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Either greedy or well informed: The reward maximization – unbiased evaluation trade-off

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Abstract

Abstract People often believe that they exert control on uncontrollable outcomes, a phenomenon that has been called illusion of control. Psychologists tend ,to attribute ,this illusion to personality variables. However, we present simulations showing,that the illusion of control ,can be explained ,at a simpler level of analysis. In brief, if a person desires an outcome and tends to act as often as possible in order to get it, this person will never be able to know that the outcome,could have occurred with the same probability if he/she had done nothing. Our simulations show that a very high probability of action is usually the best possible strategy if one ,wants to maximize the likelihood of occurrence of a desired event, but the choice of this strategy gives rise to illusion of control.
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Either greedy or well informed:
The reward maximization – unbiased evaluation trade-off
Helena Matute (matute@fice.deusto.es)
Miguel A. Vadillo (mvadillo@fice.deusto.es)
Fernando Blanco (fblanco@fice.deusto.es)
Serban C. Musca (serbancmusca@gmail.com)
Departamento de Psicología, Universidad de Deusto
Apartado 1, 48080 Bilbao, SPAIN
Abstract
People often believe that they exert control on uncontrollable
outcomes, a phenomenon that has been called illusion of
control. Psychologists tend to attribute this illusion to
personality variables. However, we present simulations
showing that the illusion of control can be explained at a
simpler level of analysis. In brief, if a person desires an
outcome and tends to act as often as possible in order to get it,
this person will never be able to know that the outcome could
have occurred with the same probability if he/she had done
nothing. Our simulations show that a very high probability of
action is usually the best possible strategy if one wants to
maximize the likelihood of occurrence of a desired event, but
the choice of this strategy gives rise to illusion of control.
Introduction
The illusion of control has been observed in many different
laboratory experiments since the initial studies by Langer
(1975). It consists of people believing that they have control
over desired outcomes that are uncontrollable but occur
frequently. As a real life example, let us think of the way
ancient tribes danced for rain, or the way many people, still
today, believe in magical rituals rather than in scientific
medicine as the best means to improve their health. These
examples should give us an idea of the prevalence and
importance of this problem in relation to human welfare.
Most explanations for this effect have been framed in
terms of personality and self-esteem protection (e.g., Alloy
& Abramson, 1982). However, and without discussing the
importance of personality variables, what we would like to
argue is that the basic tendency towards an illusion of
control is present in all of us, as it is just a consequence of
the way we interact with the world when we want to
influence the occurrence of events. We will make use of
simulations to illustrate our point.
The basic idea is a very simple one. Imagine a person who
is trying to obtain an outcome that is of crucial importance
for survival. Quite probably, this person will tend to act at
every opportunity in order to obtain it. If the outcome is
uncontrollable but occurs frequently, if this person is
responding as often as possible, the occurrence of the
outcome will surely coincide with the person’s action most
of the time. Thus, it is not strange that under such
conditions, this person will develop an illusion of control. In
order to be able to realize that the outcome would have
occurred with the same probability regardless of responding,
this person should adopt a much more scientific strategy: he
or she should test not only what happens when a response is
performed but also what happens when a response is not
performed. That is, they should respond only in 50% of the
trials so that they can equally sample both cases. However,
are people ready to test what happens in the absence of a
magical ritual when they believe that the ritual is
responsible for a very important outcome?
The many studies that have been published showing that
laboratory participants are indeed able to detect when
outcomes are uncontrollable (e.g., Shanks & Dickinson,
1987; Wasserman, 1990) would make us believe that people
do naturally behave in the scientific way described above
and naturally detect response-outcome contingencies.
However, those laboratory studies instruct their subjects
very explicitly on how to behave and what to look for. If we
manipulate the instructions that participants receive in an
uncontrollable situation, participants who are simply
instructed to obtain the outcomes tend to respond at every
opportunity (and therefore, to develop an illusion of control
as well); on the other hand, those participants who are
instructed to adopt the scientific strategy, are the ones who
are able to realize that the task is uncontrollable (Matute,
1996). In other words, people do have the cognitive capacity
to detect the absence of control, but this does not necessarily
mean that they will use it by default, in naturalistic settings.
Indeed, Matute’s (1996) studies suggested that, unless there
is a special motivation to detect the degree of control that
one has over the outcome, people will tend to respond as
much as possible, rather than in 50% of the trials. In the
present research we will show that even for an artificial
system, responding as much as possible is the best possible
strategy when its aim is to obtain an outcome that is
controllable; but the counterpart of behaving this way is that
the system will be more prone to develop an illusion of
control when faced with uncontrollable situations.
Simulations
Procedure
Our simulations are based on the Rescorla-Wagner model
(Rescorla & Wagner, 1972) model, which is one of the most
In S. Vosniadou, D. Kayser, & A. Protopapas (Eds.) (2007). Proceedings of the European
Cognitive Science Conference, EuroCogSci07 (pp. 341-346). Hove, UK: Erlbaum.
