 2, unrestr,
without costs
iCodes WADD TTB
Figure 7 . Percentage of correct predictions for each model (iCodes, WADD, TTB) and
each experimental condition (restricted search in Study 1, unrestricted search with or
without costs in Study 2). Overall percentage of correct predictions, Bayesian Information
Criterion, and percentage of participants classified for each model are plotted in the
header. Violin plots are displayed: Means are black dots, medians are black thick lines, the
borders of the box indicate the lower or upper quartile (i.e., middle 50% of all data),
whiskers indicate the minimum or maximum data point within 1.5×the interquartile
range, white dots indicate outliers, and shapes around the boxplots indicate the density
distribution of the data.
THE ATTRACTION SEARCH EFFECT 66
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Predicted mean probabilities of cue−values opened
according to iCodes
Observed proportions of cue−values opened
r = .95; r_black = .81; log−Lik = −14383; correct = 67%
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Predicted mean probabilities of cue−values opened
according to iCodes without attraction search
Observed proportions of cue−values opened
r = .89; r_black = .58; log−Lik = −14569; correct = 61%
Figure 8 . Observed participants’ proportions of cue-values opened plotted against
predicted mean probabilities of cue-values opened for all 55 concealed cue-values in all 16
cue-patterns (black and grey dots). The left display shows predictions based on iCodes
with the attraction-search effect implemented (i.e., links from option-nodes to concealed
cue-values) and the right display shows iCodes with no direct impact of options on
concealed cue-values (i.e., links between nodes and concealed cue-values removed). Black
dots indicate for each cue-pattern the concealed cue-value with the highest probability of
being searched next based on iCodes. In the headers, correlations between predicted
probabilities and observed proportions are shown for all concealed cue-values (“r”; i.e.,
black and grey dots) or for cue-values per cue-pattern that are most likely opened next
according to the model (“rblack”; i.e., black dots only). Headers also show overall
log-likelihoods of the fit between iCodes and observed cue-values searched for (“log-Lik”)
and the percentage of correctly predicted cue-values searched for by participants
(“correct”).
THE ATTRACTION SEARCH EFFECT 67
Cue−value opened
Absolute attraction search score
1st 2nd 3rd 4th 5th 6th
−.2
−.1
0
.1
.2
.3
.4
1.44
0.41 0.35
−0.12
0.28
0.18
Figure 9 . Absolute attraction search score with 95%-confidence intervals for first to sixth
cue-value opened. Numbers above upper confidence intervals indicate the effect size
(Cohen’s d) of the attraction search score for each pattern or overall in both studies. An
additional interactive boxplot of the data also showing the distribution of individual scores
can be accessed at http://coherence-based-reasoning-and-
rationality.de/materialASE/interactiveASE_absolute.html.
THE ATTRACTION SEARCH EFFECT 68
Reanalyzed Study
Absolute attraction search score (ASSc)
12345
−.1
0
.1
.2
.3
.4
.5
.6
1.09
1.74
1.07
1.37
1.15
Study 1: Bröder & Schiffer (2003; N=60)
Study 2: Bröder (2003, Exp.2; N=120)
Study 3: Bröder (2005; Exp.4a; N=60)
Study 4: Bröder & Schiffer (2006, Exp.1, N=120)
Study 5: Bröder & Schiffer (2006, Exp.2; N=120)
ASSc = p(switch option|negative value) − p(switch option|positive value)
Figure 10 . Absolute attraction search score (ASSc) for the second information purchase in
five re- analyzed studies with 95%-confidence intervals and effect sizes Cohen’s d(numbers
above confidence intervals).
THE ATTRACTION SEARCH EFFECT 69
Reanalyzed Study
Modified Attraction search score
1−3 1−4 1−5 1−6 2−3 2−4 2−5 2−6 3−3 3−4 3−5 3−6 4−3 4−4 4−5 4−6 5−3 5−4 5−5 5−6
−.1
0
.1
.2
.3
.4
.5
.6
.7
.8
0.38
3.47
1.14
1.20
−0.28
2.85
0.85
0.19
1.09
2.74
1.46
0.96
0.84
3.01
1.51
0.69
1.20
3.30
1.29 1.14
Study 1: Bröder & Schiffer (2003; N=60)
Study 2: Bröder (2003, Exp.2; N=120)
Study 3: Bröder (2005; Exp.4a; N=60)
Study 4: Bröder & Schiffer (2006, Exp.1, N=120)
Study 5: Bröder & Schiffer (2006, Exp.2; N=120)
Figure 11 . Modified attraction search scores for the 3rd to 6th information purchases in
re-analyzed Studies 1 to 5 (Bröder & Schiffer, 2003; Bröder, 2003, 2005; Bröder & Schiffer,
2006) with 95%-confidence intervals and effect sizes Cohen’s d(numbers above confidence
intervals). In the labels for the x-axis, the first number indicates the experiment and the
second number the number of the information purchase.
