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Superstitious rule generation is affected by probability and type of outcome.

When asked to solve a task without aid of explicit instructions, people often create verbal statements describing contingencies that they believe are in place. In situations in which outcomes occur independent of particular responses, specific descriptions of behavioral contingencies are inaccurate. Such descriptions have been termed superstitious su·per·sti·tious  
1. Inclined to believe in superstition.

2. Of, characterized by, or proceeding from superstition.

 rules (Heltzer & Vyse, 1994).

Superstitious rules are likely to be affected by factors which influence superstition superstition, an irrational belief or practice resulting from ignorance or fear of the unknown. The validity of superstitions is based on belief in the power of magic and witchcraft and in such invisible forces as spirits and demons.  in general, including the type or value of a reinforcement reinforcement /re·in·force·ment/ (-in-fors´ment) in behavioral science, the presentation of a stimulus following a response that increases the frequency of subsequent responses, whether positive to desirable events, or  schedule. Response-independent schedules such as fixed time (i.e., reinforcement is delivered after passage of a specified time interval) reliably engenders superstitious behavior in pigeons (Skinner Skin·ner , B(urrhus) F(rederick) 1904-1990.

American psychologist. A leading behaviorist, Skinner influenced the fields of psychology and education with his theories of stimulus-response behavior.
, 1948) and humans (Wagner & Morris, 1987). Under various reinforcement schedules, superstitious behavior is positively related to frequency of reinforcement. Ono (1987) demonstrated that fixed interval (FI) or fixed time (FT) 30-sec schedules (i.e., the first response after 30 seconds produces a consequence, or the outcome occurs after 30 seconds regardless of the emission of a response, respectively), supports significantly more superstitious responding in people than do FI or FT 60-sec schedules. Wright (1962) reported that as the probability of response-independent reinforcement increased from 0.2 to 0.8, people's responses on keys not producing response-dependent reinforcement increased as well. Moreover, Vyse (1991) showed that the likelihood of participants describing superstitious rules while playing a video game task was higher under a random ratio (RR) 2 reinforcement (i.e., probability of reinforcement is 0.5 and is independent of the number of responses emitted) schedule than under a fixed ratio (FR) 1 schedule (i.e., reinforcement was delivered following each successful completion of the operant operant /op·er·ant/ (op´er-ant) in psychology, any response that is not elicited by specific external stimuli but that recurs at a given rate in a particular set of circumstances.

). Finally, the specific type of reinforcement schedule can determine the effects of whether fixed or variable outcomes alter degree of superstitious behavior. Ono (1987) reported a greater number of superstitious responses followed fixed versus variable interval schedules, but superstitious rules were reported to be more likely when responding under a RR 2 than under a FR 2 schedule (Heltzer & Vyse, 1994).

Superstitions can also be related to environmental cues that appear in concert with reinforcement. When a cue cue,
n a stimulus that determines or may prompt the nature of a person's response.

cue Psychology Any sensory stimulus that evokes a learned patterned response. See Conditioning.
 signals the availability of reinforcement, it is termed a discriminative stimulus Noun 1. discriminative stimulus - a stimulus that provides information about what to do

stimulant, stimulus, stimulation, input - any stimulating information or event; acts to arouse action
. For example, a 'Garage Sale' sign in front of a house sets the occasion for a person's being reinforced for walking into a stranger's garage. At times, cues with no particular discriminative dis·crim·i·na·tive  
1. Drawing distinctions.

2. Marked by or showing prejudice: discriminative hiring practices.
 function are occasionally used to predict availability of reinforcement. When such cues are used to specify response-reinforcer contingencies that are fallacious, performance directed by these cues are referred to as sensory superstitions (Catania, 1992). A classic example of sensory superstitions was done by Morse and Skinner (1957) using pigeons as subjects. Pigeons pecked a key that was illuminated il·lu·mi·nate  
v. il·lu·mi·nat·ed, il·lu·mi·nat·ing, il·lu·mi·nates
1. To provide or brighten with light.

2. To decorate or hang with lights.

 with an orange light. When the response key's color was occasionally switched from orange to blue, pigeons often dramatically increased their rate of pecking in the presence of the blue light although no change had occurred in the reinforcement schedule. Similarly, participants in Ono's (1987) superstition study worked in the presence of a light whose color occasionally switched randomly from red to green to orange. Although reinforcement rates were identical in the presence of each color, 6 of 20 participants produced differential patterns of lever lever, simple machine consisting of a bar supported at some stationary point along its length and used to overcome resistance at a second point by application of force at a third point. The stationary point of a lever is known as its fulcrum.  pressing in the presence of each color.

