Despite the tremendous efforts of governments and skeptical organizations to reduce superstitions and pseudoscientific beliefs, these problems are still very common in Western societies. As an example, two in five Europeans hold superstitions (European Commission, 2010), and three in four Americans believe in the paranormal (Moore, 2005). This might seem a trivial problem at first glance, but it implies that financial, medical, or political decisions, at both the individual and societal levels, are often based on ungrounded beliefs rather than on reliable knowledge. In order to reduce the incidence of superstitious and pseudoscientific thinking—and, in general, all types of ungrounded beliefs—it will be important to understand how these irrational beliefs develop, in which cases they are increased, and, particularly, which manipulations can be used to reduce them. Given the aim of most Western societies to become knowledge-based societies one day, investigating how this can be accomplished has become a priority.

The illusion of control is a particular type of ungrounded belief. It occurs when we believe that our behavior controls an outcome that is actually uncontrollable. An example is the belief that we can recover from a disease by means that are actually useless, just because a certain pill that one is taking coincides with spontaneous remission of the symptoms. Another example is the belief that we are controlling the outcome of a lottery just because we selected the ticket ourselves and it happened to be the lucky one. This is a robust experimental finding, both in the laboratory (e.g., Alloy & Abramson, 1979; Langer, 1975; Matute, 1996; Msetfi, Murphy, Simpson, & Kornbrot, 2005) and on the Internet (e.g., Blanco, Matute, & Vadillo, 2009; Matute, Vadillo, Vegas, & Blanco, 2007).

It should be noted, however, that most experiments on the illusion of control have only studied what could be called generative-positive illusions. These are illusions in which the action is thought to generate a desired outcome that is actually out of the participant’s control (e.g., wearing a lucky charm is assumed to generate fortune; a bogus treatment is thought to generate recovery from illness). By positive illusions, we refer not only to cases of positive reinforcement or reward, such as the superstitions that might occur when our behavior is followed by a lottery prize (e.g., Alloy & Abramson, 1979; Langer, 1975; Skinner, 1948). Escape contingencies are also generative-positive scenarios, in which desired outcomes (e.g., the termination of a headache) can follow a given behavior (e.g., taking an innocuous herb) and therefore can reinforce this behavior and enhance our belief in its effectiveness (e.g., Matute, 1995, 1996). In both cases, uncontrollable desired outcomes are known to strengthen the behavior that, by chance, has preceded them.

To our knowledge, however, very little laboratory evidence exists on generative-negative illusions. These would be analogous to punishment conditions, because the action is thought to generate undesired outcomes, though in this case the outcomes are actually uncontrollable (e.g., walking under a ladder, breaking a mirror, or sitting in row 13 are supposed to generate bad luck). The present research is concerned with this type of illusion. For brevity, we will use the terms positive and negative illusions through the article, although in all cases we will be dealing with generative illusions—that is, those in which the action is thought to generate the occurrence of the outcome, which is desired in the case of positive illusions, and undesired in the case of negative illusions.Footnote 1

One of the variables that most strongly affects positive illusions is p(O), the probability with which the desired outcome occurs. Many experiments have shown that the higher the p(O), the stronger the illusion (e.g., Alloy & Abramson, 1979; Blanco, Matute, & Vadillo, 2013; Matute, 1995; Msetfi et al., 2005; Musca, Vadillo, Blanco, & Matute, 2010; Wright, 1962). It is not surprising, therefore, that pseudoscientific remedies are generally used to treat diseases that involve a high rate of spontaneous relief, such as back pain. The high probability of the outcome (in this example, temporary relief) makes it very difficult for governments and scientific organizations to convince people that many pseudoscientific treatments for back pain are useless. As a consequence, practitioners of alternative medicine are known to provide 40 % of primary care for back pain in the USA (White House Commission on Complementary and Alternative Medicine Policy, 2002). This is a serious public health problem.