342
widely used in the area of learning research to simulate how
people learn to associate potential causes and effects (like,
for example, responses and outcomes). This model is
formally equivalent to the delta rule (Widrow & Hoff, 1960)
used to train two-layer distributed neural networks through a
gradient descent learning procedure. In the Rescorla-
Wagner model the change ( n
R
VΔ) in the strength of the
association between a potential cause (in our case, the
system’s response, R) and a potential effect (a desired
outcome) after each learning trial, takes place according to
the following equation:
)( 1
=Δ n
t
n
RVkV
λ
(1)
where k is a learning rate parameter that reflect the
associability of the cause, α, and that of the effect, β,
(
β
α
=K in the original Rescorla & Wagner model); λ
reflects the asymptote of the curve (which is assumed to be
1 in trials in which the outcome is present and 0 otherwise),
and 1n
t
V is the strength with which the effect can be
predicted by the sum of the strengths that all the possible
causes that are present in the current trial had in trial n-1.
For example, in a simulation of the illusion of control, there
should be at least two possible causes for the occurrence of
the outcome: one is the system’s response, R, the other one
is the context in which the response takes place (see, e.g.,
Shanks & Dickinson, 1987). Thus, for instance, when the
outcome occurs but there is no response, the occurrence of
the outcome will be attributed to other, background or
contextual, potential causes. By the same reasoning, when
the outcome occurs after a response has been given, the
outcome will be attributed to both the response and the
context, as a function of their respective associability. The
task of the learner will be to learn how much is due to his or
her own response, how much is due to other, unspecified
potential causes. In general, contexts are assumed to be of
low associability, thus, in all the simulations that we will
report, k will be 0.10 for the context and 0.30 for the
response. Also, it is often the case in many published
simulations of this model that k takes different values as a
function of whether the outcome occurs or as a function of
age-related or species-related differences in sensitivity to the
outcome. However, for the sake of simplicity we have
preferred to ignore these additional parameters in our
simulations. Thus, the value of k, for both the context and
the response, will be kept constant, regardless of whether
the outcome occurs or not. For each simulation, 100
learning trials and 500 iterations will be run.
In all simulations, the probability that the outcome occurs
when the system makes a response, p(O|R), will be 0.75.
The probability that the outcome occurs when there is no
response, p(O|noR), will be 0.75 in some simulations and 0
in others. When those two probabilities are identical (e.g.,
both of them are 0.75), the outcome is said to be
noncontingent on the response, or, in other words,
uncontrollable. In this case, the actual contingency is 0 (i.e.,
0.75 – 0.75). When these two probabilities are different (i.e.,
0.75 and 0, respectively), then the outcome is controllable
Figure 1: In Simulation 1 outcomes occur with a probability
of 0.75 and are uncontrollable ( i.e., they occur regardless of
whether the system responds or not). The judgment of
control is shown to depend on the probability of responding.
(See main text for simulation details.)
(i.e., there is a positive contingency of 0.75). Thus, we will
test both controllable and uncontrollable conditions. The
reason why we are using a high probability of the outcome’s
occurrence (i.e., 0.75) both in controllable and
uncontrollable conditions is that the illusion of control is
more readily observed in uncontrollable conditions when the
outcome occurs frequently (e.g., Alloy & Abramson, 1979;
Matute, 1995).
The strength of the association between the response and
the outcome is taken as an index of the strength of the
response-outcome causal relation perceived by the system
(i.e., the judgment of control). Thus, an illusion of control
will be observed anytime when the strength of the
association between the response and the outcome becomes
higher than zero in a noncontingent situation.
Across simulations we will manipulate the probability
that the system responds in each trial, p(R). In the first set of
simulations we will compare the effect of different
probabilities of responding, ranging from 0.1 to 1.0. In the
second set of simulations, probabilities of responding will
not be fixed, as they will change with experience.
Results
Simulations using a fixed p(R) Simulation 1 considers a
noncontingent situation where the outcome occurs in 75%
of the trials, regardless of whether there is a response or not.
The results of this simulation, presented in Figure 1, show
that the illusion of control is dependent on the probability of
responding: As the probability of acting approaches 1, the
illusion of control becomes stronger and more persistent
over trials.
Now, if responding with a very high probability produces
such illusions, why do people tend to respond so much?
Wouldn’t it make more sense to be less active so that the
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Figure 2. In Simulation 2 the outcome is said to be
controllable because it occurs in 75% of the occasions in
which the system responds and never in its absence.
Simulation 2 shows that the number of outcomes that is
obtained after 100 trials is considerably reduced as the
probability of responding departs from 1.
actual contingency could be accurately detected? If a system
is trying to find out how much control is available over an
uncontrollable outcome, this system should, as shown in
Simulation 1, be quite passive. A low probability of
responding will certainly allow the system to correctly
detect the uncontrollability of the outcome and would not
affect the amount of the outcomes obtained, since in
uncontrollable situations responding with a high or low
probability does not affect the amount of outcomes that can
be obtained.