In all the studies described above, superstitions were supported by the presentation of rewards. Superstitious behavior can also be induced through negative reinforcement. For example, Cerutti (1991) instructed participants that pressing panels could prevent uncontrollable tones. He reported that under mixed random or mixed fixed reinforcement schedules, participants believed that their presses effectively prevented the tones. Similarly, Stegman and McReynolds (1978) reported that 6 of 10 people exposed to response-independent presentations of an aversive aversive /aver·sive/ (ah-ver´siv) characterized by or giving rise to avoidance; noxious.

 tone developed a superstitious belief that pressing a button eliminated the noxious noxious adj. harmful to health, often referring to nuisances.  stimulus. Very little research has examined superstition formation resulting from noncontingent delivery of punishment because such a procedure frequently produces learned helplessness learned helplessness

In psychology, a mental state in which a laboratory subject forced to bear aversive stimuli becomes unable or unwilling to avoid subsequent applications, even if they are “escapable,” presumably through having learned that situational
 (Maier & Seligman, 1976).

In addition to reinforcement contingencies, superstitious beliefs are associated with personality traits. One trait trait (trat)
1. any genetically determined characteristic; also, the condition prevailing in the heterozygous state of a recessive disorder, as the sickle cell trait.

2. a distinctive behavior pattern.
 of particular interest is locus of control locus of control
A theoretical construct designed to assess a person's perceived control over his or her own behavior. The classification internal locus indicates that the person feels in control of events; external locus
. People who believe that they largely control their own destiny are said to exhibit an internal locus of control, whereas people who believe that chance or outside forces determine their fate exhibit an external locus of control (Myers, 1995, p. 489). Positive correlations Noun 1. positive correlation - a correlation in which large values of one variable are associated with large values of the other and small with small; the correlation coefficient is between 0 and +1
direct correlation
 are reported between degree of external locus of control and self-oriented superstitions, paranormal paranormal,
adj 1. outside the realm of normal experience or scientific explanation.
n 2. collective term for anomalous phenomena.
 and irrational ir·ra·tion·al
Not rational; marked by a lack of accord with reason or sound judgment.

irrational adjective Unreasonable, illogical
 beliefs (Peterson, 1978; Tobacyk, Nagot, & Miller, 1988; Tobacyk & Tobacyk, 1992).

The current study further examined how superstitious rules are affected by different reinforcement schedules. Participants were engaged in a discriminated operant task in which they could press one of two buttons in the presence of a visual display. Because Heltzer and Vyse (1994) observed higher likelihood of superstitious rules under random reinforcement schedules, we compared the likelihood of and confidence in rules generated by positive outcomes occurring randomly on 25, 50, and 75% of the trials. This study also directly compared the processes of reinforcement and punishment on superstition: For half of the subjects outcomes were point presentation, whereas for the other half 'incorrect' responding resulted in the loss of a point. Finally, the relationship between rule generation and an individual's score on a locus of control inventory was examined.


Participants, Setting, and Apparatus

One hundred and fifty undergraduate students at a small, northeastern, liberal arts liberal arts, term originally used to designate the arts or studies suited to freemen. It was applied in the Middle Ages to seven branches of learning, the trivium of grammar, logic, and rhetoric, and the quadrivium of arithmetic, geometry, astronomy, and music.  institution served as participants. All participants ranged in age from 17 to 22 years. Most students received course credit for participation. Sessions were conducted using a Zenith zenith, in astronomy, the point in the sky directly overhead; more precisely, it is the point at which the celestial sphere is intersected by an upward extension of a plumb line from the observer's location.  286 computer that was located in a windowless room measuring 1.8 m x 2.0 m. The keyboard was located directly in front of the screen, as is typical with regular use. Participants were assigned to the different conditions using block-randomization.


Superstitious rule generation was examined using a 2 (gain or lose points) x 3 (probability of outcome = 0.75, 0.5, or 0.25) between subject x 4 (rounds of 25 trials) within subject design. This design allowed the examination of the effects of type of consequence and probability of outcome on rule generation. By breaking the session up into four rounds we were able to examine the progression of superstitious rule generation over 100 trials.


Participants were engaged in a self-paced 100-trial computer task. Upon entering the testing room, participants read and signed an informed consent sheet. The experimenters then read the following instructions:

You will be presented with a computerized computerized

adapted for analysis, storage and retrieval on a computer.

computerized axial tomography
see computed tomography.
, problem-solving game that will display 100 letter-number combinations. You should respond by choosing either the [A] or the [L] key and then pressing the [Enter] key. The computer will tell you when you earn a point. Otherwise, the computer will move on to the next letter-number combination. After every 25 rounds, the computer will pause and ask you to answer a short questionnaire. When you are done with each portion of the questionnaire as indicated by the stop sign, press the [Enter] key and continue the game. When you finish the game, the computer will ask you to fill out the remainder of the questionnaire. After you have done so, tell the experimenters that you are done. If you have any questions, please ask them now; we will be unable to answer questions during the experiment. You may work at your own pace. When you are ready to begin, press the [Enter] key and try to figure out how points are earned.