Given that the probability of occurrence of an uncontrollable outcome lies, by definition, outside of the individual’s control, a question of interest is which other variables could be used to reduce the incidence and impact of illusions of control when p(O) is high. One variable that has been shown to be effective in the reduction of positive illusions is the probability with which the potential cause occurs, p(C). In principle, the potential cause could be either an action performed by the person or an external event (e.g., the cause could be either one’s taking a pill or reading about other people taking it). We will use the term p(C) to refer to either type of cause (see Yarritu, Matute, & Vadillo, 2013, for a discussion of this point).

Importantly, people who believe that a certain action generates a desired event tend to perform this action with high frequency (Matute, 1996). In some cases, such as when using alternative medicines and miracle products, this behavior is further motivated by the alleged absence of secondary effects (see Blanco, Barberia, & Matute, 2014). Thus, p(C) typically tends to be very high in all of these cases. Given the high-p(O) conditions for which pseudoscientific products are typically used (i.e., relief is frequent), this high p(C) will result in a high number of accidental product–relief coincidences that will reinforce the illusion of control. In line with this prediction, participants who act more frequently to obtain desired outcomes have been shown in the laboratory to exhibit stronger positive illusions than do those who are less active (Blanco, Matute, & Vadillo, 2011, 2012; Hannah & Beneteau, 2009; Matute, 1996). In sum, a recurrent finding in experiments studying the illusion of control is that positive illusions occur when the desired outcome is frequent (such as remission of back pain) and are strengthened when the participant acts with a high probability. In consequence, reducing the probability of the potential cause (in this case, the probability of following the treatment) has been proposed as an effective means to reduce positive illusions (Barberia, Blanco, Cubillas, & Matute, 2013; Matute, Yarritu, & Vadillo, 2011).

Another strategy that recent research has shown effective in reducing positive illusions of control consists of suggesting to the experimental participants that an alternative cause might produce the desired outcome. This strategy has sometimes been used in isolation (e.g., Vadillo, Matute, & Blanco, 2013), but it has most often been used in combination with the reduction-of-p(C) approach, and the combination of these two strategies has been shown to be most effective. That is, warning people that an alternative cause might account for the occurrence of the outcome, and suggesting to them that the best that they can do to find out whether their own behavior or an alternative cause is producing the outcome is to reduce their p(C) to a medium level (e.g., using the treatment in about 50 % of the trials), has been shown to be highly effective in reducing positive illusions of control (Barberia et al., 2013; Blanco et al., 2012; Matute, 1996).

Thus, previous research has shown that this combined strategy is effective at reducing positive illusions. However, and contrary to what has been the norm in the laboratory, real-life illusions and superstitions are often negative rather than positive illusions (see Wiseman & Watt, 2004). Thus, it is unclear whether the strategies that have been developed so far will be effective in these cases. Indeed, cultural studies have shown that superstitions are often negative; that is, many of them are based on the idea that certain behaviors will be followed by undesired outcomes (e.g., Aeschleman, Rosen, & Williams, 2003; Blum & Blum, 1974). The prevalence of negative illusions in real life is also reflected in the fact that the most widely used scale to measure superstitious beliefs, Tobacyk’s (Tobacyk, 1988; Tobacyk & Milford, 1983) Paranormal Belief Scale, includes only items on negative illusions, similar to the examples of breaking a mirror or walking under a ladder mentioned above (see Wiseman & Watt, 2004, for a discussion). Likewise (and once again, contrary to what has occurred in the laboratory), the majority of the studies that have been conducted in applied, real-life settings have focused on negative rather than positive illusions. These applied studies have often shown an association between (negative) superstitious beliefs and low psychological adjustment (Wiseman & Watt, 2004). This result can be regarded as the opposite of what is generally observed within the experimental literature on positive illusions, which are sometimes found to be adaptive (e.g., Alloy & Clements, 1992; Blanco et al., 2009; McKay & Dennett, 2009; Taylor & Brown, 1988). Indeed, Wiseman and Watt looked at both positive and negative illusions in what has probably been the largest applied study to date, a massive newspaper survey. They used positive items such as crossing one’s fingers and carrying a lucky charm, in addition to the standard negative items generally used in applied research on superstitions. They found interactions between superstition type (positive vs. negative) and neuroticism, and between superstition type and life satisfaction, with negative superstitions being more strongly associated with higher neuroticism and lower life satisfaction than are positive superstitions.