However, let us now imagine a situation in which the
outcome effectively depends on the subject’s behavior.
Thus, in Simulation 2, the outcome is controllable. Assume,
for example, that the outcome occurs in 75% of the
occasions in which the system responds, and it never occurs
when the system does not respond. This case is shown in
Figure 2: A system that acts with a probability of 1 will be
able to obtain more outcomes than a system responding with
at a lower probability. As the probability of responding
drops down from 1, the percentage of desired outcomes
obtained is reduced. This, of course, is true for any positive
contingency situation (and the opposite is true for negative
contingency). Thus, for any condition that depends on our
performing a given action, the best thing we can do in order
to maximize reward is to perform the action just in all
occasions (Simulation 2). The bad news is that this strategy
will produce an illusion of control when the outcome is
uncontrollable (Simulation 1).
It is clear that the best strategy to maximize the number of
outcomes are not optimal when the goal is to know how
much control one has over the outcome. If the outcome
happens to be uncontrollable, the high p(R) strategy will
provide the user with data that is too noisy and incomplete
to accurately calculate the actual contingency, thus giving
Figure 3. Simulation 3 uses the same controllable condition
as Simulation 2 (i.e., the outcome occurs in 75% of the
occasions in which the subject responds and never in the
absence of responding), but here the dependent variable is
the judgment of control (associative strength). Simulation 3
shows that, even in contingent conditions, the high p(R)
strategy is not the best one with respect to contingency
detection.
rise to illusion of control. But, is the high p(R) strategy
problematic only in noncontingent situations?
Simulation 3 compares the detection of contingency that
can take place in a contingent situation when the probability
of responding is 1 as compared to when it is reduced (up to
0.1). Simulation 3 was conducted in the same conditions as
Simulation 2, but the dependent variable is now the strength
of the association (or judgment of control) rather than the
number of outcomes obtained. Thus, it considers a
contingent relation in which the outcome occurs in 75% of
the trials in which the subject responds and never when
there is no response. As can be seen in Figure 3, even when
the outcome is contingent on responding – and therefore, the
best thing one can do to maximize reward is to respond in
all occasions (cf. Simulation 2) – the high p(R) strategy
prevents the accurate detection of the contingency. In this
case, the actual contingency is 0.75. Even a subject
responding with a very low probability (0.1) will be able to
produce a much better judgment of control than one who
responds always. In this later case, there is no illusion in our
high p(R) system because the outcome is contingent on
responding, but the contingency that this system perceives
between the response and the outcome is lower than the one
that is actually present.
This may seem surprising at first. However, as was the
case in the noncontingent conditions shown in Simulation 1,
if the system responds in every single trial, it cannot know
what happens when there is no response. In this case, the
subject is just exposed to what happens when the response is
given in a given context. And, according to Equation 1, the
increment in the strength of the association that can be
accrued in a given trial depends not only on the strength of
the association between the response and the outcome in the
344
Figure 4. Sigmoid function for the probability of responding
based on the perceived controllability of the outcome ( i.e.,
on the strength of the response-outcome association).
previous trial, but also on the strength with which the other
cues that are present (e.g., the context) are already
associated with the outcome. This means that the associative
strength that could be accrued by the response in a given
trial will be shared by the response and the context (as a
function of their relative associability; k in the equation, and
their associative strength in the previous trial; 1n
t
V in the
equation). By the same reasoning, the trials in which the
response does not occur (in systems in which the p(R) is
different from 1), can only affect the strength of the context.
And, because in the contingent situation we are testing in
Simulation 3, the outcome does not occur when there is no
response, these no-response trials will reduce the strength of
the context alone. Moreover, the reduction of the strength of
the context will in turn have the (indirect) effect of
increasing the strength of the response. This is because, after
the context strength has been reduced, when a response is
given in a subsequent trial, the competition that the context
can exert for associative strength will be lower. In this way
the response will get a larger proportion of the available
strength in all systems responding with a p(R) lower than 1
in Simulation 3 (see Equation 1). However, a system that
responds with a p(R) of 1 does not have information on
what happens when the response is absent and just the
context is present. In other words, there are no context-alone
trials that will help the system discard the potential causal
role of the context. If this is so, then the associative strength
accrued by the response and the context in each trial
(appreciate that they always occur in compound in this
system) are shared between the two of them as a function of
their respective ks. This is why it is impossible for a subject
responding at every opportunity to accurately detect
contingencies, not only in uncontrollable situations but also
in controllable ones. As shown in Simulation 3, a subject
responding with a probability of 0.9, or even 0.1 will be
much more accurate in the detection of the actual
Figure 5. In Simulation 4 uncontrollable outcomes occur
with a probability of 0.75. The illusion of control is more
intense and persistent when the system's p(R) varies
according to the strength of the response than when this
probability is fixed.
contingency than a subject responding all the time, even
when the outcome is controllable. Still, one has to keep in
mind that these would not be good strategies if what we
want is to maximize reward.