The instructions for the point-loss conditions were identical except for the following. Instead of reading "the computer will tell you when you earn a point," the script read "the computer will tell you when you lost a point." Similarly, the final sentence referred to losing rather than earning points.

Upon initiation of the session, the computer displayed letter (A, B, C, or D) digit (1, 2, 3, or 4) pairings. The computer randomly selected the letter, digit, and spatial location (top or bottom of the screen), resulting in 32 possible letter-digit-location combinations. Depending upon group assignment, points were either randomly awarded or subtracted with 0.75, 0.5, and 0.25 probabilities. When points were awarded, the computer displayed "You have earned one point!!" at the center of a blank screen for 2 seconds before proceeding to the next trial. When points were subtracted, the display read "Sorry, you have lost one point!!" For trials in which points were neither added nor subtracted, the computer cleared the screen for 0.5 seconds before proceeding to the next trial.

The computer paused after every 25 trials (i.e., after Trials 25, 50, 75, and 100), and instructions on the screen told participants to turn to the appropriate page of a multi-page survey. The survey requested that participants write down their estimations of how points were being earned or lost, and to indicate the degree (on a scale of 1-9) of confidence they had in their suggestions. When the 100th trial was completed, participants had to answer several additional questions, including:

Please estimate how many points you think you earned (or lost - depending upon the condition): -----

Which characteristics of the game did you consider necessary to earn (or to avoid losing) points?

- I tried to match A or L to specific letter-number combinations. Y N

- I tried pressing A or L a certain number of times. Y N

- A response on a prior round effected the appropriate response on a later round. Y N

- The rule depended on the letter that was on the screen. Y N

- The rule depended on the number that was on the screen. Y N

Given these possible conditions, do you think you could do better if allowed to play again? Y N

Finally, participants completed Rotter's Internal-External (I-E) Locus of Control Survey (1966) before being debriefed. Rotter's I-E Scale is one of the most commonly used measurement in inferring locus of control, and generally held to be reliable and valid (Marsh & Richards, 1988; Victor, 1971).

Analysis of Data

We chose to use nonparametric tests to analyze the data because the distributions of most dependent variables were not normal. These nonparametric tests also have the advantage of being more sensitive to medians than to means, and the distributions suggested that medians were the most appropriate measurement of central tendency for the current data.

The effects of type of outcome (i.e., gaining or losing points) were examined using a Mann-Whitney U test Mann-Whitney U test, See test, Mann-Whitney U.
. The effects of outcome probability were interpreted using a Kruskal-Wallis Analysis of Variance (ANOVA anova

see analysis of variance.

ANOVA Analysis of variance, see there
). Because participants gaining points on 75% and those losing points on 25% of their trials experienced equal probabilities of positive or desired outcomes (i.e., the desired outcome in the point-gain condition is to gain a point and the desired outcome in the point-loss condition is to avoid losing a point), they were grouped together for this analysis. Similarly, those gaining points 50% and losing points 50% of the time were paired, as were those gaining points on 25% and those losing points on 75% of their trials. This resulted in three different levels of desired or positive outcomes: 75%, 50%, and 25%.

Any statement suggesting that a particular response pattern or contingency between the display and a response could produce reinforcement was considered to be a superstitious rule. Confidence level in the rule was based upon the degree of confidence indicated by the participant on the questionnaire. Participants who indicated that they could not figure out any rule (or stated that point assignment was random) yet assigned a high degree of confidence to their assertion were assigned confidence levels of 0 for superstitious rules with our rationale because we were looking for Looking for

In the context of general equities, this describing a buy interest in which a dealer is asked to offer stock, often involving a capital commitment. Antithesis of in touch with.
 level of confidence in superstitious rules - not lack of a rule.

It is possible that participants were responding according to according to
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

 a rule without being aware of it. People tend to repeat responses followed by positive outcomes and change responses followed by aversive outcomes. This pattern is often termed a Win-Stay Lose-Shift strategy. Thus in addition to stated rules, participants' responses were examined according to a win-stay lose-shift strategy. For each trial following a positive outcome, responses were examined to see if participants pressed the same key. Repeating a response was coded as win-stay, and switching to the other key was coded as win-shift. A similar coding was done following trials in which positive outcomes did not occur (lose-stay and lose-shift, depending upon whether participants pressed the same or alternate key An alternate key (or secondary key) is any candidate key which is not selected to be the primary key (PK).

