Competition, superstition and the illusion of control

The effects of reinforcement schedule and competition on generating superstitious behaviors and beliefs were examined in 72 people. Superstition was induced by having participants respond to turn on a tone under a concurrent 2—lever Variable Interval (VI) Extinction (EXT) schedule. During the session, stimulus lights would occasionally be illuminated, although they did not signal any change in contingency. Attributing importance to the inactive lever, a pattern of switching between levers, or to the illumination of the lights were considered to be superstitious beliefs. Participants were either run alone or in pairs, and manipulation of the reinforcement schedule resulted in groups which were matched in probability of reinforcement, as well as in groups which were mismatched. Reinforcement schedule (VI 30” versus VI 60”) and competitive situation did not affect degree of superstitious belief, except when people were placed in a “winning” condition. However, Superstition was associated with participants’ belief in improved future performance and with participants’ perceived skill relative to their opponents. Results are discussed in terms of relationships between superstition, the illusion of control, and self-efficacy. Differences between experimentally-induced and commonly held superstitions are also discussed.     

Doxastic Voluntarism and the Function of Epistemic Evaluations

Control of our own beliefs is allegedly required for the truth of epistemic evaluations, such as “S ought to believe that p”, or “S ought to suspend judgment (and so refrain from any belief) whether p”. However, we cannot usually believe or refrain from believing at will. I agree with a number of recent authors in thinking that this apparent conflict is to be resolved by distinguishing reasons for believing that give evidence that p from reasons that make it desirable to believe that p whether or not p is true. I argue however that there is a different problem, one that becomes clearer in light of this solution to the first problem. Someone’s approval of our beliefs is at least often a non-evidential reason to believe, and as such cannot change our beliefs. Ought judgments aim to change the world. But ‘ought to believe’ judgments can’t do that by changing the belief, if they don’t give evidence. So I argue that we should instead regard epistemic ought judgments as aimed mainly at influencing assertions that express the belief and other actions based on the belief, in accord with recent philosophical claims that we have epistemic norms for assertion and action.     

The generality of selective observing

Four rats obtained food pellets by poking a key and 5-s presentations of the discriminative stimuli by pressing a lever. Every 1 or 2 min, the prevailing schedule of reinforcement for key poking alternated between rich (either variable-interval [VI] 30 s or VI 60 s) and lean (either VI 240 s, VI 480 s, or extinction) components. While the key was dark (mixed-schedule stimulus), no exteroceptive stimulus indicated the prevailing schedule. A lever press (i.e., an observing response), however, illuminated the key for 5 s with either a steady light (S+), signaling the rich reinforcement schedule, or a blinking light (S-), signaling the lean reinforcement schedule. One goal was to determine whether rats would engage in selective observing (i.e., a pattern of responding that maintains contact with S+ and decreases contact with S-). Such a pattern was found, in that a 5-s presentation of S+ was followed relatively quickly by another observing response (which likely produced another 5-s period of S+), whereas exposure to S- resulted in extended breaks from observing. Additional conditions demonstrated that the rate of observing remained high when lever presses were effective only when the rich reinforcement schedule was in effect (S+ only condition), but decreased to a low level when lever presses were effective only during the lean reinforcement component (S- only condition) or when lever presses had no effect (in removing the mixed stimulus or presenting the multiple-schedule stimuli). These findings are consistent with relativistic conceptualizations of conditioned reinforcement and extend the generality of selective observing to procedures in which the experimenter controls the duration of stimulus presentations, the schedule components both offer intermittent food reinforcement, and rats serve as subjects.     

A direct comparison of four methods for eliminating a response

Thirty-two rats pressed one lever (lever A) on a VI 30-sec schedule of food reinforcement and were then shifted to one of four procedures for eliminating the lever A response: extinction, differential reinforcement of other behavior, reinforcement of a different response (pole pushing), and reinforcement of a similar response (pressing lever B). Effectiveness of a response-elimination procedure was measured by (1) how quickly lever A response rate fell to a low level when the procedure was in effect, (2) how much lever A responding recovered when the procedure was discontinued, and (3) how resistant lever A responding was to reinstatement when the VI reinforcement schedule was reimposed. No one method was superior by all three measures. Extinction produced the most variable behavior, while differential reinforcement of other behavior produced the least. Reinforcing alternative behavior produced the greatest recovery in the original lever A response when the response-elimination procedure was discontinued.     