Simulations using a modifiable p(R) One could argue that
our previous simulations use artificial conditions, in that
living organisms do not keep a fixed probability of
responding regardless of what they learn; by contrast, they
vary their probability of responding as a function of how
strongly they believe that the response is the cause of the
outcome. Thus, let us now suppose that if a response is very
strongly associated to the outcome (in other words, the
system believes the response is the cause of the outcome),
the probability of responding will be stronger.
Simulation 4 (see Figure 5) is similar to the previous
ones, but here the probability of responding is increased or
reduced as a function of the strength of the association that
is being learned. To this end, we use a simple sigmoid
function that increases the probability of responding when
the association increases and reduces it otherwise:
)1/(1)( 1
+= n
R
V
eRp
θ
(2)
For the present purposes, the parameter describing the
slope of the sigmoid function, θ, was set to 5. Figure 4
depicts the different values that p(R) can receive depending
on the strength of the response-outcome association. As
there can be seen, a system acting according to this equation
will simply tend to respond with a very high probability
when the response is apparently causing the outcome. If the
perceived contingency between the response and the
outcome is negative (that is, if the system believes that the
345
response actually prevents the occurrence of the outcome),
the probability of responding would be near 0. Finally,
when the associative strength is near 0 and, therefore, the
system believes that the outcomes are uncontrollable, the
probability of response is intermediate.
Note that in Equation 2 the probability of responding is
dependent on the strength of the association. This implies
that for the first trial the probability of responding is to
some extent arbitrary, because for the first trial there is no
prior associative strength upon which to compute the
probability of responding. In Simulation 4, the probability
of responding for the first trial was set to the intermediate
value of 0.50.
Thus, Simulation 4 corresponds to a more natural
condition than the previous ones, in that cognitive systems
generally vary their probability of responding according to
the strength of the association that they have formed
between the response and the outcome (or, in other words,
the strength that they attribute to their own response as a
cause of the outcome). As can be seen in Figure 5, the
illusion of control that is developed in this way is even more
intense and persistent than the one produced by a fixed p(R),
as that used in Simulation 1.
But let us now suppose that not only do subjects vary
their probability of responding as a function of what they
learn, but also that different subjects probably start up from
different backgrounds, beliefs, strategies… and
personalities. This should at least produce some initial
biases. These differences in the initial conditions, even
though they are subsequently subject to a common learning
function that will tend to make them similar to each other at
asymptote, could perhaps produce important differences in
the speed and slope of learning.
Simulation 5 tests whether the apparently innocuous little
biases that many people may have during the initial stages
of a new task (e.g. being more of less active), can have a
profound effect on the strength and the durability of the
illusion of control. This simulation is very similar to
Simulation 4, but here two systems that are sensitive to the
strength of the association ( i.e., that use a sigmoid function,
as in Simulation 4) are compared. The probability of making
a response in the very first trial is what we manipulated
here. The difference between the two systems is that the
probability of responding in the first trial is 0.1 for one of
them and 0.9 for the other. In all remaining trials, the
probability of responding in both systems is computed
according to Equation 2.
The results are presented in Figure 6. The initial bias –
that represent the tendency to respond more or less due to
previous history, background, beliefs, or personality –
though implemented only in the very first trial still has an
effect after 100 trials.
Discussion
The illusion of control is at the roots of many real world
problems, like the reluctance of many people to believe in
scientific medicine and the proliferation in today’s world of
so many magical and pseudoscientific remedies for almost
everything. It is generally believed to be part of naïve
Figure 6. In Simulation 5 uncontrollable outcomes occur
with a probability of 0.75 regardless of whether the system
responds or not, as in Simulation 4. The two systems here
considered do vary their probability of responding according
to the strength of the association between the response and
the outcome, but one of them starts with a stronger bias to
act in the very first trial. This initial, first trial bias still has
an effect on performance after 100 trials.
personalities, but we have shown that it is potentially a
much more prevalent problem that can occur in all cognitive
systems. Indeed, it is a logical consequence of how we
interact with the world. Even though personality variables
can also have an important influence and can surely be
responsible for individual differences among people, they
are not the only variables that are responsible, nor the only
ones that should be taken into account when trying to set
therapies and policies to eradicate this illusion. As shown in
our simulations, the main problem has to do with what the
goal of the system is. If our goal in the world is to maximize
the number of rewards (and this is an important goal for
survival that can certainly have been favored by evolution as
an adequate strategy for many occasions), then the system
will try to respond as much as possible in order to obtain
those outcomes. As shown in Simulation 2, only those
subjects responding in all possible occasions will get the
majority of the available rewards when the situation is
controllable (of course, this would be irrelevant if the
situation were noncontingent). Thus it would not be strange
that a default strategy in many people and even in animals
would be to respond as much as possible. What is clear from
our simulations is that this strategy, while optimal when one
wants to maximize reward, is quite a bad one in the
occasions in which the goal of the system is not to obtain
the outcome, but to analyze to what degree it is controllable.
Therefore, it is to some extent contradictory trying to
maximize control over the environment and, at the same
time, trying to make accurate inferences about the world.
