Gambler's fallacy

From Wikipedia, the free encyclopedia

 

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa). In situations where the outcome being observed is truly random and consists of independent trials of a random process, this belief is false. The fallacy can arise in many situations, but is most strongly associated with gambling, where it is common among players.

The term "Monte Carlo fallacy" originates from the best known example of the phenomenon, which occurred in the Monte Carlo Casino in 1913.

Examples

Coin toss

Simulation of coin tosses: Each frame, a coin is flipped which is red on one side and blue on the other. The result of each flip is added as a coloured dot in the corresponding column. As the pie chart shows, the proportion of red versus blue approaches 50-50 (the law of large numbers). But the difference between red and blue does not systematically decrease to zero.

The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. The outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is 1/2 (one in two). The probability of getting two heads in two tosses is 1/4 (one in four) and the probability of getting three heads in three tosses is 1/8 (one in eight). In general, if A_i is the event where toss i of a fair coin comes up heads, then:

${\displaystyle \Pr \left(\bigcap _{i=1}^{n}A_{i}\right)=\prod _{i=1}^{n}\Pr(A_{i})={1 \over 2^{n}}}$.

If after tossing four heads in a row, the next coin toss also came up heads, it would complete a run of five successive heads. Since the probability of a run of five successive heads is 1/32 (one in thirty-two), a person might believe that the next flip would be more likely to come up tails rather than heads again. This is incorrect and is an example of the gambler's fallacy. The event "5 heads in a row" and the event "first 4 heads, then a tails" are equally likely, each having probability 1/32. Since the first four tosses turn up heads, the probability that the next toss is a head is:

${\displaystyle \Pr \left(A_{5}|A_{1}\cap A_{2}\cap A_{3}\cap A_{4}\right)=\Pr \left(A_{5}\right)={\frac {1}{2}}}$.

While a run of five heads has a probability of 1/32 = 0.03125 (a little over 3%), the misunderstanding lies in not realizing that this is the case only before the first coin is tossed. After the first four tosses, the results are no longer unknown, so their probabilities are at that point equal to 1 (100%). The reasoning that it is more likely that a fifth toss is more likely to be tails because the previous four tosses were heads, with a run of luck in the past influencing the odds in the future, forms the basis of the fallacy.

Why the probability is 1/2 for a fair coin

If a fair coin is flipped 21 times, the probability of 21 heads is 1 in 2,097,152. The probability of flipping a head after having already flipped 20 heads in a row is 1/2. This is an application of Bayes' theorem.

This can also be shown without knowing that 20 heads have occurred, and without applying Bayes' theorem. Assuming a fair coin:

• The probability of 20 heads, then 1 tail is 0.5²⁰ × 0.5 = 0.5²¹
• The probability of 20 heads, then 1 head is 0.5²⁰ × 0.5 = 0.5²¹

The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail. These two outcomes are equally as likely as any of the other combinations that can be obtained from 21 flips of a coin. All of the 21-flip combinations will have probabilities equal to 0.5²¹, or 1 in 2,097,152. Assuming that a change in the probability will occur as a result of the outcome of prior flips is incorrect because every outcome of a 21-flip sequence is as likely as the other outcomes. In accordance with Bayes' theorem, the likely outcome of each flip is the probability of the fair coin, which is 1/2.

Other examples

The fallacy leads to the incorrect notion that previous failures will create an increased probability of success on subsequent attempts. For a fair 16-sided die, the probability of each outcome occurring is 1/16 (6.25%). If a win is defined as rolling a 1, the probability of a 1 occurring at least once in 16 rolls is:

${\displaystyle 1-\left[{\frac {15}{16}}\right]^{16}\,=\,64.39\%}$

The probability of a loss on the first roll is 15/16 (93.75%). According to the fallacy, the player should have a higher chance of winning after one loss has occurred. The probability of at least one win is now:

${\displaystyle 1-\left[{\frac {15}{16}}\right]^{15}\,=\,62.02\%}$

By losing one toss, the player's probability of winning drops by two percentage points. With 5 losses and 11 rolls remaining, the probability of winning drops to around 0.5 (50%). The probability of at least one win does not increase after a series of losses; indeed, the probability of success actually decreases, because there are fewer trials left in which to win. The probability of winning will eventually equal the probability of winning a single toss, which is 1/16 (6.25%) and occurs when only one toss is left.

Reverse position

After a consistent tendency towards tails, a gambler may also decide that tails has become a more likely outcome. This is a rational and Bayesian conclusion, bearing in mind the possibility that the coin may not be fair; it is not a fallacy. Believing the odds to favor tails, the gambler sees no reason to change to heads. However it is a fallacy that a sequence of trials carries a memory of past results which tend to favor or disfavor future outcomes.

The inverse gambler's fallacy described by Ian Hacking is a situation where a gambler entering a room and seeing a person rolling a double six on a pair of dice may erroneously conclude that the person must have been rolling the dice for quite a while, as they would be unlikely to get a double six on their first attempt.

Retrospective gambler's fallacy

Researchers have examined whether a similar bias exists for inferences about unknown past events based upon known subsequent events, calling this the "retrospective gambler's fallacy".