Drug discrimination in rats under concurrent variable-interval variable-interval schedules

Eight rats were trained to discriminate pentobarbital from saline under a concurrent variable-interval (VI) VI schedule, on which responses on the pentobarbital-biased lever after pentobarbital were reinforced under VI 20 s and responses on the saline-biased lever were reinforced under VI 80 s. After saline, the reinforcement contingencies programmed on the two levers were reversed. The rats made 62.3% of their responses on the pentobarbital-biased lever after pentobarbital and 72.2% on the saline-biased lever after saline, both of which are lower than predicted by the matching law. When the schedule was changed to concurrent VI 50 s VI 50 s for test sessions with saline and the training dose of pentobarbital, responding on the pentobarbital-biased lever after the training dose of pentobarbital and on the saline-biased lever after saline became nearly equal, even during the first 2 min of the session, suggesting that the presence or absence of the training drug was exerting minimal control over responding and making the determination of dose-effect relations of drugs difficult to interpret. When the pentobarbital dose-response curve was determined under the concurrent VI 50-s VI 50-s schedule, responding was fairly evenly distributed on both levers for most rats. Therefore, 6 additional rats were trained to respond under a concurrent VI 60-s VI 240-s schedule. Under this schedule, the rats made 62.6% of their responses on the pentobarbital-biased lever after pentobarbital and 73.5% of their responses on the saline-biased lever after saline, which also is lower than the percentages predicted by perfect matching. When the schedule was changed to a concurrent VI 150-s VI 150-s schedule for 5-min test sessions with additional drugs, the presence or absence of pentobarbital continued to control responding in most rats, and it was possible to generate graded dose-response curves for pentobarbital and other drugs using the data from these 5-min sessions. The dose-response curves generated under these conditions were similar to the dose-response curves generated using other reinforcement schedules and other species.     

Resurgence and downshifts in alternative reinforcement rate

Resurgence refers to an increase in a previously suppressed target behavior with a relative worsening of conditions for a more recently reinforced alternative behavior. This experiment examined the relation between resurgence and the magnitude of a reduction in the rate of reinforcement for the alternative behavior. Groups of both male and female rats initially pressed a target lever for food on a variable-interval (VI) 30-s schedule. In a second phase, responding to the target lever was extinguished for all groups and pressing an alternative lever was reinforced on a VI 10-s schedule. Next, the rate of reinforcement for alternative behavior was reduced differentially across groups by arranging extinction, VI 80-s, VI 40-s, VI 20-s, or continued VI 10-s reinforcement. Target responding increased as an exponential function of the magnitude of the reduction in alternative reinforcement rates. With the exception that males appeared to show higher rates of target responding in baseline and higher rates of alternative responding in other phases, the overall pattern of responding across phases was not meaningfully different between sexes. The pattern of both target and alternative response rates across sessions and phases was well described quantitatively by the Resurgence as Choice in Context model.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

Methodological and theoretical improvements in the study of superstitious beliefs and behaviour

Via four studies (N = 901), we developed an improved Belief in Superstition Scale (BSS) composed of three distinct components (belief in bad luck, belief in good luck, and the belief that luck can be changed), whose structure was supported through exploratory (Study 1) and confirmatory (Studies 2 and 3) factor analyses using divergent samples. We found that among theoretical predictors, higher ‘chance’ locus of control (i.e., the belief that chance/fate controls one's life) best predicted all three BSS subscales (Studies 2–3). In Study 3, we found that BSS subscale scores were reliable, but largely invariant across age and education with a non‐general psychology sample. In Study 4, the BSS subscales best predicted participants’ superstitious attitudes and behaviour in a new lottery drawing paradigm among other commonly used superstition scales. Taken together, our results indicate that the BSS is a valuable addition to the burgeoning research on superstitious attitudes and behaviour.     

Instrumental performance on negative schedules

Three experiments examined the performance of rats pressing a lever for food reinforcement on a schedule in which high rates of response resulted in lowered rates of reinforcement (i.e. a schedule with a negative component). In Experiment 1, rats responded on a variable interval (VI) schedule with a conjoint component such that every 30 responses a reinforcement programmed by the VI schedule was cancelled. These subjects generally emitted a lower response rate than rats responding on a VI schedule yoked to the former subjects with respect to the delivery of reinforcement, although response rate differences were sometimes not large. Similar response-rate effects were obtained in Experiment 2 using a within-subject yoking procedure. In Experiment 3, reinforced interresponse times were matched on negative and VI schedules yoked in terms of reinforcement rate, and the response rate emitted in these conditions were similar. These results give support to theories of instrumental conditioning that stress the strengthening and shaping properties of reinforcement.     