THE ATTRACTION SEARCH EFFECT 70
Appendix A
Search-rates for All Cue-values in All Conditions
In the following Appendix C, Appendix D, and Appendix E, observed proportions of
cue-values opened first by participants for each cue-pattern and version are displayed. For
example in Study 2 pattern 4, in 83% of all cases participants chose to open cue 1 for
option A and in the remaining 17% cases participants chose to open cue 2 for option B
when the first cue for option B was negative. When the first cue for option B was positive
instead, participants chose to search for the less valid cue 2 for option B in 54% of all cases
which results in an attraction search score of the size .83 .46 = .37.
THE ATTRACTION SEARCH EFFECT 71
Appendix B
Rationality of the Attraction Search Effect in Study 1 and Study 2
In this Appendix, we discuss whether search of evidence for the more attractive option is
rational or irrational in that it leads to better or worse decisions for the cue-patterns used
in Study 1 and Study 2. To test whether making a correct decision is related to the
magnitude of an individuals’ attraction search effect, we ran a logistic multilevel-regression
with making a correct decision as dependent binary variable (1 = correct, 0 = incorrect)
and the centered individual attraction search score as predictor. The regression includes
random intercepts for participants and types of cue-pattern as well as two dummy variables
to control for the (three) experimental conditions. We find no significant relation between
the size of the attraction search score and the odds of making a correct decision (b= 1.02,
p=.24).
In a next step, we analyzed potential relations between attraction search and correct
decisions in more detail for each of the cue-patterns. However, no significant differences
between patterns were observed. In detail, for some cue-patterns, searching the cue-value
of the more attractive option coincides with searching a more valid cue-value (i.e.,
cue-patterns 1, 3 and 4 version 1 and cue-pattern 2 and 5 version 2 in Table 1). For those
“beneficial” cue-patterns, one would expect that odds for a correct decision increase when
the attraction search score increases. For “detrimental” cue-patterns where search for the
cue-value of the more attractive option leads to inspection of a less valid cue-value (i.e.,
cue-patterns 1, 3 and 4 version 2 and cue-pattern 2 and 5 version 1 in Table 1), one would
expect higher attraction search scores resulting in lower odds of making a correct decision.
There should be no relation in cases where the type of search is not correlated with cue
validity (i.e., cue-patterns 6, 7, and 8 for both versions). To test these relations
statistically, we added to the multilevel model reported above two centered
dummy-variables comparing either beneficial (dummyben) or detrimental patterns
(dummydet) to neutral patterns. We included two 2-way interaction terms for testing the
THE ATTRACTION SEARCH EFFECT 72
proposed relation between the attraction search score and the type of cue-pattern (i.e.,
dummyben ×ASSc and dummydet ×ASSc). Both interactions did not reach significance
(ps> .18). Hence, based on our data we conclude that search for cue-values of the more
attractive option does not lead to higher odds of making a correct decision.
The rationality of information search can also be assessed by testing whether looking
up a piece of information maximally increases the probability of making a correct decision
in case persons would apply a rational or approximately rational strategy for information
integration (Baron, Beattie, & Hershey, 1988; Nelson, 2005; Nelson et al., 2010). For the
analysis, we calculated for each of the 128 trials the probability of choosing the better
option after searching either the most valid available information from the more attractive
or the less attractive option according to the naïve Bayesian solution. Search of cue-values
for the more attractive option would lead to an average probability of .84 of making a
correct decision whereas search for cue-values of the less attractive option would lead to an
average probability of .83. This difference of 1% more correct decisions is not statistically
significant (t(254) = 0.43,p=.66). This indicates that the cue-patterns used in studies 1
and 2—that were well suited for demonstrating attraction search effects—cannot be used to
demonstrate its detrimental (i.e. biasing) or beneficial effects on the rationality of choice.
More generally, these analyses show by example that attraction-based search does not
necessarily lead to better or worse outcomes. They leave open the broader question
whether it is in general appropriate to show this attraction-based search or not. This would
be the question of the ecological rationality of this search principle which would require an
analysis of the structural properties of “typical” or “modal” decision environments.
THE ATTRACTION SEARCH EFFECT 73
Appendix C
Observed Proportions of Cue-values Searched for All Eight Cue-patterns in Study 1.