For example, a relational database with a table "employee" could have attributes like "employee_id", "bank_acct_no", and so on.
, respectively). Raw numbers were then standardized standardized

pertaining to data that have been submitted to standardization procedures.

standardized morbidity rate
see morbidity rate.

standardized mortality rate
see mortality rate.
 by conversion into percentages of trials in which a particular outcome occurred (e.g., if a participant emitted 35 win-stay responses and they had 50 positive outcomes, they were given a score of 70% for the win-stay strategy).

Several summary scores were also generated. Because participants had four opportunities to indicate a rule (i.e., every 25 trials), we summated the number of times in which rules were suggested. Thus, a participant who stated a rule following each round earned a score of 4, whereas a participant who stated a rule following only one round earned a score of 1. Similarly, we were able to obtain a 'total confidence' score by summating the degrees of confidence suggested by participants over the four rounds.

We were also interested in whether or not the various experimental conditions affect the ability of participants to discriminate dis·crim·i·nate  
v. dis·crim·i·nat·ed, dis·crim·i·nat·ing, dis·crim·i·nates

 the occurrence of positive and negative outcomes. First, we asked participants to estimate how many points they earned (or lost) over the entire session. Accuracy of point estimation In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter.

More formally, it is the application of a point estimator to the data.
 was determined by taking the absolute value of difference between number of points estimated earned or lost and number of points actually earned or lost. Mann-Whitney and Kruskal-Wallis tests were used where appropriate.

The locus of control score generated by Rotter's I-E Scale was related to other dependent variables with a Spearman spear·man  
A man, especially a soldier, armed with a spear.
 rank correlation In statistics, rank correlation is the study of relationships between different rankings on the same set of items. It deals with measuring correspondence between two rankings, and assessing the significance of this correspondence.  coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.


Finally, participants' responses on the survey question posing whether or not they thought they could improve their performance if allowed to play again were examined. Even if a person did not suggest any rules throughout the session, answering this question affirmatively af·fir·ma·tive  
1. Asserting that something is true or correct, as with the answer "yes": an affirmative reply.

 indicates that the participant did not discriminate the random nature of the task. The effects of type and probability of outcome on belief in improved future performance were analyzed an·a·lyze  
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.

2. Chemistry To make a chemical analysis of.

 using a chi square chi square (kī),
n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies.


All the results are summarized in Tables 1 and 2. Five participants failed to provide estimates of the number of points received. Findings for each dependent variable will be described individually:

[TABULAR tab·u·lar
1. Having a plane surface; flat.

2. Organized as a table or list.

3. Calculated by means of a table.


resembling a table.


Rule Generation

A Friedman's Rank Test for Correlated cor·re·late  
v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates
1. To put or bring into causal, complementary, parallel, or reciprocal relation.

 Samples on a round of 25 trials indicated that rule generation did not differ according to round [[X.sup.2] (3) = 3.59, p [greater than] 0.10], so analyses on rule generation were done on the summary scores for the four rounds. Rule generation was affected by both type and probability of consequence. Participants in the point-gaining conditions tended to generate more total rules than did those in the point-loss conditions (U = 2277, p [less than] 0.05). Furthermore, rules were more likely to be suggested following higher probabilities of positive outcomes [H(2) = 32.81, p [less than] 0.01].

Confidence in Rule

As was the case for rule generation, there was no effect of round of 25 trials [[X.sup.2](3) = 4.49, p [greater than] 0.10), so analyses on confidence were done on the four-round composite score. The Kruskal-Wallis test revealed that participants receiving frequent positive outcomes tended to have higher confidence levels in their rules than did those on leaner reinforcement schedules [H(2) = 52.45, p [less than] 0.01]. Because the confidence levels may have been skewed skewed

curve of a usually unimodal distribution with one tail drawn out more than the other and the median will lie above or below the mean.

skewed Epidemiology adjective Referring to an asymmetrical distribution of a population or of data
 by the assignment of '0' values to participants stating that they could not find any rules, data for participants who reported rules over all four rounds of 25 trials were analyzed separately. Again, higher levels of confidence were associated with higher probabilities of positive outcomes [H(2) = 6.22, p [less than] 0.05].

There were no significant differences in the ranking of confidence between participants in the point-gain versus the point-loss conditions (U = 2493, p = 0.12).