An example of a retrospective gambler's fallacy would be to observe multiple successive "heads" on a coin toss and conclude from this that the previously unknown flip was "tails". Real world examples of retrospective gambler's fallacy have been argued to exist in events such as the origin of the Universe. In his book Universes, John Leslie argues that "the presence of vastly many universes very different in their characters might be our best explanation for why at least one universe has a life-permitting character". Daniel M. Oppenheimer and Benoît Monin argue that "In other words, the 'best explanation' for a low-probability event is that it is only one in a multiple of trials, which is the core intuition of the reverse gambler's fallacy." Philosophical arguments are ongoing about whether such arguments are or are not a fallacy, arguing that the occurrence of our universe says nothing about the existence of other universes or trials of universes. Three studies involving Stanford University students tested the existence of a retrospective gamblers' fallacy. All three studies concluded that people have a gamblers' fallacy retrospectively as well as to future events. The authors of all three studies concluded their findings have significant "methodological implications" but may also have "important theoretical implications" that need investigation and research, saying "[a] thorough understanding of such reasoning processes requires that we not only examine how they influence our predictions of the future, but also our perceptions of the past."

Childbirth

In 1796, Pierre-Simon Laplace described in A Philosophical Essay on Probabilities the ways in which men calculated their probability of having sons: "I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls." The expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter. This essay by Laplace is regarded as one of the earliest descriptions of the fallacy.

After having multiple children of the same sex, some parents may believe that they are due to have a child of the opposite sex. While the Trivers–Willard hypothesis predicts that birth sex is dependent on living conditions, stating that more male children are born in good living conditions, while more female children are born in poorer living conditions, the probability of having a child of either sex is still regarded as near 0.5 (50%).

Monte Carlo Casino

Perhaps the most famous example of the gambler's fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in a row is (18/37)^26-1 or around 1 in 66.6 million, assuming the mechanism is unbiased. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an imbalance in the randomness of the wheel, and that it had to be followed by a long streak of red.

Non-examples

Non-independent events

The gambler's fallacy does not apply in situations where the probability of different events is not independent. In such cases, the probability of future events can change based on the outcome of past events, such as the statistical permutation of events. An example is when cards are drawn from a deck without replacement. If an ace is drawn from a deck and not reinserted, the next draw is less likely to be an ace and more likely to be of another rank. The probability of drawing another ace, assuming that it was the first card drawn and that there are no jokers, has decreased from 4/52 (7.69%) to 3/51 (5.88%), while the probability for each other rank has increased from 4/52 (7.69%) to 4/51 (7.84%). This effect allows card counting systems to work in games such as blackjack.

Bias

In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this probability is so small, if it happens, it may well be that the coin is somehow biased towards landing on heads, or that it is being controlled by hidden magnets, or similar. In this case, the smart bet is "heads" because Bayesian inference from the empirical evidence — 21 heads in a row — suggests that the coin is likely to be biased toward heads. Bayesian inference can be used to show that when the long-run proportion of different outcomes is unknown but exchangeable (meaning that the random process from which the outcomes are generated may be biased but is equally likely to be biased in any direction) and that previous observations demonstrate the likely direction of the bias, the outcome which has occurred the most in the observed data is the most likely to occur again.

For example, if the a priori probability of a biased coin is say 1%, and assuming that such a biased coin would come down heads say 60% of the time, then after 21 heads the probability of a biased coin has increased to about 32%.

The opening scene of the play Rosencrantz and Guildenstern Are Dead by Tom Stoppard discusses these issues as one man continually flips heads and the other considers various possible explanations.

Changing probabilities

If external factors are allowed to change the probability of the events, the gambler's fallacy may not hold. For example, a change in the game rules might favour one player over the other, improving his or her win percentage. Similarly, an inexperienced player's success may decrease after opposing teams learn about and play against their weaknesses. This is another example of bias.

Psychology

Origins

The gambler's fallacy arises out of a belief in a law of small numbers, leading to the erroneous belief that small samples must be representative of the larger population. According to the fallacy, streaks must eventually even out in order to be representative. Amos Tversky and Daniel Kahneman first proposed that the gambler's fallacy is a cognitive bias produced by a psychological heuristic called the representativeness heuristic, which states that people evaluate the probability of a certain event by assessing how similar it is to events they have experienced before, and how similar the events surrounding those two processes are. According to this view, "after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red", so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out. When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0.5 in any short segment than would be predicted by chance, a phenomenon known as insensitivity to sample size. Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones. The representativeness heuristic is also cited behind the related phenomenon of the clustering illusion, according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.

The gambler's fallacy can also be attributed to the mistaken belief that gambling, or even chance itself, is a fair process that can correct itself in the event of streaks, known as the just-world hypothesis. Other researchers believe that belief in the fallacy may be the result of a mistaken belief in an internal locus of control. When a person believes that gambling outcomes are the result of their own skill, they may be more susceptible to the gambler's fallacy because they reject the idea that chance could overcome skill or talent.

Variations

Some researchers believe that it is possible to define two types of gambler's fallacy: type one and type two. Type one is the classic gambler's fallacy, where individuals believe that a particular outcome is due after a long streak of another outcome. Type two gambler's fallacy, as defined by Gideon Keren and Charles Lewis, occurs when a gambler underestimates how many observations are needed to detect a favorable outcome, such as watching a roulette wheel for a length of time and then betting on the numbers that appear most often. For events with a high degree of randomness, detecting a bias that will lead to a favorable outcome takes an impractically large amount of time and is very difficult, if not impossible, to do. The two types differ in that type one wrongly assumes that gambling conditions are fair and perfect, while type two assumes that the conditions are biased, and that this bias can be detected after a certain amount of time.