This means that, if a given outcome is important enough for
people, the attempts they make to control it will surely
346
interfere with the ability to accurately assess the degree of
control they actually have.
In sum, imagine that twenty people were suddenly
infected with an unknown mortal disease and that, for some
reason, you suspect that medicine X might cure them.
Would you be ready to test this medicine just in one half of
your patients so as to check that the medicine is actually
working? This is actually the difference between scientific
reasoning and every day reasoning. As we have shown,
none of these strategies can be said to be better than the
other one; it is only a matter of choosing the right one at the
right time. Thus if we would like people to apply more
scientific reasoning to their everyday life, perhaps we
should start by trying to convince them to test passive
responding in situations in which the outcome is
unimportant for them. In this way, they will be able to learn
what they need about skepticism so that the next time they
face a serious problem they will be able to actively chose
the p(R) strategy that best complies with their own goals.
Acknowledgments
Support for this research was provided by Grant SEJ406
from Junta de Andalucía. Fernando Blanco was supported
by a F.P.I. fellowship from Gobierno Vasco (Ref.:
BFI04.484). We would like to thank Cristina Orgaz for
valuable discussions on these points. Correspondence
concerning this article should be addressed to Helena
Matute, Departamento de Psicología, Universidad de
Deusto, Apartado 1, 48080 Bilbao, Spain. E-mail:
matute@fice.deusto.es.
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... About the measurement of illusion of control, in addition to the classical self-reported scales typically used to measure the phenomenon, like judgment of control scales, associative theories have been used to model it Matute, Vadillo, Blanco, & Musca, 2007;Presson & Benassi, 1996;Stefan & David, 2013). Robert Rescorla and Allan Wagner proposed the causal, associative, and mathematical Rescorla-Wagner (RW) model to explain the quantity of learning that occurs on each trial along a sequence of a Pavlovian learning process (Gazzaniga, 2010;Hollis, 1997;Rescorla, 1966;Rescorla & Wagner, 1972). ...
... From the original sequence of stimuli presented to each participant and his/her respective actions, the calculus of the surprising 4 differences between what actually happened, λ, and the expected product, ΣV, resulted in a strong correlation indicating that the sequences of events (stimuli and actions) may be a predictor of the illusion (self-reported on the judgment of control scale) for each combination of valence and probability. Recent studies have shown that an artificial learning system using the algorithm of the RW model developed illusions when the outcome occurred frequently and the system acted frequently Matute, Vadillo, Blanco, & Musca, 2007) and demonstrated that the probability of responding is a better predictor of judgments of control than actual contingency (Blanco et al., 2011). Blanco and Matute (2015) demonstrated in their light bulb experiment that the asymptotic pattern observed in the RW model sequence at the end of the training resembles the results on the judgment of control scale. ...
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Individuals interpret themselves as causal agents when executing an action to achieve an outcome, even when action and outcome are independent. How can illusion of control be managed? Once established, does it decay? This study aimed to analyze the effects of valence, probability of the outcome [p(O)] and probability of the actions performed by the participant [p(A)], on the magnitude of judgments of control and corresponding associative measures (including Rescorla–Wagner’s, Probabilistic Contrast, and Cheng’s Power Probabilistic Contrast models). A traffic light was presented on a computer screen to 81 participants who tried to control the green or red lights by pressing the spacebar, after instructions describing a productive or a preventive scenario. There were 4 blocks of 50 trials under all of 4 different p(O)s in random order (0.10, 0.30, 0.70, and 0.90). Judgments were assessed in a bidimensional scale. The 2 × 4 × 4 mixed experimental design was analyzed through General Linear Models, including factor group (between-subject valence), and block and p(O) (within subjects). There was a small effect of group and a large and direct effect of p(O) on judgments. Illusion was reported by 66% of the sample and was positive in the productive group. The oscillation of p(O) produced stronger illusions; decreasing p(O)s produced nil or negative illusions. Only Rescorla–Wagner’s could model causality properly. The reasons why p(A) and the other models could not generate significant results are discussed. The results help to comprehend the importance of keeping moderate illusions in productive and preventive scenarios.
... Arguably the most prominent model of associative learning is the Rescorla-Wagner model (Rescorla and Wagner, 1972). This is a conditioning model which has been successfully applied to causal-learning phenomena (Tangen and Allan, 2004), including biased estimation of causality Matute, Vadillo, Blanco, and Musca, 2007). The Rescorla-Wagner model proposes that the learning of contingencies between stimuli is driven by a prediction error-correction mechanism. ...
... By virtue of reinforcement, once a causal illusion has been formed, the actions that are thought to be useful to produce an outcome become more and more likely, which in turn strengthens the illusion (Matute et al., 2007). This is how irrational ritualsalthough useless to produce the intended effect-may be beneficial because they foster active behavioral styles (Beck and Forstmeier, 2007). ...