Locus of Control

A person's score on the locus of control scale was not related to likelihood of rule generation (r = 0.05, p = 0.30) or degree of confidence in one's rule (r = 0.10, p = 0.11). However, locus of control did covary with several dependent variables. Participants indicating an internal locus of control tended to underestimate the number of points to a greater extent (r = -0.25, p [less than] 0.002) and attempted more of the six possible strategies suggested by the experimenters in the final survey (r = -0.21, p [less than] 0.005) than did those indicating an external locus of control.

Point Estimation

Participants in the point-gain conditions tended to underestimate how many points they gained to a significantly greater extent than did participants losing points estimated points lost (U = 1508, p [less than] 0.001). The number of points estimated won or lost by participants was not affected by outcome probability [H(2) = 0.23, p = ns]. Those losing points tended to have more accurate estimates of points lost than those gaining points had of points gained (U = 2183, p [less than] 0.04). Finally, accuracy of point estimation was significantly related to outcome probability [H(2) = 6.57, p [less than] 0.05] in a nonsystematic fashion; the highest degree of accuracy was seen under the 75% desired outcome conditions, and the lowest degree of accuracy followed the 50% desired outcome conditions.

Win-Stay, Lose-Shift Strategies

Participants losing points employed a win-stay lose-shift strategy more frequently than did those gaining points (U = 2233, p [less than] 0.015). In examining the specific strategy that accounted for this, it turned out that there were no significant effects following trials in which positive events occurred. However, subjects gaining points employed a lose-stay strategy more frequently than did those losing points (U = 2183, p [less than] 0.01). Conversely con·verse 1  
intr.v. con·versed, con·vers·ing, con·vers·es
1. To engage in a spoken exchange of thoughts, ideas, or feelings; talk. See Synonyms at speak.

, participants losing points employed a lose-shift strategy significantly more often (U = 2135, p [less than] 0.01). Finally, the probability of positive outcome was not at all related to the overall win-stay lose-shift strategy [H(2) = 1.60, p = ns], nor to any of the specific strategies [H(2) ranging from 0.02 to 0.96].

Improved Performance If Allowed to Play Again?

When asked whether they could do better if allowed to play again, participants in the point-gain conditions were more likely to reply affirmatively than were those in the point-loss conditions [[X.sup.2](1) = 36.81, p [greater than] 0.001]. Similarly, participants with higher probability of positive outcomes responded affirmatively more often when questioned about the likelihood of doing better ([X.sup.2](2) = 116.07, p [greater than] 0.0001) (Table 3).
Table 3

Comparisons of Percentage of Participants Expressing Belief in
Improved Future Performance

                       Probability of Desired Outcome

Type of Outcome      75%      50%      25%      Average

Gaining Points       92%      60%      56%        69.3%
Losing Points        72%      48%      36%          52%
Average              82%      54%      46%


When relationships between behavior and reinforcement are not clear, people frequently engage in stereotyped, superstitious responses. Consistent with previous research (e.g., Ono, 1987; Wright, 1962), we found that superstitious behaviors generated by random reinforcement are also sensitive to reinforcement schedule; superstitious rules are more likely and support higher confidence levels under richer than leaner reinforcement schedules. Moreover, we found that people are more likely to create superstitious rules under conditions of reinforcement than under punishment, although the level of confidence in generated rules does not differ significantly between the operations.

Once attained, rules tend to guide future responding and can make people insensitive in·sen·si·tive  
1. Not physically sensitive; numb.

a. Lacking in sensitivity to the feelings or circumstances of others; unfeeling.

 to the actual contingencies in place (e.g., Baron & Galizio, 1983; Hayes, Brownstein, Haas, & Greenway, 1986; Hayes, Brownstein, Zettle, Rosenfarb, & Korn, 1986; Shimoff, Catania, & Matthews, 1981). The degree of stimulus control Stimulus control
We refer to stimulus control when a discriminative stimulus changes the probability of a behavior (operant response). The discriminative stimulus comes to control behavior when it predicts something about the consequences of that behavior.
 rules have over behavior is related to their accuracy. For example, Hayes, Brownstein, Haas, et al. (1986) demonstrated that participants given accurate rules for responding under a complex reinforcement schedule demonstrated higher levels of resistance to extinction extinction, in biology, disappearance of species of living organisms. Extinction occurs as a result of changed conditions to which the species is not suited.  than did participants given inaccurate rules. Although none of the rules generated in the current study were accurate, their perceived accuracy was directly related to reinforcement density; participants receiving desired outcomes on 75% of their trials would perceive their rules as being more accurate than those receiving those outcomes on only 25% of their trials, resulting in an extended adherence adherence /ad·her·ence/ (ad-her´ens) the act or condition of sticking to something.

immune adherence
 to the rule. Ninness and Ninness (1998) reported that providing fallacious rules during response-independent reinforcement induced high rates and extended durations of superstitious behavior. Indeed, they suggest that superstitious rules can function as well as an accurate rule as long as it maintains the "occasional appearance" of a response-consequence relationship. In our study, the more often this appearance was met, the more likely it is that a superstitious rule was established.