Another variety, known as the retrospective gambler's fallacy, occurs when individuals judge that a seemingly rare event must come from a longer sequence than a more common event does. The belief that an imaginary sequence of die rolls is more than three times as long when a set of three sixes is observed as opposed to when there are only two sixes. This effect can be observed in isolated instances, or even sequentially. Another example would involve hearing that a teenager has unprotected sex and becomes pregnant on a given night, and concluding that she has been engaging in unprotected sex for longer than if we hear she had unprotected sex but did not become pregnant, when the probability of becoming pregnant as a result of each intercourse is independent of the amount of prior intercourse.

Relationship to hot-hand fallacy

Another psychological perspective states that gambler's fallacy can be seen as the counterpart to basketball's hot-hand fallacy, in which people tend to predict the same outcome as the previous event - known as positive recency - resulting in a belief that a high scorer will continue to score. In the gambler's fallacy, people predict the opposite outcome of the previous event - negative recency - believing that since the roulette wheel has landed on black on the previous six occasions, it is due to land on red the next. Ayton and Fischer have theorized that people display positive recency for the hot-hand fallacy because the fallacy deals with human performance, and that people do not believe that an inanimate object can become "hot." Human performance is not perceived as random, and people are more likely to continue streaks when they believe that the process generating the results is nonrandom. When a person exhibits the gambler's fallacy, they are more likely to exhibit the hot-hand fallacy as well, suggesting that one construct is responsible for the two fallacies.

The difference between the two fallacies is also found in economic decision-making. A study by Huber, Kirchler, and Stockl in 2010 examined how the hot hand and the gambler's fallacy are exhibited in the financial market. The researchers gave their participants a choice: they could either bet on the outcome of a series of coin tosses, use an expert opinion to sway their decision, or choose a risk-free alternative instead for a smaller financial reward. Participants turned to the expert opinion to make their decision 24% of the time based on their past experience of success, which exemplifies the hot-hand. If the expert was correct, 78% of the participants chose the expert's opinion again, as opposed to 57% doing so when the expert was wrong. The participants also exhibited the gambler's fallacy, with their selection of either heads or tails decreasing after noticing a streak of either outcome. This experiment helped bolster Ayton and Fischer's theory that people put more faith in human performance than they do in seemingly random processes.

Neurophysiology

While the representativeness heuristic and other cognitive biases are the most commonly cited cause of the gambler's fallacy, research suggests that there may also be a neurological component. Functional magnetic resonance imaging has shown that after losing a bet or gamble, known as riskloss, the frontoparietal network of the brain is activated, resulting in more risk-taking behavior. In contrast, there is decreased activity in the amygdala, caudate, and ventral striatum after a riskloss. Activation in the amygdala is negatively correlated with gambler's fallacy, so that the more activity exhibited in the amygdala, the less likely an individual is to fall prey to the gambler's fallacy. These results suggest that gambler's fallacy relies more on the prefrontal cortex, which is responsible for executive, goal-directed processes, and less on the brain areas that control affective decision-making.

The desire to continue gambling or betting is controlled by the striatum, which supports a choice-outcome contingency learning method. The striatum processes the errors in prediction and the behavior changes accordingly. After a win, the positive behavior is reinforced and after a loss, the behavior is conditioned to be avoided. In individuals exhibiting the gambler's fallacy, this choice-outcome contingency method is impaired, and they continue to make risks after a series of losses.

Possible solutions

The gambler's fallacy is a deep-seated cognitive bias and can be very hard to overcome. Educating individuals about the nature of randomness has not always proven effective in reducing or eliminating any manifestation of the fallacy. Participants in a study by Beach and Swensson in 1967 were shown a shuffled deck of index cards with shapes on them, and were instructed to guess which shape would come next in a sequence. The experimental group of participants was informed about the nature and existence of the gambler's fallacy, and were explicitly instructed not to rely on run dependency to make their guesses. The control group was not given this information. The response styles of the two groups were similar, indicating that the experimental group still based their choices on the length of the run sequence. This led to the conclusion that instructing individuals about randomness is not sufficient in lessening the gambler's fallacy.

An individual's susceptibility to the gambler's fallacy may decrease with age. A study by Fischbein and Schnarch in 1997 administered a questionnaire to five groups: students in grades 5, 7, 9, 11, and college students specializing in teaching mathematics. None of the participants had received any prior education regarding probability. The question asked was: "Ronni flipped a coin three times and in all cases heads came up. Ronni intends to flip the coin again. What is the chance of getting heads the fourth time?" The results indicated that as the students got older, the less likely they were to answer with "smaller than the chance of getting tails", which would indicate a negative recency effect. 35% of the 5th graders, 35% of the 7th graders, and 20% of the 9th graders exhibited the negative recency effect. Only 10% of the 11th graders answered this way, and none of the college students did. Fischbein and Schnarch theorized that an individual's tendency to rely on the representativeness heuristic and other cognitive biases can be overcome with age.

Another possible solution comes from Roney and Trick, Gestalt psychologists who suggest that the fallacy may be eliminated as a result of grouping. When a future event such as a coin toss is described as part of a sequence, no matter how arbitrarily, a person will automatically consider the event as it relates to the past events, resulting in the gambler's fallacy. When a person considers every event as independent, the fallacy can be greatly reduced.