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality.     

Observing behavior in monkeys (Macaca arctoides): Support for the information hypothesis

A single lever, discrete-trials observing procedure was used with stumptailed monkeys (Macaca arctoides). Lever-presses during a trial produced colored key lights (IS⁺ and IS^?) which signaled whether the trial would end with response-independent food or without food. During the baseline period, both IS⁺ and IS^? were produced on a variable-interval (VI) 15-sec schedule which began operating at the onset of the trial. The two experimental conditions involved a combination of this VI schedule and a DRL schedule. In one of these conditions, only a response that both met the VI requirement and was preceded by at least 6 sec of nonresponding could produce IS^? on nonfood trials, while the schedule for IS⁺ on food trials remained VI 15 sec. In the other experimental condition, the schedules for producing the two stimuli were the reverse. All subjects eventually learned to produce either IS⁺ or IS^? on the combined VI-DRL schedule. These data support an information hypothesis of observing in monkeys and contrast with data from pigeons which support a conditioned reinforcement hypothesis.     

Beliefs about relationships in relation to television viewing, soap opera viewing, and self-monitoring

Undergraduates (n=188) completed: a survey of television and soap opera viewing habits; the Relationship Beliefs Inventory, measuring dysfunctional relationship beliefs; and Snyder's Self-Monitoring Scale. It was hypothesized was that there would be positive associations between viewing habits and endorsement of dysfunctional relationship beliefs. Results supported this hypothesis. High television viewing was associated with the belief “the sexes are different,” and high soap opera viewing was associated with the belief “mindreading is expected” between partners. High self-monitors watched television more for escape than low self-monitors. Implications for research on dysfunctional relationship beliefs are discussed.     

Beliefs about relationships in relation to television viewing, soap opera viewing, and self-monitoring

Undergraduates (n=188) completed: a survey of television and soap opera viewing habits; the Relationship Beliefs Inventory, measuring dysfunctional relationship beliefs; and Snyder's Self-Monitoring Scale. It was hypothesized was that there would be positive associations between viewing habits and endorsement of dysfunctional relationship beliefs. Results supported this hypothesis. High television viewing was associated with the belief “the sexes are different,” and high soap opera viewing was associated with the belief “mindreading is expected” between partners. High self-monitors watched television more for escape than low self-monitors. Implications for research on dysfunctional relationship beliefs are discussed.     

On the role of beliefs in observational flavor conditioning

In previous research (Baeyens, Vansteenwegen et al., 1996) we demonstrated that when observers consume a series of CS+ and CS−flavored drinks while simultaneously watching a videotaped model who synchronically drinks identical drinks and facially expresses his evaluation (dislike to CS+, neutral to CS−) of the liquids, the observers acquire a dislike for CS+ flavored relative to CS−flavored drinks. The aim of the present experiments was to test some predictions derived from a “direct conditioning” theory of such observational flavor learning. Using the same observational flavor conditioning procedure, we investigated (Exp. 1) the effect of manipulating the observers’ belief concerning the relationship between the drinks that they and the model were consuming (same/different/no information). Observational flavor conditioning was obtained when observers were led to believe that they were drinking the same drinks as the model did, and when they were not informed about this relationship, but not when told to be drinking different drinks. At the same time, however, the observers were not able to correctly identify the source of the model’s expression of dislike: They showed no CS-US contingency-awareness. Whereas the former finding suggests the causal involvement of conscious beliefs and cognitive inference processes in observational learning, the latter is more in line with the idea that the model’s facial expressions may act like a US’ which is automatically associated with the paired flavor CS+, without any involvement of conscious beliefs or cognitive inferences. These two crucial findings were replicated in Exp. 2. Also, we obtained evidence in this study that the belief manipulation affected learning through its influence on the observers’ attention for the model’s facial evaluative expressions. These results can be integrated either by a cognitive theory allowing the beliefs on which the inferences are based to be of an implicit nature, or by a “direct conditioning” theory that conceives of the US’ as an interpreted event, rather than as a mechanistically and invariantly acting physical entity.     