That people continue to respond according to inaccurate rules under the densest schedule of reinforcement appears contrary to results reported by Newman, Buffington, and Hemmes (1995), who found that sensitivity in discriminating dis·crim·i·nat·ing  
a. Able to recognize or draw fine distinctions; perceptive.

b. Showing careful judgment or fine taste:
 between accurate and fallacious instructions decreased as schedule of reinforcement became leaner. However, in the Newman et al. study, externally generated rules were suggested to participants and a response-contingent reinforcement schedule was in place. In the present study, rules were self-generated and consequences occurred independent of particular responses. Thus, the source of the inaccurate rule, or the response-contingent or independent nature of the task could account for the disparate results. It is quite possible that lean reinforcement schedules interfere with the ability to discern dis·cern  
v. dis·cerned, dis·cern·ing, dis·cerns
1. To perceive with the eyes or intellect; detect.

2. To recognize or comprehend mentally.

 accuracy of actual response-reinforcement contingencies, whereas rich schedules interfere with the ability to discern when such schedules are response-independent.

We found that reinforcement (i.e., gaining points) resulted in a greater likelihood of suggesting rules than did punishment (i.e., losing points). There are several possible explanations accounting for the relatively decreased degree of superstitious rule generation in participants in the point-loss situation. First, because there was in fact no response-outcome contingency, decreased rule generation may reflect an increased sensitivity to the random nature of the reinforcement schedule. In a direct comparison of reinforcement and punishment on mathematical problem Mathematical problem may mean two slightly different things, both closely related to mathematical games:
general meaning
a question that can be answered with the help of mathematics ; formal meaning : any tuple (S, C( ), r
 solving, Jackson and Molloy (1983) found that participants in the punishment conditions were more accurate in their responses. Perhaps the loss conditions (i.e., negative punishment) in the current study increased the accuracy of detection of randomness. Increased sensitivity to errors following losses may be caused by negative consequences intensifying in·ten·si·fy  
v. in·ten·si·fied, in·ten·si·fy·ing, in·ten·si·fies
1. To make intense or more intense:
 the stimulus control of prevailing contingencies. Vyse (1997) points out that reinforcement often mirrors the economic construct of diminished marginal utility marginal utility

In economics, the additional satisfaction or benefit (utility) that a consumer derives from buying an additional unit of a commodity or service. The law of diminishing utility implies that utility or benefit is inversely related to the number of units
, resulting in losses often seeming subjectively greater in size than do gains of equal magnitude. Following a loss, people might be more motivated mo·ti·vate  
tr.v. mo·ti·vat·ed, mo·ti·vat·ing, mo·ti·vates
To provide with an incentive; move to action; impel.

 to identify the factors controlling behavioral outcomes. Indeed, decreased stimulus control of false rules following loss of reinforcement is suggested by Galizio's (1979) finding that elimination of instruction-following occurs when inaccurate instructions resulted in participants contacting a monetary loss contingency.

Repeated exposure to aversive events that are unpredictable and uncontrollable can result in the expectation that behavior has little effect on the environment (Maier & Seligman, 1976; Overmier & Seligman, 1968). This effect is termed learned helplessness. Learned helplessness and superstitions appear contradictory; in superstitious behavior, people believe they have control over uncontrollable outcomes, and in helplessness helplessness,
n a perception held by a person because of which he or she feels powerless or unable to act independently. Typically associated with persons diagnosed with chronic disease.
 such outcomes produce a belief in the futility Futility
See also Despair, Frustration.