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In the last decades, cognitive Psychology has provided researchers with a powerful background and the rigor of experimental methods to better understand why so many people believe in pseudoscience, paranormal phenomena and superstitions. According to recent evidence, those irrational beliefs could be the unintended result of how the mind evolved to use heuristics and reach conclusions based on scarce and incomplete data. Thus, we present visual illusions as a parallel to the type of fast and frugal cognitive bias that underlies pseudoscientific belief. In particular, we focus on the causal illusion, which consists of people believing that there is a causal link between two events that coincide just by chance. The extant psychological theories that can account for this causal illusion are described, as well as the factors that are able to modulate the bias. We also discuss that causal illusions are adaptive under some circumstances, although they often lead to utterly wrong beliefs. Finally, we mention several debiasing strategies that have been proved effective in fighting the causal illusion and preventing some of its consequences, such as pseudoscientific belief.
... Thus, the significant differences between groups in the judgments were more likely due to the participants who showed a degree of illusion in either direction (generative or preventive). As we argued elsewhere (Matute, Vadillo, Blanco, & Musca, 2007), associative theories are good candidates to model illusions of control and related phenomena. According to the influential Rescorla-Wagner model (Rescorla & Wagner, 1972), an individual's judgment of control would be given by the strength of the association between the representation of the action and the representation of the outcome, V A . ...
... We used the original Rescorla-Wagner model to simulate our data with the trial sequences produced by each participant. The parameter values were taken from a previous publication in which the effects of P(O) and P(A) on control estimations were successfully reproduced (Matute et al., 2007): a A = 0.6, a Ctx = 0.2, b O = 0.5, and bØ O = 0.5. It is a usual assumption that the salience of the action (or the target stimulus) is greater than that of the context, hence a A > a Ctx . ...
Article
Most previous research on illusions of control focused on generative scenarios, in which participants' actions aim to produce a desired outcome. By contrast, the illusions that may appear in preventive scenarios, in which actions aim to prevent an undesired outcome before it occurs, are less known. In this experiment, we studied two variables that modulate generative illusions of control, the probability with which the action takes place, P(A), and the probability of the outcome, P(O), in two different scenarios: generative and preventive. We found that P(O) affects the illusion in symmetrical, opposite directions in each scenario, while P(A) is positively related to the magnitude of the illusion. Our conclusion is that, in what concerns the illusions of control, the occurrence of a desired outcome is equivalent to the nonoccurrence of an undesired outcome, which explains why the P(O) effect is reversed depending on the scenario.
... On this account, the IoC is largely driven by the frequency of occasions on which an individual acts in an environment. Differences in the number of times a response is made leads to differences in the data/evidence that is obtained, consequently the IoC can arise in simulations of a standard associative learning model, such as the Rescorla-Wagner model (Matute et al. 2007). In order to most accurately perceive the degree of contingency between an action and an outcome, an agent should only make an action on half the available trials, so as to understand the number of times in which the outcome occurs in the absence of the action, as well as in the presence of the action. ...
... It is clear to us that a conflation of skill-and chance-based situations can result in an increased likelihood of people demonstrating an IoC (e.g., Langer 1975). Likewise, in repeated choice tasks an associative learning account (e.g., Matute et al. 2007) provides a good account of the data, and could well be the best explanation for the data in such contexts. Moreover, associations between active involvement and frequent positively reinforced outcomes can be explained using a control heuristic in which people's judgments of control are informed by the perceived connection between their own action and the desired outcome, and their intention to achieve the outcome (Thompson et al. 1998). ...
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In the absence of an objective contingency, psychological studies have 2 shown that people nevertheless attribute outcomes to their own actions. Thus, by 3 wrongly inferring control in chance situations people appear to hold false beliefs con4 cerning their agency, and are said to succumb to an illusion of control (IoC). In the 5 current article, we challenge traditional conceptualizations of the illusion by examin6 ing the thesis that the IoC reflects rational and adaptive decision making. Firstly, we 7 propose that the IoC is a by-product of a rational uncertain judgment (“the likelihood 8 that I have control over a particular outcome”). We adopt a Bayesian perspective to 9 demonstrate that, given their past experience, people should be prone to ascribing 10 skill to chance outcomes in certain situations where objectively control does not exist. 11 Moreover, existing empirical evidence fromthe IoC literature is shown to support such 12 an account. Secondly, from a decision-theoretic perspective, in many consequential 13 situations, underestimating the chance of controlling a situation carriesmore costs than 14 overestimating that chance. Thus, situations will arise in which people will incorrectly 15 assign control to events in which outcomes result from chance, but the attribution is 16 based on rational processes.
... As already mentioned, the cue-density bias (the effect of the probability of actions on the judgments of causality) is readily explained by models such as that of Rescorla and Wagner (1972). We have conducted simulations that show this feature of the model Matute, Vadillo, Blanco, & Musca, 2007). ...