Thus, an important question is whether the strategies that have already been shown to reduce positive illusions could also be used to reduce negative illusions. Unfortunately, little experimental work has been conducted on how negative illusions could be reduced. In principle, this might imply that strategies that have already proven successful at reducing positive illusions in the laboratory, such as highlighting the existence of alternative causes while reducing the probability of the potential cause, might even work in the opposite way in the case of negative illusions. In positive-illusion experiments in which the occurrence of a desired event could be attributed either to the participant’s own behavior or to an alternative cause, the availability of an alternative cause reduced the illusion that the participants’ behavior was controlling the outcome. However, in the case of negative illusions, it is not clear that the availability of an alternative cause would reduce the illusion. When people keep being exposed to uncontrollable undesired events, the existence of an alternative cause might allow them to attribute the occurrence of these bad events to the external cause rather than to their own behavior. This might increase the belief that, on those occasions on which the bad events do not occur, their own behavior was responsible. If this is true, the strategies that have been found effective at reducing positive illusions might need to be used differently in the case of negative illusions.

The present experiment was designed to test this view. We hypothesized that knowing that the undesired outcomes might be occurring independently of one’s behavior (i.e., due to an alternative cause) could strengthen the development and maintenance of the illusion of control. In that case, an enhancement, rather than a reduction, of the illusion should be expected when the standard combined strategy is used.

Method

Participants and apparatus

Twenty undergraduate students from Deusto University volunteered to take part in the experiment. They were randomly assigned to each of two groups, resulting in ten participants per group. All participants performed the experiment on personal computers in individual cabins. The session took about 30 min, including debriefing.

Procedure and design

This experiment used the Flashes task, a computerized program that has previously been used in experiments investigating positive illusions of control (e.g., Blanco et al., 2009, 2012; Matute et al., 2007; Vadillo et al., 2013). Participants were told that the computer screen was not working properly and that some blue-and-white flashes would appear from time to time. When they appeared, the flashes always had a duration of 1 s. The participants’ task was to fix the screen so that it would stay black for as much time as possible. The participants were instructed that whenever the screen was black, a new trial would start, and this was a signal of their opportunity to use the spacebar on their keyboard to make the screen stay black. Importantly, they were told that, if they succeeded, the screen would stay black for an additional 5-s period, and that if they failed, the flashes would reappear almost immediately (after a delay of 1 s). Therefore, the occurrence of flashes was given aversive (undesired) value through the instructions.Footnote 2

All participants were exposed to a randomized sequence of 50 flashes that occurred independently of their behavior. The sequence was preprogrammed so that 75 % of the black-screen intervals between flashes lasted for just 1 s, and the remaining 25 % lasted for 5 s. Thus, given that participants had been instructed that their goal was to maintain the black screen for as much time as possible and that, if they failed, the flashes would reappear after 1 s, this meant that 75 % of the trials involved punishment of their attempts to maintain the black screen.Footnote 3

Half of our volunteers (control group) were not given any additional instructions. On the basis of previous research, we assumed that, while trying to maintain the black screen, they would press the spacebar on most trials. We also predicted that they would develop a weak illusion of control (recall that the undesired outcome would occur often, and thus would follow most of their actions, so they would have little room to believe that they had any control). By contrast, the other group (experimental group) was also warned that the spacebar might malfunction (i.e., they were given a potential alternative cause of the failures to keep the screen black), so that in order to prevent the flashes, they should first test whether they actually had any control. To this end, it was suggested that pressing the spacebar on about 50 % of the trials would be a good strategy to learn whether the spacebar was working properly, and thus whether they had any control over the flashes. Therefore, this group was exposed to the combination of the two strategies that, as mentioned above, is effective at reducing positive illusions.