Cues Pattern 1 Pattern 2 Pattern 3 Pattern 4
A B A B A B A B
Cue 1 + + (–) 41% (60%) x 78% (51%) – (+)
Cue 2 + (x) + 45% (27%) 9% (10%) x – (+) 22% (49%)
Cue 3 92% (72%) + 2% (1%) 2% (2%) 73% (66%) + +
Cue 4 8% (28%) 1% (0%) 1% (0%) 27% (34%) +
Pattern 5 Pattern 6 Pattern 7 Pattern 8
A B A B A B A B
Cue 1 + (–) 43% (65%) + (–) – (+) + (–) – (+) +
Cue 2 + (–) 5% (8%) 86% (20%) 14% (80%) 86% (23%) 13% (74%) +
Cue 3 49% (21%) 3% (3%) + + 49% (36%) 51% (63%)
Cue 4 0% (1%) 0% (1%) + 0% (3%) + (0%) 0% (1%)
THE ATTRACTION SEARCH EFFECT 74
Appendix D
Observed Proportions of Cue-values Searched for All Eight Cue-patterns in Study 2 With Information Costs.
Cues Pattern 1 Pattern 2 Pattern 3 Pattern 4
A B A B A B A B
Cue 1 + + (–) 38% (64%) x 83% (46%) – (+)
Cue 2 + (x) + 46% (21%) 11% (11%) x – (+) 17% (54%)
Cue 3 90% (74%) + 1% (1%) 1% (1%) 76% (60%) + +
Cue 4 10% (26%) 2% (1%) 0% (0%) 24% (40%) +
Pattern 5 Pattern 6 Pattern 7 Pattern 8
A B A B A B A B
Cue 1 + (–) 41% (72%) + (–) – (+) + (–) – (+) +
Cue 2 + (–) 4% (5%) 85% (22%) 15% (78%) 82% (24%) 17% (74%) +
Cue 3 46% (15%) 7% (6%) + + 47% (35%) 51% (62%)
Cue 4 2% (2%) 0% (1%) + 1% (2%) + (1%) 2% (2%)
THE ATTRACTION SEARCH EFFECT 75
Appendix E
Observed Proportions of Cue-values Searched for All Eight Cue-patterns in Study 2 Without Information Costs.
Cues Pattern 1 Pattern 2 Pattern 3 Pattern 4
A B A B A B A B
Cue 1 + + (–) 72% (80%) x 74% (69%) – (+)
Cue 2 + (x) + 23% (13%) 3% (5%) x – (+) 26% (31%)
Cue 3 90% (90%) + 1% (0%) 1% (0%) 93% (88%) + +
Cue 4 10% (10%) 0% (0%) 0% (0%) 7% (12%) +
Pattern 5 Pattern 6 Pattern 7 Pattern 8
A B A B A B A B
Cue 1 + (–) 76% (89%) + (–) – (+) + (–) – (+) +
Cue 2 + (–) 3% (4%) 66% (39%) 34% (61%) 65% (39%) 34% (60%) +
Cue 3 20% (5%) 0% (1%) + + 50% (42%) 50% (57%)
Cue 4 1% (0%) 0% (0%) + 1% (1%) + (0%) 0% (0%)
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Whereas classic work in judgment and decision making has focused on the deviation of intuition from rationality,more recent research has focused on the performance of intuition in real-world environments. Borrowing from both approaches, we investigate to which extent competing models of intuitive probabilistic decision making overlap with choices according to the axioms of probability theory and how accurate those models can be expected to perform in real-world environments. Specifically, we assessed to which extent heuristics, models implementing weighted additive information integration (WADD), and the parallel constraint satisfaction (PCS) network model approximate the Bayesian solution and how often they lead to correct decisions in a probabilistic decision task. PCS andWADD outperform simple heuristics on both criteria with an approximation of 88.8% and a performance of 73.7%. Results are discussed in the light of selection of intuitive processes by reinforcement learning.
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Evaluates psychological and mathematical models that have been applied to individual juror decision making and identifies 3 research goals: to gain insight into adult cognition in a complex, naturally occurring reasoning task, to extend existing psychological models of decision making and judgment, and to provide empirical data on questions of interest to the legal community. A task analysis is presented in the form of an ideal juror model to describe and evaluate empirical research with respect to these goals. Component processes proposed in each model and empirical findings are compared across models and in relation to the task analysis. Models examined include information integration, Bayesian, Poisson, sequential weighting, and nonmodels. It is concluded that laboratory model applications to actual complex reasoning tasks must be based on thorough task analyses to avoid conflict between research goals and to facilitate generalization to natural settings. (130 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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