American Scene, The

portrays Americans as having secured necessities; now looking for amenities. [Am. Lit.: The American Scene]


performs the useless and supererogatory. [Fr.
 of responding. This inverse relationship A inverse or negative relationship is a mathematical relationship in which one variable decreases as another increases. For example, there is an inverse relationship between education and unemployment — that is, as education increases, the rate of unemployment  between the two constructs has led some to suggest that belief in control over response-independent outcomes protects people from the development of learned helplessness (e.g., Langer, 1975; Matute, 1994). Matute (1995) pointed out that many experiments in superstition used positive reinforcement positive reinforcement,
n a technique used to encourage a desirable behavior. Also called
positive feedback, in which the patient or subject receives encouraging and favorable communication from another person.
 (e.g., points, food, or money) whereas most experiments examining learned helplessness involved escape from aversive stimuli (e.g., escape from shock or noise). Thus, the type of consequence might be partially responsible for determining which occurs. In our study, the difference in rule generation between participants gaining as opposed to those losing points indicates that superstitious beliefs are more likely to occur under conditions of positive reinforcement. Furthermore, learned helplessness is suggested by our finding that relatively fewer participants in the point-loss condition believed that they could do better if allowed to play again. Finally, participants expressing belief in improved future performance had higher degrees of confidence in a greater number of rules than those believing their performance could not be improved upon, further illustrating the reciprocal Bilateral; two-sided; mutual; interchanged.

Reciprocal obligations are duties owed by one individual to another and vice versa. A reciprocal contract is one in which the parties enter into mutual agreements.
 relationship between helplessness and superstition.

Operant research on superstition has an analog in the construct of illusion of control Illusion of control is the tendency for human beings to believe they can control, or at least influence, outcomes that they demonstrably have no influence over. Experimental demonstration  discussed by social psychologists The following is a list of academics, both past and present, who are widely renowned for their groundbreaking contributions to the field of social psychology.

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  • Robert P.
. In this line of research, participants are asked to assess their degree of control over noncontingent rewards. People will often exaggerate the degree to which they believe their own actions have control over various events (e.g., Alloy alloy (ăl`oi, əloi`) [O. Fr.,=combine], substance with metallic properties that consists of a metal fused with one or more metals or nonmetals.  & Abramson, 1979; Langer, 1975). Illusion of control has been shown to be related to many of the same factors examined in the current study. Alloy and Abramson (1979) demonstrated that illusion of control is proportional to the frequency of reinforcement. In a series of experiments, they had participants indicate the degree to which they believed their actions could account for the turning on of a green light. Random illumination illumination, in art
illumination, in art, decoration of manuscripts and books with colored, gilded pictures, often referred to as miniatures (see miniature painting); historiated and decorated initials; and ornamental border designs.
 on 75% of trials produced a higher illusion of control than did random illumination on 25% of trials. In another experiment, Alloy and Abramson (Experiment 3) compared the effects of reinforcement versus punishment on illusion of control. Participants could either gain $0.25 when a green light came on, or lose the same amount when it did not, with the probability of light illumination being 50% for either group. They found a high degree of illusion of control for those gaining, but virtually no illusion of control for those losing money.

Our results are similar in many ways to Alloy and Abramson's. We found that superstitious rule generation (and confidence in the rule) increased according to probability of positive consequence. Furthermore, the increased levels of confidence in future success at playing the game observed in participants gaining as opposed to losing points mirrors the increased illusion of control demonstrated by subjects gaining as opposed to losing money. However, there are some key differences between our and Alloy and Abramson's findings. Whereas they found that participants in the point-loss groups did not demonstrate any illusion of control, the majority of our participants still reported some degree of superstitious rule and belief in future improvement. This difference may be due to the types of reinforcers gained or lost. Our participants worked for points, a reinforcer reinforcer /re·in·forc·er/ (-in-for´ser) any stimulus that produces reinforcement, a positive r. being a desirable event strengthening responses preceding its occurrence and a negative r.  with mostly intrinsic value Intrinsic Value

1. The value of a company or an asset based on an underlying perception of the value.

2. For call options, this is the difference between the underlying stock's price and the strike price.
. Furthermore, those in the loss condition did not really lose anything of real value. Alloy and Abramson's subjects worked for money, a much more valuable reinforcer. They either started at $0.00 and gained $5.00, or started with $5.00 and lost all their money - definitely a meaningful gain or loss. Although studies examining the effects of manipulating reinforcer value on superstition or illusion of control have not been directly attempted, there is evidence that they may be related to reinforcer efficacy. Biner, Angle, Park, Mellinger, and Barber A barber (from the Latin barba, "beard") is someone whose occupation is to cut any type of hair, give shaves, and trim beards. In previous times, barbers also performed surgery and dentistry.  (1995) showed that in a task with a food reinforcer, illusion of control was positively related to degree of food deprivation DEPRIVATION, ecclesiastical Punishment. A censure by which a clergyman is deprived of his parsonage, vicarage, or other ecclesiastical promotion or dignity. Vide Ayliffe's Parerg. 206; 1 Bl. Com. 393. : Hungry participants were more confident that they could win a lottery for the food. Similarly, Biner et al. found that individuals from lower income areas (i.e., money deprived) are more likely to have higher degree of illusion of control in playing a lottery than are people from more affluent neighborhoods. A thorough comparison of the effects that presentation or removal of reinforcers of various types and efficacies has on superstition or illusion of control could further illuminate il·lu·mi·nate  
v. il·lu·mi·nat·ed, il·lu·mi·nat·ing, il·lu·mi·nates
1. To provide or brighten with light.