Once participants had been exposed to all 50 flashes, they were asked the following question: “To what extent have you been able to control the onset of the flashes?” Participants answered by entering a numeric value between 0 and 100, with 0 being no control and 100 being perfect control over the flash onset. This subjective judgment of control was our dependent variable.

Results

First, we made sure that the instructions worked as planned to induce a lower p(C) in the experimental group. As in the previous studies, the p(C) of each participant was computed as the number of trials on which the participant pressed the spacebar, divided by 50, the total number of trials. A t test showed that the mean probability of pressing the spacebar was significantly lower in the experimental group (M = .44, SEM = .092) than in the control group (M = .77, SEM = .081), t(18) = 2.70, p < .05, d = 1.21, which indicates that the instructions worked as intended.

The judgments of control were significantly higher than 0 in both groups, both ts(9) > 3.26, ps < .05. Given that a judgment of 0 would be the appropriate rating for the present situation, in which the occurrences of the outcome were preprogrammed and independent of the participants’ behavior, this result indicated that both groups showed significant illusions of control. As expected, however, the judgments of control were significantly lower in the control group (M = 23.30, SEM = 5.83) than in the experimental group (M = 48.80, SEM = 10.14), t(18) = 2.18, p < .05, d = 0.96. The result of the control group makes sense, given that participants were acting to maintain the black screen, while the undesired flashes kept coming back after a very short delay (1 s) on 75 % of the trials. Thus, the illusion of being able to control the flashes could not be high in the control group. However, producing fewer responses and being able to attribute the occurrence of those frequent flashes to an alternative cause in the experimental group seemed to favor the belief that whenever the flashes did not appear or took longer to reappear, this was due to the participant’s behavior being effective. Therefore, contrary to what happens when desired outcomes occur frequently, when undesired outcomes occur frequently, the availability of an alternative cause to which the undesired outcomes can be attributed enhances the illusion, rather than reduce it.

Discussion

As expected, the results observed in this research replicated those observed with positive illusions (e.g., Blanco et al., 2011, 2012; Hannah & Beneteau, 2009; Matute, 1996), except that they were in the opposite direction. In experiments exploring positive illusions, the illusion became weaker when p(C) was lower and when an alternative cause was available to which the outcome could be attributed (Barberia et al., 2013; Blanco et al., 2012; Hannah & Beneteau, 2009; Matute, 1996; Vadillo et al., 2013). What the present research shows is that, in cases in which uncontrollable undesired outcomes occur frequently, if people act frequently, as they do by default, their behavior often seems to be punished, so they conclude that their degree of control is weak. However, if we instruct them from the beginning to reduce their p(C) and provide them with an alternative cause for the occurrence of those frequent undesired outcomes, then they probably feel that their behavior is no longer (or at least is not as frequently) punished. Thus, participants may confirm their belief that, on the few occasions on which those undesired events do not occur, this is due to their having control over them (e.g., “I did not pick number 13, so this is why I was lucky”). Therefore, the illusion that their behavior is appropriate becomes stronger when they reduce their p(C) and attribute the occurrence of undesired outcomes to external causes than when they act frequently and receive frequent punishment. In sum, if one aims to prevent illusions of control in cases in which the outcomes following the action are undesired, it might be better to ask participants to increase, rather than reduce, the frequency of their behavior (see note 3 for a discussion of the similarities and differences between positive and negative illusions).