On the role of beliefs in observational flavor conditioning

In previous research (Baeyens, Vansteenwegen et al., 1996) we demonstrated that when observers consume a series of CS+ and CS−flavored drinks while simultaneously watching a videotaped model who synchronically drinks identical drinks and facially expresses his evaluation (dislike to CS+, neutral to CS−) of the liquids, the observers acquire a dislike for CS+ flavored relative to CS−flavored drinks. The aim of the present experiments was to test some predictions derived from a “direct conditioning” theory of such observational flavor learning. Using the same observational flavor conditioning procedure, we investigated (Exp. 1) the effect of manipulating the observers’ belief concerning the relationship between the drinks that they and the model were consuming (same/different/no information). Observational flavor conditioning was obtained when observers were led to believe that they were drinking the same drinks as the model did, and when they were not informed about this relationship, but not when told to be drinking different drinks. At the same time, however, the observers were not able to correctly identify the source of the model’s expression of dislike: They showed no CS-US contingency-awareness. Whereas the former finding suggests the causal involvement of conscious beliefs and cognitive inference processes in observational learning, the latter is more in line with the idea that the model’s facial expressions may act like a US’ which is automatically associated with the paired flavor CS+, without any involvement of conscious beliefs or cognitive inferences. These two crucial findings were replicated in Exp. 2. Also, we obtained evidence in this study that the belief manipulation affected learning through its influence on the observers’ attention for the model’s facial evaluative expressions. These results can be integrated either by a cognitive theory allowing the beliefs on which the inferences are based to be of an implicit nature, or by a “direct conditioning” theory that conceives of the US’ as an interpreted event, rather than as a mechanistically and invariantly acting physical entity.     

Precise instructions determine participants’ memory search strategy in judgments of relative order in short lists

Memory often requires knowledge of the order of events. Previous findings about immediate judgments of relative order in short, subspan lists are variable regarding whether participants’ strategy is to search memory in the forward direction, starting from the first list item and progressing toward the end item, or in the backward direction, starting from the end item and progressing toward the start. We asked whether wording of the instructions influences participants’ search direction. Participants studied sequences of three to six consonants, and for an immediate, two-item probe of each list, judged which probe was presented earlier (“earlier” instruction) or later (“later” instruction) on the list. Forward and backward searches were supported for “earlier” and “later” instructions, respectively. Our findings suggest that participants have more than one effective strategy for order judgments in short lists, and that subtle instructional differences can bias memory search in either the forward or backward direction.     

Religion and pseudo-religion: an elusive boundary

This paper examines the possibility of setting a boundary between religion and “pseudo-religion” (or superstition). Philosophers of religion inspired by Ludwig Wittgenstein’s ideas, in particular, insist that religious language-use can be neither legitimated nor criticized from the perspective of non-religious language-games. Thus, for example, the “theodicist” requirement that the existence of evil should be theoretically reconciled with theism can be argued to be pseudo-religious (superstitious). Another example discussed in the paper is the relation between religion and morality. The paper concludes by reflecting on the issue of relativism arising from the Wittgensteinian contention that the religion vs. pseudo-religion division can only be drawn within a religious framework, and on Wittgenstein’s own suggestion that the religious person “uses a picture”.     

Human sensitivity to reinforcement feedback functions

Two experiments investigated human sensitivity to the temporally extended aspects of reinforcement schedules. Experiment 1 investigated human sensitivity to the extended and local aspects of three reinforcement schedules: variable ratio (VR), variable interval (VI), and variable-interval-plus-linear-feedback (VI+) schedules. Experiment 2 investigated this sensitivity on two reinforcement schedules: VI and VI+ schedules. In both experiments, there was evidence of sensitivity to the temporally extended aspects of the schedule: There were differences between the response rate on the VI+ and yoked-VI schedules, but no statistical difference in rates of response between the VR and VI+ schedules. The VI+ versus VI difference was much more pronounced when a lower response force needed to depress a lever was used. These results suggest that human subjects do show some sensitivity to temporally extended aspects of schedules of reinforcement.     

Variable-interval reinforcement schedule value influences responding following REM sleep deprivation

The effects of rapid-eye movement sleep deprivation (REMSD) in rats were studied in relation to variable-interval (VI) reinforcement schedule value. Initially, lever pressing was maintained on a VI 30-s schedule of food pellet delivery. After a baseline was established, rats were repeatedly exposed to 96 hr of REMSD and control conditions of an equivalent duration. Responding decreased following REMSD but not after exposure to control conditions. Lever pressing was then maintained on a VI 15-s schedule of food pellet delivery and exposure to the REMSD and control conditions was repeated. Under this condition following repeated REMSD exposures, rates of lever pressing became similar to baseline responding. A VI 30-s schedule of food pellet delivery was then reinstated and REMSD and control conditions were repeated. Lever pressing following exposure to the REMSD condition decreased for 3 of 4 rats. Results suggest that VI schedule value influences the effects of REMSD on responding.