Roney and Trick told participants in their experiment that they were betting on either two blocks of six coin tosses, or on two blocks of seven coin tosses. The fourth, fifth, and sixth tosses all had the same outcome, either three heads or three tails. The seventh toss was grouped with either the end of one block, or the beginning of the next block. Participants exhibited the strongest gambler's fallacy when the seventh trial was part of the first block, directly after the sequence of three heads or tails. The researchers pointed out that the participants that did not show the gambler's fallacy showed less confidence in their bets and bet fewer times than the participants who picked with the gambler's fallacy. When the seventh trial was grouped with the second block, and was perceived as not being part of a streak, the gambler's fallacy did not occur. 

Roney and Trick argued that instead of teaching individuals about the nature of randomness, the fallacy could be avoided by training people to treat each event as if it is a beginning and not a continuation of previous events. They suggested that this would prevent people from gambling when they are losing, in the mistaken hope that their chances of winning are due to increase based on an interaction with previous events.

Users

Studies have found that asylum judges, loan officers, baseball umpires and lotto players employ the gambler's fallacy consistently in their decision-making.

Illusion of control

From Wikipedia, the free encyclopedia

 

The illusion of control is the tendency for people to overestimate their ability to control events; for example, it occurs when someone feels a sense of control over outcomes that they demonstrably do not influence. The effect was named by psychologist Ellen Langer and has been replicated in many different contexts. It is thought to influence gambling behavior and belief in the paranormal. Along with illusory superiority and optimism bias, the illusion of control is one of the positive illusions.

The illusion might arise because people lack direct introspective insight into whether they are in control of events. This has been called the introspection illusion. Instead they may judge their degree of control by a process that is often unreliable. As a result, they see themselves as responsible for events when there is little or no causal link. In one study, college students were in a virtual reality setting to treat a fear of heights using an elevator. Those who were told that they had control, yet had none, felt as though they had as much control as those who actually did have control over the elevator. Those who were led to believe they did not have control said they felt as though they had little control.

Psychological theorists have consistently emphasized the importance of perceptions of control over life events. One of the earliest instances of this is when Adler argued that people strive for proficiency in their lives. Heider later proposed that humans have a strong motive to control their environment and Wyatt Mann hypothesized a basic competence motive that people satisfy by exerting control. Wiener, an attribution theorist, modified his original theory of achievement motivation to include a controllability dimension. Kelley then argued that people's failure to detect noncontingencies may result in their attributing uncontrollable outcomes to personal causes. Nearer to the present, Taylor and Brown argued that positive illusions, including the illusion of control, foster mental health.

The illusion is more common in familiar situations, and in situations where the person knows the desired outcome. Feedback that emphasizes success rather than failure can increase the effect, while feedback that emphasizes failure can decrease or reverse the effect. The illusion is weaker for depressed individuals and is stronger when individuals have an emotional need to control the outcome. The illusion is strengthened by stressful and competitive situations, including financial trading. Although people are likely to overestimate their control when the situations are heavily chance-determined, they also tend to underestimate their control when they actually have it, which runs contrary to some theories of the illusion and its adaptiveness. People also showed a higher illusion of control when they were allowed to become familiar with a task through practice trials, make their choice before the event happens like with throwing dice, and when they can make their choice rather than have it made for them with the same odds. People are more likely to show control when they have more answers right at the beginning than at the end, even when the people had the same number of correct answers.

By proxy

At times, people attempt to gain control by transferring responsibility to more capable or “luckier” others to act for them. By forfeiting direct control, it is perceived to be a valid way of maximizing outcomes. This illusion of control by proxy is a significant theoretical extension of the traditional illusion of control model. People will of course give up control if another person is thought to have more knowledge or skill in areas such as medicine where actual skill and knowledge are involved. In cases like these it is entirely rational to give up responsibility to people such as doctors. However, when it comes to events of pure chance, allowing another to make decisions (or gamble) on one's behalf, because they are seen as luckier is not rational and would go against people's well-documented desire for control in uncontrollable situations. However, it does seem plausible since people generally believe that they can possess luck and employ it to advantage in games of chance, and it is not a far leap that others may also be seen as lucky and able to control uncontrollable events.

In one instance, a lottery pool at a company decides who picks the numbers and buys the tickets based on the wins and losses of each member. The member with the best record becomes the representative until they accumulate a certain number of losses and then a new representative is picked based on wins and losses. Even though no member is truly better than the other and it is all by chance, they still would rather have someone with seemingly more luck to have control over them.

In another real-world example, in the 2002 Olympics men's and women's hockey finals, Team Canada beat Team USA but it was later believed that the win was the result of the luck of a Canadian coin that was secretly placed under the ice before the game. The members of Team Canada were the only people who knew the coin had been placed there. The coin was later put in the Hockey Hall of Fame where there was an opening so people could touch it. People believed they could transfer luck from the coin to themselves by touching it, and thereby change their own luck.

Demonstration

The illusion of control is demonstrated by three converging lines of evidence: 1) laboratory experiments, 2) observed behavior in familiar games of chance such as lotteries, and 3) self-reports of real-world behavior.

One kind of laboratory demonstration involves two lights marked "Score" and "No Score". Subjects have to try to control which one lights up. In one version of this experiment, subjects could press either of two buttons. Another version had one button, which subjects decided on each trial to press or not. Subjects had a variable degree of control over the lights, or none at all, depending on how the buttons were connected. The experimenters made clear that there might be no relation between the subjects' actions and the lights. Subjects estimated how much control they had over the lights. These estimates bore no relation to how much control they actually had, but was related to how often the "Score" light lit up. Even when their choices made no difference at all, subjects confidently reported exerting some control over the lights.