Article
The human cognitive system is fine-tuned to detect patterns in the environment with the aim of predicting important outcomes and, eventually, to optimize behavior. Built under the logic of the least-costly mistake, this system has evolved biases to not overlook any meaningful pattern, even if this means that some false alarms will occur, as in the case of when we detect a causal link between two events that are actually unrelated (i.e., a causal illusion). In this review, we examine the positive and negative implications of causal illusions, emphasizing emotional aspects (i.e., causal illusions are negatively associated with negative mood and depression) and practical, health-related issues (i.e., causal illusions might underlie pseudoscientific beliefs, leading to dangerous decisions). Finally, we describe several ways to obtain control over causal illusions, so that we could be able to produce them when they are beneficial and avoid them when they are harmful.
... These overestimations are larger when the outcome (1E) or the cue (1F) is very frequent, and even larger when both of them are very frequent (1G). Therefore, the model also provides a nice explanation for cue-and outcome-density biases (Matute, Vadillo, Blanco, & Musca, 2007;Shanks, 1995;Vadillo & Luque, 2013). ...
Article
Decades of research in causal and contingency learning show that people’s estimations of the degree of contingency between two events are easily biased by the relative probabilities of those two events. If two events co-occur frequently, then people tend to overestimate the strength of the contingency between them. Traditionally, these biases have been explained in terms of relatively simple single-process models of learning and reasoning. However, more recently some authors have found that these biases do not appear in all dependent variables and have proposed dual-process models to explain these dissociations between variables. In the present paper we review the evidence for dissociations supporting dual-process models and we point out important shortcomings of this literature. Some dissociations seem to be difficult to replicate or poorly generalizable and others can be attributed to methodological artefacts. Overall, we conclude that support for dual-process models of biased contingency detection is scarce and inconclusive.
... Nevertheless, in the absence of more convincing evidence about the role of personal involvement in the illusion of control, it seems more parsimonious to assume that a single process (biased contingency detection due to a high probability of the cause) is responsible for the illusions previously attributed to personal involvement (Alloy et al., 1985). Indeed, Matute, Vadillo, Blanco, and Musca (2007) have shown that even an artificial learning system using a very simple and popular learning algorithm such as the Rescorla and Wagner (1972) model will develop these illusions when the outcome occurs frequently and the system acts frequently. On the other hand, although the influence of self-protection may not be ruled out in all cases in which people develop illusions of control, what our results show is that this influence is not necessary to account for all instances of the illusion of control reported in the literature. ...
Article
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The illusion of control consists of overestimating the influence that our behavior exerts over uncontrollable outcomes. Available evidence suggests that an important factor in development of this illusion is the personal involvement of participants who are trying to obtain the outcome. The dominant view assumes that this is due to social motivations and self-esteem protection. We propose that this may be due to a bias in contingency detection which occurs when the probability of the action (i.e., of the potential cause) is high. Indeed, personal involvement might have been often confounded with the probability of acting, as participants who are more involved tend to act more frequently than those for whom the outcome is irrelevant and therefore become mere observers. We tested these two variables separately. In two experiments, the outcome was always uncontrollable and we used a yoked design in which the participants of one condition were actively involved in obtaining it and the participants in the other condition observed the adventitious cause-effect pairs. The results support the latter approach: Those acting more often to obtain the outcome developed stronger illusions, and so did their yoked counterparts.
Thesis
Si près d’un français sur deux joue au moins une fois par an, on remarque spécifiquement, entre 2010 et 2014, une augmentation de 11,5% du nombre de joueurs parmi les 45-75 ans (Observatoire Des Jeux [ODJ], 2015). Les aînés de 55 à 64 ans sont d’ailleurs les premiers consommateurs de jeux de hasard et d’argent (Institut National de la Statistique et des Etudes Economiques [INSEE], 2016). Peu d’auteurs ont toutefois investigué la question du vieillissement des joueurs dans les JHA, impliquant un manque de données empiriques conséquent (Tse et al., 2012). Pourtant, les jeux de hasard et d’argent (JHA) font l’objet d’un domaine d’étude qui connaît un essor important depuis les années 2000. En plus d'une grande quantité de travaux sur la population générale, de nombreuses recherches ont porté sur les adolescents et les jeunes, considérés comme une population vulnérable (Kairouz et al., 2013). Vulnérables eux aussi (Subramaniam et al. 2015 ; Tse et al. 2012 ; Wainstein et al. 2008), les aînés constituent une population préoccupante en raison de leur exposition à la fois à des offres de jeu de plus en plus abondantes et à de puissants facteurs de risque spécifiques à l'âge. En l’absence de référents théoriques permettant d’appréhender le renouvellement des conduites de jeu des aînés, deux facteurs déterminants ont été convoqués dans cette thèse : l’illusion de contrôle et la prise de risque. Concept polysémique, l'illusion de contrôle demeure à ce jour encore discutable, en termes de définition et de mesure, malgré le grand nombre d’études l’ayant examiné (Masuda, Sakagami, & Hirota, 2002). Cette thèse a ainsi poursuivi un double objectif : élaborer et valider une échelle multidimensionnelle de l’illusion de contrôle dont le format matriciel (Bonnel, 2016) met en exergue les valences affectives positives et négatives ; identifier les mécanismes cognitifs spécifiques à l'âge qui sous-tendent le comportement de jeu dans le vieillissement normal. Les perspectives temporelles (Zimbardo & Boyd, 1999) constituant par ailleurs un bon indicateur des comportements à risque dans un certain nombre de domaines (e.g., santé, environnement), les relations entre âge, perspectives temporelles (PT), illusion de contrôle et prise de risque ont été interrogées. Au bilan, les résultats suggèrent que les aînés constituent une population spécifique en termes de cognitions et de comportements liés au jeu, sous certaines conditions. L'inclusion des PT dans les évaluations des comportements à risque permettrait de développer des mesures préventives sur mesure, destinées à empêcher ou diminuer le risque que les aînés développent un problème de jeu, dont les conséquences sont plus délétères pour cette population.