Contrary to the general assumption that negative illusions are weak and almost nonexistent (e.g., Alloy & Abramson, 1979), our results have shown that negative illusions can be intense, too (in line with Aeschleman et al., 2003; Bloom, Venard, Harden, & Seetharaman, 2007), but are developed and maintained in exactly the opposite way as positive illusions. In a classic experiment, Alloy and Abramson (1979, Exp. 3) concluded that negative illusions were much weaker than positive illusions. However, a close inspection of that experiment suggests that their claim might have been unwarranted. In their experiment, participants tried to control the onset of a light in order to obtain coins as a reward. One group won coins on 50 % of the trials (win group), whereas the other group lost coins on 50 % of the trials (lose group). Thus, the frequency of the “earned-coin” outcome was 50 % in the win group and 0 % in the lose group, and the frequency of the “lost-coin” outcome was 50 % in the lose group and 0 % in the win group. Thus, the problem is that p(O) was confounded with outcome valence in their experiment. Participants in the two groups were exposed to neither the same p(O) nor the same response–outcome contingencies. If participants focused on the coins, as they probably did, those in the win group had a high reinforcement rate. By contrast, participants in the lose group had 50 % of their responses punished and none of their actions rewarded. Whenever they thought that they had found a way to control the light, they possibly repeated that response, and they lost one more coin. Importantly, participants in the lose group were exposed to exactly the opposite contingencies to those that are known to increase the illusion of control. That is, rather than a high frequency of the desired outcome, they were under a zero-reinforcement schedule.

Our results are consistent with a study by Rudski, Lischner, and Albert (1999). Their participants earned or lost points randomly, on 75 %, 50 %, or 25 % of trials (depending on the condition). The illusion of control was higher under conditions of maximal (75 %) gain or minimal (25 %) loss. Moreover, a study conducted by Aeschleman et al. (2003) presented similar results. In Aeschleman et al.’s study, the participants’ goal was to produce and maintain the word GOOD on the computer screen, or to prevent and remove the word BAD. The results showed that the strongest illusion took place with the lower percentage of the word BAD (see also Bloom et al., 2007, for related evidence).

The studies of Rudski et al. (1999) and Aeschleman et al. (2003) refer to the opposite effect that the p(O) has when the outcome is undesired, as compared to when it is desired. To the best of our knowledge, however, the effect of manipulating the existence of alternative causes and p(C) had not yet been investigated with regard to negative illusions. This is important, since the combination of a medium p(C) and a warning about alternative causes has been suggested as an evidence-based strategy to reduce the illusion of control. Our results show that in the case of negative illusions, this strategy should be used in just the opposite way as with positive illusions. That is, insisting on the existence of alternative causes and on the need to act on about 50 % of the trials increases negative illusions, rather than reducing them.

Although the p(C) effect detected in our experiment can be framed straightforwardly in terms of operant conditioning (i.e., adventitious punishment of actions), the effect of the second component of the combined treatment to decrease the illusion (i.e., the availability of alternative causes) could also be discussed in light of inferential theories of causal learning. Most of these theories emphasize the crucial role of structure and counterfactuals in normative causal reasoning (see, e.g., Sloman, 2013). To answer a question framed in causal terms, the participants must evaluate the target cause’s power to produce the outcome when it is isolated from a background where other alternative causes may be present (Cheng, 1997). In the experimental group, we suggested to participants that they reduce p(C) while their attention was explicitly drawn to alternative causes (i.e., the possible malfunction of the spacebar). According to theories based on inferences that make use of causal structures, these two factors might have facilitated the attribution of the frequent undesired outcomes to the alternative cause, therefore increasing the causal power attributed to the target cause. Because p(C) was low in this group, participants were exposed to many trials in which they did not act but the undesired outcome still took place. The counterfactual reasoning would imply asking themselves what would have happened if they had pressed the spacebar on those trials. The availability of a potential alternative cause for the flash (i.e., the spacebar malfunctioning) could lead to the conclusion that we already sketched out above, which is that their behavior was an effective cause, responsible for those few trials on which the aversive outcome was not present—hence, the strong illusion of control that we observed in this group. In any case, our experiment was not designed to test theories of structure-based causal inference. Thus, we cannot reach any conclusion concerning the relative ability of these theories to account for the general finding that we have reported and that we believe to be important: that reducing p(C) while suggesting that other causes might be operating in the background strengthens, rather than weakens, the negative illusion of control. This should be taken into account in analyses of real-life conditions in which uncontrollable undesired outcomes occur at a high rate.