Ellen Langer's research demonstrated that people were more likely to behave as if they could exercise control in a chance situation where "skill cues" were present. By skill cues, Langer meant properties of the situation more normally associated with the exercise of skill, in particular the exercise of choice, competition, familiarity with the stimulus and involvement in decisions. One simple form of this effect is found in casinos: when rolling dice in a craps game people tend to throw harder when they need high numbers and softer for low numbers.

In another experiment, subjects had to predict the outcome of thirty coin tosses. The feedback was rigged so that each subject was right exactly half the time, but the groups differed in where their "hits" occurred. Some were told that their early guesses were accurate. Others were told that their successes were distributed evenly through the thirty trials. Afterwards, they were surveyed about their performance. Subjects with early "hits" overestimated their total successes and had higher expectations of how they would perform on future guessing games. This result resembles the irrational primacy effect in which people give greater weight to information that occurs earlier in a series. Forty percent of the subjects believed their performance on this chance task would improve with practice, and twenty-five percent said that distraction would impair their performance.

Another of Langer's experiments—replicated by other researchers—involves a lottery. Subjects are either given tickets at random or allowed to choose their own. They can then trade their tickets for others with a higher chance of paying out. Subjects who had chosen their own ticket were more reluctant to part with it. Tickets bearing familiar symbols were less likely to be exchanged than others with unfamiliar symbols. Although these lotteries were random, subjects behaved as though their choice of ticket affected the outcome. Participants who chose their own numbers were less likely to trade their ticket even for one in a game with better odds.

Another way to investigate perceptions of control is to ask people about hypothetical situations, for example their likelihood of being involved in a motor vehicle accident. On average, drivers regard accidents as much less likely in "high-control" situations, such as when they are driving, than in "low-control" situations, such as when they are in the passenger seat. They also rate a high-control accident, such as driving into the car in front, as much less likely than a low-control accident such as being hit from behind by another driver.

Explanations

Ellen Langer, who first demonstrated the illusion of control, explained her findings in terms of a confusion between skill and chance situations. She proposed that people base their judgments of control on "skill cues". These are features of a situation that are usually associated with games of skill, such as competitiveness, familiarity and individual choice. When more of these skill cues are present, the illusion is stronger.

Suzanne Thompson and colleagues argued that Langer's explanation was inadequate to explain all the variations in the effect. As an alternative, they proposed that judgments about control are based on a procedure that they called the "control heuristic". This theory proposes that judgments of control to depend on two conditions; an intention to create the outcome, and a relationship between the action and outcome. In games of chance, these two conditions frequently go together. As well as an intention to win, there is an action, such as throwing a die or pulling a lever on a slot machine, which is immediately followed by an outcome. Even though the outcome is selected randomly, the control heuristic would result in the player feeling a degree of control over the outcome.

Self-regulation theory offers another explanation. To the extent that people are driven by internal goals concerned with the exercise of control over their environment, they will seek to reassert control in conditions of chaos, uncertainty or stress. One way of coping with a lack of real control is to falsely attribute oneself control of the situation.

The core self-evaluations (CSE) trait is a stable personality trait composed of locus of control, neuroticism, self-efficacy, and self-esteem. While those with high core self-evaluations are likely to believe that they control their own environment (i.e., internal locus of control), very high levels of CSE may lead to the illusion of control.

Benefits and costs to the individual

Taylor and Brown have argued that positive illusions, including the illusion of control, are adaptive as they motivate people to persist at tasks when they might otherwise give up. This position is supported by Albert Bandura's claim that "optimistic self-appraisals of capability, that are not unduly disparate from what is possible, can be advantageous, whereas veridical judgements can be self-limiting". His argument is essentially concerned with the adaptive effect of optimistic beliefs about control and performance in circumstances where control is possible, rather than perceived control in circumstances where outcomes do not depend on an individual's behavior.

Bandura has also suggested that:

"In activities where the margins of error are narrow and missteps can produce costly or injurious consequences, personal well-being is best served by highly accurate efficacy appraisal."

Taylor and Brown argue that positive illusions are adaptive, since there is evidence that they are more common in normally mentally healthy individuals than in depressed individuals. However, Pacini, Muir and Epstein have shown that this may be because depressed people overcompensate for a tendency toward maladaptive intuitive processing by exercising excessive rational control in trivial situations, and note that the difference with non-depressed people disappears in more consequential circumstances.

There is also empirical evidence that high self-efficacy can be maladaptive in some circumstances. In a scenario-based study, Whyte et al. showed that participants in whom they had induced high self-efficacy were significantly more likely to escalate commitment to a failing course of action. Knee and Zuckerman have challenged the definition of mental health used by Taylor and Brown and argue that lack of illusions is associated with a non-defensive personality oriented towards growth and learning and with low ego involvement in outcomes. They present evidence that self-determined individuals are less prone to these illusions. In the late 1970s, Abramson and Alloy demonstrated that depressed individuals held a more accurate view than their non-depressed counterparts in a test which measured illusion of control. This finding held true even when the depression was manipulated experimentally. However, when replicating the findings Msetfi et al. (2005, 2007) found that the overestimation of control in nondepressed people only showed up when the interval was long enough, implying that this is because they take more aspects of a situation into account than their depressed counterparts. Also, Dykman et al. (1989) showed that depressed people believe they have no control in situations where they actually do, so their perception is not more accurate overall. Allan et al. (2007) has proposed that the pessimistic bias of depressives resulted in "depressive realism" when asked about estimation of control, because depressed individuals are more likely to say no even if they have control.