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Depressive realism consists of the lower personal control over uncontrollable events perceived by depressed as compared to nondepressed individuals. In this article, we propose that the realism of depressed individuals is caused not by an increased accuracy in perception, but by their more comprehensive exposure to the actual environmental contingencies, which in turn is due to their more pas-sive pattern of responding. To test this hypothesis, dysphoric and nondysphoric participants were exposed to an uncontrollable task and both their probability of responding and their judgment of control were assessed. As was expected, higher levels of depression correlated negatively with probability of responding and with the illusion of control. Implications for a therapy of depression are discussed.
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Recent research has shown superstitious behaviour and illusion of control in human subjects exposed to the negative reinforcement conditions that are traditionally assumed to lead to the opposite outcome (i.e. learned helplessness). The experiments reported in this paper test the generality of these effects in two different tasks and under different conditions of percentage (75% vs. 25%) and distribution (random vs. last-trials) of negative reinforcement (escape from uncontrollable noise). All three experiments obtained superstitious behaviour and illusion of control and question the generality of learned helplessness as a consequence of exposing humans to uncontrollable outcomes.
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Do people previously exposed to uncontrollable aversive events, like naturally depressed people, fail to succumb to an illusion of control in a situation in which events occur noncontingently but are associated with success? Depressed and nondepressed college students were assigned to one of three groups that make up the typical triad used in studies of learned helplessness: controllable noises, uncontrollable noises, or no noises. Following pretreatment, subjects judged how much control they had in a noncontingency learning problem. For half of the subjects, events were noncontingent and associated with failure; whereas for the remaining subjects, events were noncontingent but associated with success. Contrary to the predictions of learned helplessness theory, nondepressed subjects previously exposed to uncontrollable noises showed a robust illusion of control in the condition in which events were noncontingent but associated with success, whereas nondepressed subjects previously exposed to controllable noises judged control accurately. Depressed subjects also judged control accurately regardless of their previous noise experience, The results were interpreted as consistent with the egotism hypothesis.
Article
Experiments in which subjects are asked to analytically assess response-outcome relationships have frequently yielded accurate judgments of response-outcome independence, but more naturalistically set experiments in which subjects are instructed to obtain the outcome have frequently yielded illusions of control The present research tested the hypothesis that a differential probability of responding p(R), between these two traditions could be at the basis of these different results Subjects received response-independent outcomes and were instructed either to obtain the outcome (naturalistic condition) or to behave scientifically in order to find out how much control over the outcome was possible (analytic condition) Subjects in the naturalistic condition tended to respond at almost every opportunity and developed a strong illusion of control Subjects in the analytic condition maintained their p(R) at a point close to 5 and made accurate judgments of control The illusion of control observed in the naturalistic condition appears to be a collateral effect of a high tendency to respond in subjects who are trying to obtain an outcome, this tendency to respond prevents them from learning that the outcome would have occurred with the same probability if they had not responded
Article
Conducted a series of 6 studies involving 631 adults to elucidate the "illusion of control" phenomenon, defined as an expectancy of a personal success probability inappropriately higher than the objective probability would warrant. It was predicted that factors from skill situations (competition, choice, familiarity, involvement) introduced into chance situations would cause Ss to feel inappropriately confident. In Study 1 Ss cut cards against either a confident or a nervous competitor; in Study 2 lottery participants were or were not given a choice of ticket; in Study 3 lottery participants were or were not given a choice of either familiar or unfamiliar lottery tickets; in Study 4, Ss in a novel chance game either had or did not have practice and responded either by themselves or by proxy; in Study 5 lottery participants at a racetrack were asked their confidence at different times; finally, in Study 6 lottery participants either received a single 3-digit ticket or 1 digit on each of 3 days. Indicators of confidence in all 6 studies supported the prediction. (38 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Associative accounts of causality judgment The psychology of learning and motivation
  • D R Shanks
  • A Dickinson
Shanks, D. R., & Dickinson, A. (1987). Associative accounts of causality judgment. In G. H. Bower (Ed.), The psychology of learning and motivation, Vol. 21 (pp. 229- 261). San Diego, CA: Academic Press.