2. To decorate or hang with lights.

 these differences.

The personality trait of locus of control covaries with various forms of superstition and paranormal beliefs (e.g., Tobacyk, Nagot, & Miller, 1988; Tobacyk & Tobacyk, 1992). However, the current study found no relationship between participants' level of locus of control and superstitious rule generation. Our results are in accord with several reported findings on the relationship between superstition and locus of control. Tennen and Sharpe (1983) asked participants to judge the amount of control they had over the onset of a noncontingent green light in one of two conditions: 25% light onset and 75% light onset. They

found that illusion of control was not related to scores of locus of control, with illusion of control being higher in the 75% onset condition regardless of score on the locus of control scale. Similarly, using surveys measuring the use of superstitious rituals across various sports, Bleak and Frederick (1998) report that score on a locus of control survey does not play a significant role in determining the use of specific rituals. Thus, locus of control is not a good predictor for superstition as a generic concept. Indeed, people receiving internal locus of control scores may report a higher degree of superstitious behavior in some tasks. For example, 'internals' tend to give higher estimation estimation

In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator.
 of success when actively involved in a telekinesis telekinesis /tele·ki·ne·sis/ (-ki-ne´sis)
1. movement of an object produced without contact.

2. the ability to produce such movement.telekinet´ic
 task (Benassi, Sweeny, & Drevno, 1979).

In the survey competed by our participants upon finishing the 100 trials, 6 possible strategies that could be employed while playing the game were suggested. Locus of control was correlated with number of strategies attempted; people whose scores suggested an internal control were more likely to have attempted more of those strategies. Although it is possible that we missed several strategies that are used primarily by people reporting an external locus of control, the data suggest that people who felt more in charge of events occurring in their lives made more attempts at 'solving' the game. Participants with survey scores suggesting an internal locus of control also tended to underestimate their number of final points in the game. We can not offer any sound speculation why that is the case. Indeed, because people with an internal locus of control tend to believe that their own behavior maximizes good outcomes and minimizes bad outcomes (Baron & Byrne, 1991), one might expect that such people would overestimate o·ver·es·ti·mate  
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
 the number positive outcomes and underestimate the aversive ones.

Point estimation was also affected by type of consequence; participants receiving points were much less accurate in estimating their point totals than were those losing points. This explanation makes sense in the context of people becoming 'risk aversive' in the face of diminished marginal utility. If losing points is deemed more aversive than gaining point, it would follow that increased vigilance VIGILANCE. Proper attention in proper time.
     2. The law requires a man who has a claim to enforce it in proper time, while the adverse party has it in his power to defend himself; and if by his neglect to do so, he cannot afterwards establish such claim, the
 would be associated with point loss, as was evidenced by the high degree of accuracy of point tracking over an experimental session exhibited by subjects in the point-loss conditions. Furthermore, participants gaining points tended to underestimate the number of points obtained. The modest value of the reinforcer may exaggerate any effect of diminishing marginal utility; points on this task might decrease in relative value fairly quickly. Conversely, the concept of diminished marginal utility is brought into question by the nonsignificant non·sig·nif·i·cant  
1. Not significant.

2. Having, producing, or being a value obtained from a statistical test that lies within the limits for being of random occurrence.
 effect of outcome schedule level on point estimation. One would expect that as number of points increased, participants would begin to underestimate the total number obtained, yet this was not the case.

In sum, superstitious rules were more likely to be obtained under conditions of frequent positive reinforcement. Denser reinforcement schedules encouraged greater creation of superstitious rules and exaggerated participants' confidence in their veracity veracity (vras´itē),
, interfering with the ability to contact the actual random nature of the task. When mild punishment was used instead of reinforcement, the number of people suggesting superstitious rules decreased. Thompson, Armstrong and Thomas (1998) suggested that just as belief that one can control one's own outcomes when such outcomes are rewarding can provide a variety of benefits including emotional well being, enhanced coping with stress, and improved performance, it is reasonable to suppose that situations with negative outcomes might motivate someone to diminish their feeling of control over a situation. Thus, the relatively decreased level of rule generation in the loss conditions may somewhat reflect this protective phenomenon.


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Author:Rudski, Jeffrey M.; Lischner, Mark I.; Albert, Lori M.
Publication:The Psychological Record
Date:Mar 22, 1999
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