A number of studies have found a link between a sense of control and health, especially in older people.

Fenton-O'Creevy et al. argue, as do Gollwittzer and Kinney, that while illusory beliefs about control may promote goal striving, they are not conducive to sound decision-making. Illusions of control may cause insensitivity to feedback, impede learning and predispose toward greater objective risk taking (since subjective risk will be reduced by illusion of control).

Applications

Psychologist Daniel Wegner argues that an illusion of control over external events underlies belief in psychokinesis, a supposed paranormal ability to move objects directly using the mind. As evidence, Wegner cites a series of experiments on magical thinking in which subjects were induced to think they had influenced external events. In one experiment, subjects watched a basketball player taking a series of free throws. When they were instructed to visualise him making his shots, they felt that they had contributed to his success.

One study examined traders working in the City of London's investment banks. They each watched a graph being plotted on a computer screen, similar to a real-time graph of a stock price or index. Using three computer keys, they had to raise the value as high as possible. They were warned that the value showed random variations, but that the keys might have some effect. In fact, the fluctuations were not affected by the keys. The traders' ratings of their success measured their susceptibility to the illusion of control. This score was then compared with each trader's performance. Those who were more prone to the illusion scored significantly lower on analysis, risk management and contribution to profits. They also earned significantly less.

Placebo

From Wikipedia, the free encyclopedia

 

Placebos are typically inert tablets, such as sugar pills

 

A placebo (/pləˈsiːboʊ/ plə-SEE-boh) is an inert substance or treatment which is designed to have no therapeutic value. Common placebos include inert tablets (like sugar pills), inert injections (like saline), sham surgery, and other procedures.

In general, placebos can affect how patients perceive their condition and encourage the body's chemical processes for relieving pain and a few other symptoms, but have no impact on the disease itself. Improvements that patients experience after being treated with a placebo can also be due to unrelated factors, such as regression to the mean (a natural recovery from the illness). The use of placebos as treatment in clinical medicine raises ethical concerns, as it introduces dishonesty into the doctor–patient relationship.

In drug testing and medical research, a placebo can be made to resemble an active medication or therapy so that it functions as a control; this is to prevent the recipient or others from knowing (with their consent) whether a treatment is active or inactive, as expectations about efficacy can influence results. In a clinical trial any change in the placebo arm is known as the placebo response, and the difference between this and the result of no treatment is the placebo effect.

The idea of a placebo effect—a therapeutic outcome derived from an inert treatment—was discussed in 18th century psychology but became more prominent in the 20th century. An influential 1955 study entitled The Powerful Placebo firmly established the idea that placebo effects were clinically important, and were a result of the brain's role in physical health. A 1997 reassessment found no evidence of any placebo effect in the source data, as the study had not accounted for regression to the mean.

Definitions

The word "placebo", Latin for "I will please", dates back to a Latin translation of the Bible by St Jerome.

The American Society of Pain Management Nursing define a placebo as "any sham medication or procedure designed to be void of any known therapeutic value".

In a clinical trial, a placebo response is the measured response of subjects to a placebo; the placebo effect is the difference between that response and no treatment. It is also part of the recorded response to any active medical intervention.

Any measurable placebo effect is termed either objective (e.g. lowered blood pressure) or subjective (e.g. a lowered perception of pain).

Effects

Placebos can improve patient-reported outcomes such as pain and nausea. This effect is unpredictable and hard to measure, even in the best conducted trials. For example, if used to treat insomnia, placebos can cause patients to perceive that they are sleeping better, but do not improve objective measurements of sleep onset latency. A 2001 Cochrane Collaboration meta-analysis of the placebo effect looked at trials in 40 different medical conditions, and concluded the only one where it had been shown to have a significant effect was for pain.

By contrast, placebos do not appear to affect the actual diseases, or outcomes that are not dependent on a patient's perception. One exception to the latter is Parkinson's disease, where recent research has linked placebo interventions to improved motor functions.

Measuring the extent of the placebo effect is difficult due to confounding factors. For example, a patient may feel better after taking a placebo due to regression to the mean (i.e. a natural recovery or change in symptoms). It is harder still to tell the difference between the placebo effect and the effects of response bias, observer bias and other flaws in trial methodology, as a trial comparing placebo treatment and no treatment will not be a blinded experiment. In their 2010 meta-analysis of the placebo effect, Asbjørn Hróbjartsson and Peter C. Gøtzsche argue that "even if there were no true effect of placebo, one would expect to record differences between placebo and no-treatment groups due to bias associated with lack of blinding."

Hróbjartsson and Gøtzsche concluded that their study "did not find that placebo interventions have important clinical effects in general." Jeremy Howick has argued that combining so many varied studies to produce a single average might obscure that "some placebos for some things could be quite effective." To demonstrate this, he participated in a systematic review comparing active treatments and placebos using a similar method, which generated a clearly misleading conclusion that there is "no difference between treatment and placebo effects".

Factors influencing the power of the placebo effect

Louis Lasagna helped make placebo-controlled trials a standard practice in the U.S.. He also believed "warmth, sympathy, and understanding" had therapeutic benefits.

 

A review published in JAMA Psychiatry found that, in trials of antipsychotic medications, the change in response to receiving a placebo had increased significantly between 1960 and 2013. The review's authors identified several factors that could be responsible for this change, including inflation of baseline scores and enrollment of fewer severely ill patients. Another analysis published in Pain in 2015 found that placebo responses had increased considerably in neuropathic pain clinical trials conducted in the United States from 1990 to 2013. The researchers suggested that this may be because such trials have "increased in study size and length" during this time period.

Children seem to have greater response than adults to placebos.

Some studies have investigated the use of placebos where the patient is fully aware that the treatment is inert, known as an open-label placebo. A May 2017 meta-analysis found some evidence that open-label placebos have positive effects in comparison to no treatment, but said the result should be treated with "caution" and that further trials were needed.

Symptoms and conditions

A 2010 Cochrane Collaboration review suggests that placebo effects are apparent only in subjective, continuous measures, and in the treatment of pain and related conditions.

Pain

Placebos are believed to be capable of altering a person's perception of pain. "A person might reinterpret a sharp pain as uncomfortable tingling."

One way in which the magnitude of placebo analgesia can be measured is by conducting "open/hidden" studies, in which some patients receive an analgesic and are informed that they will be receiving it (open), while others are administered the same drug without their knowledge (hidden). Such studies have found that analgesics are considerably more effective when the patient knows they are receiving them.

Depression

In 2008, a controversial meta-analysis led by psychologist Irving Kirsch, analyzing data from the FDA, concluded that 82% of the response to antidepressants was accounted for by placebos. However, there are serious doubts about the used methods and the interpretation of the results, especially the use of 0.5 as cut-off point for the effect-size. A complete reanalysis and recalculation based on the same FDA data discovered that the Kirsch study suffered from "important flaws in the calculations". The authors concluded that although a large percentage of the placebo response was due to expectancy, this was not true for the active drug. Besides confirming drug effectiveness, they found that the drug effect was not related to depression severity.

Another meta-analysis found that 79% of depressed patients receiving placebo remained well (for 12 weeks after an initial 6–8 weeks of successful therapy) compared to 93% of those receiving antidepressants. In the continuation phase however, patients on placebo relapsed significantly more often than patients on antidepressants.

Negative effects

A phenomenon opposite to the placebo effect has also been observed. When an inactive substance or treatment is administered to a recipient who has an expectation of it having a negative impact, this intervention is known as a nocebo (Latin nocebo = "I shall harm"). A nocebo effect occurs when the recipient of an inert substance reports a negative effect or a worsening of symptoms, with the outcome resulting not from the substance itself, but from negative expectations about the treatment.

Another negative consequence is that placebos can cause side-effects associated with real treatment.

Withdrawal symptoms can also occur after placebo treatment. This was found, for example, after the discontinuation of the Women's Health Initiative study of hormone replacement therapy for menopause. Women had been on placebo for an average of 5.7 years. Moderate or severe withdrawal symptoms were reported by 4.8% of those on placebo compared to 21.3% of those on hormone replacement.

Ethics

In research trials

Knowingly giving a person a placebo when there is an effective treatment available is a bioethically complex issue. While placebo-controlled trials might provide information about the effectiveness of a treatment, it denies some patients what could be the best available (if unproven) treatment. Informed consent is usually required for a study to be considered ethical, including the disclosure that some test subjects will receive placebo treatments.

The ethics of placebo-controlled studies have been debated in the revision process of the Declaration of Helsinki. Of particular concern has been the difference between trials comparing inert placebos with experimental treatments, versus comparing the best available treatment with an experimental treatment; and differences between trials in the sponsor's developed countries versus the trial's targeted developing countries.

Some suggest that existing medical treatments should be used instead of placebos, to avoid having some patients not receive medicine during the trial.

In medical practice

The practice of doctors prescribing placebos that are disguised as real medication is controversial. A chief concern is that it is deceptive and could harm the doctor–patient relationship in the long run. While some say that blanket consent, or the general consent to unspecified treatment given by patients beforehand, is ethical, others argue that patients should always obtain specific information about the name of the drug they are receiving, its side effects, and other treatment options. This view is shared by some on the grounds of patient autonomy. There are also concerns that legitimate doctors and pharmacists could open themselves up to charges of fraud or malpractice by using a placebo. Critics also argued that using placebos can delay the proper diagnosis and treatment of serious medical conditions.

About 25% of physicians in both the Danish and Israeli studies used placebos as a diagnostic tool to determine if a patient's symptoms were real, or if the patient was malingering. Both the critics and the defenders of the medical use of placebos agreed that this was unethical. The British Medical Journal editorial said, "That a patient gets pain relief from a placebo does not imply that the pain is not real or organic in origin ...the use of the placebo for 'diagnosis' of whether or not pain is real is misguided." A survey in the United States of more than 10,000 physicians came to the result that while 24% of physicians would prescribe a treatment that is a placebo simply because the patient wanted treatment, 58% would not, and for the remaining 18%, it would depend on the circumstances.

Referring specifically to homeopathy, the House of Commons of the United Kingdom Science and Technology Committee has stated:

In the Committee's view, homeopathy is a placebo treatment and the Government should have a policy on prescribing placebos. The Government is reluctant to address the appropriateness and ethics of prescribing placebos to patients, which usually relies on some degree of patient deception. Prescribing of placebos is not consistent with informed patient choice—which the Government claims is very important—as it means patients do not have all the information needed to make choice meaningful. A further issue is that the placebo effect is unreliable and unpredictable.

In his 2008 book Bad Science, Ben Goldacre argues that instead of deceiving patients with placebos, doctors should use the placebo effect to enhance effective medicines. Edzard Ernst has argued similarly that "As a good doctor you should be able to transmit a placebo effect through the compassion you show your patients." In an opinion piece about homeopathy, Ernst argued that it is wrong to approve an ineffective treatment on the basis that it can make patients feel better through the placebo effect. His concerns are that it is deceitful and that the placebo effect is unreliable. Goldacre also concludes that the placebo effect does not justify the use of alternative medicine.

Mechanisms

Expectation plays a clear role. A placebo presented as a stimulant may trigger an effect on heart rhythm and blood pressure, but when administered as a depressant, the opposite effect.

Psychology

The "placebo effect" may be related to expectations

 

In psychology, the two main hypotheses of placebo effect are expectancy theory and classical conditioning.

In 1985, Irving Kirsch hypothesized that placebo effects are produced by the self-fulfilling effects of response expectancies, in which the belief that one will feel different leads a person to actually feel different. According to this theory, the belief that one has received an active treatment can produce the subjective changes thought to be produced by the real treatment. Placebos can act similarly through classical conditioning, wherein a placebo and an actual stimulus are used simultaneously until the placebo is associated with the effect from the actual stimulus. Both conditioning and expectations play a role in placebo effect, and make different kinds of contribution. Conditioning has a longer-lasting effect, and can affect earlier stages of information processing. Those who think a treatment will work display a stronger placebo effect than those who do not, as evidenced by a study of acupuncture.

Additionally, motivation may contribute to the placebo effect. The active goals of an individual changes their somatic experience by altering the detection and interpretation of expectation-congruent symptoms, and by changing the behavioral strategies a person pursues. Motivation may link to the meaning through which people experience illness and treatment. Such meaning is derived from the culture in which they live and which informs them about the nature of illness and how it responds to treatment.

Placebo analgesia

Functional imaging upon placebo analgesia suggests links to the activation, and increased functional correlation between this activation, in the anterior cingulate, prefrontal, orbitofrontal and insular cortices, nucleus accumbens, amygdala, the brainstem periaqueductal gray matter, and the spinal cord.

It has been known that placebo analgesia depends upon the release in the brain of endogenous opioids since 1978. Such analgesic placebos activation changes processing lower down in the brain by enhancing the descending inhibition through the periaqueductal gray on spinal nociceptive reflexes, while the expectations of anti-analgesic nocebos acts in the opposite way to block this.

Functional imaging upon placebo analgesia has been summarized as showing that the placebo response is "mediated by "top-down" processes dependent on frontal cortical areas that generate and maintain cognitive expectancies. Dopaminergic reward pathways may underlie these expectancies". "Diseases lacking major 'top-down' or cortically based regulation may be less prone to placebo-related improvement".

Brain and body

In conditioning, a neutral stimulus saccharin is paired in a drink with an agent that produces an unconditioned response. For example, that agent might be cyclophosphamide, which causes immunosuppression. After learning this pairing, the taste of saccharin by itself is able to cause immunosuppression, as a new conditioned response via neural top-down control. Such conditioning has been found to affect a diverse variety of not just basic physiological processes in the immune system but ones such as serum iron levels, oxidative DNA damage levels, and insulin secretion. Recent reviews have argued that the placebo effect is due to top-down control by the brain for immunity and pain. Pacheco-López and colleagues have raised the possibility of "neocortical-sympathetic-immune axis providing neuroanatomical substrates that might explain the link between placebo/conditioned and placebo/expectation responses." There has also been research aiming to understand underlying neurobiological mechanisms of action in pain relief, immunosuppression, Parkinson's disease and depression.

Dopaminergic pathways have been implicated in the placebo response in pain and depression.

Confounding factors

Placebo-controlled studies, as well as studies of the placebo effect itself, often fail to adequately identify confounding factors. False impressions of placebo effects are caused by many factors including:

• Regression to the mean (natural recovery or fluctuation of symptoms)
• Additional treatments
• Response bias from subjects, including scaling bias, answers of politeness, experimental subordination, conditioned answers;
• Reporting bias from experimenters, including misjudgment and irrelevant response variables.
• Non-inert ingredients of the placebo medication having an unintended physical effect

History

A quack treating a patient with Perkins Patent Tractors by James Gillray, 1801. John Haygarth used this remedy to illustrate the power of the placebo effect.

 

The word placebo was used in a medicinal context in the late 18th century to describe a "commonplace method or medicine" and in 1811 it was defined as "any medicine adapted more to please than to benefit the patient". Although this definition contained a derogatory implication it did not necessarily imply that the remedy had no effect.

Placebos have featured in medical use until well into the twentieth century. In 1955 Henry K. Beecher published an influential paper entitled The Powerful Placebo which proposed idea that placebo effects were clinically important. Subsequent re-analysis of his materials, however, found in them no evidence of any "placebo effect".

Placebo-controlled studies

The placebo effect makes it more difficult to evaluate new treatments. Clinical trials control for this effect by including a group of subjects that receives a sham treatment. The subjects in such trials are blinded as to whether they receive the treatment or a placebo. If a person is given a placebo under one name, and they respond, they will respond in the same way on a later occasion to that placebo under that name but not if under another.

Clinical trials are often double-blinded so that the researchers also do not know which test subjects are receiving the active or placebo treatment. The placebo effect in such clinical trials is weaker than in normal therapy since the subjects are not sure whether the treatment they are receiving is active.