Ignoring Statistical Principles in Inductive Heuristics-Preliminary Version of Planned Journal Article!!

Ignoring statistics (particularly probability) in heuristic inductive thinking-

Dr. Munish Alagh, PDF-IIM(A).

Inductive Thinking involves, generalising from the particular to the general.

Heuristics, involve cognitive short-cuts to make a decision easily.

Heuristics people use in inductive reasoning tasks often do not respect the required statistical principles. People consequently overlook statistical variables such as sample size, correlation, and base rate when they solve inductive reasoning problems[1]

Statistical Problems and Nonstatistical Heuristics

As we have seen, people often solve inductive problems by use of a variety of intuitive heuristics—rapid and more or less automatic judgmental rules of thumb. These include the representativeness heuristic (Kahneman & Tversky, 1972, 1973), the availability heuristic (Tversky & Kahneman, 1973), and the anchoring heuristic (Tversky & Kahneman, 1974). In problems where these heuristics diverge from the correct statistical approach, people commit serious errors of inference. The following heuristics, the biases they lead to and the statistical principles that are ignored therein are discussed[2] :

Ø      Representativeness.

Ø      Adjustment and Anchoring.

Ø      Availability.

Representativeness:

According to Kahneman and Tversky (1974) there are three types of probabilistic questions with which people are concerned.

What is the probability that object A belongs to class B?

What is the probability that event A originates from process B?

What is the probability that process B will generate event A?

People answer such questions by relying on the representativeness heuristic according to which probabilities are evaluated by the degree to which A is representative of B, that is, by the degree to which A resembles B. For example, when A is highly representative of  B, the probability that A originates from B is judged to be high. On the other hand, if A is not similar to B, the probability that A originates from B is judged to be low.

There is  a type of research on problems of a particular type which has shown that people order the occupations by probability and by similarity in exactly the same way.^[3] They consider that a person, Steve, whose probability that he is a librarian, for example, is assessed by the degree to which he is representative of, or similar to, the stereotype of a librarian. This is known as the representativeness heuristic.

Infact people who are asked to assess probability are not stumped, because they do not try to judge probability as statisticians and philosophers use the word. A question about probability or likelihood activates a mental shotgun, evoking answers to easier questions. Judging probability by representativeness has important virtues: the intuitive impressions that it produces are often-indeed, usually-more accurate than chance guesses would be.^[4]

This approach to the judgement of probability however leads to serious errors, because similarity, or representativeness, is not influenced by several factors that should affect judgments of probability:

Insensitivity to prior probability of outcomes: 

One of the factors that have no effect on representativeness but should have a major effect on probability is the prior probability, or base-rate frequency, of the outcomes. In case of Steve, for example, the fact that there are many more farmers than librarians in the population should enter into any reasonable estimate of the probability that Steve is a librarian rather than a farmer. Considerations of base-rate frequency, however, do not affect the similarity if people evaluate probability by representativeness, therefore, prior probabilities will be neglected. Certain differing prior probabilities were given for two professions to subjects, in two different cases, also the personality description of several individuals, allegedly sampled at random from a group of 100 professionals, including both the occupations were given. The subjects were asked to assess, for each description, the probability that it belonged to one of the occupations. The odds that any particular description belongs to any one of the professions should be higher when the prior probability of that particular occupation is more. However subjects in the two conditions produced essentially the same probability judgements. Apparently, subjects evaluated the likelihood that a particular description belonged to a particular occupation, from the two, by the degree to which the description was representative of the two stereotypes, with little or no regard for the prior probabilities of the categories.

The subjects used prior probabilities correctly when they had no other information. However, prior probabilities were effectively ignored when a description was introduced, even when this description was totally uninformative. Evidently, people respond differently when given no evidence and when given worthless evidence. When no specific evidence is given, prior probabilities are ignored.^[5]

Nisbett and Borgida (1975),quoted in The reference stated above[6] showed that consensus information, that is, base rate information about the behaviour of a sample of people in a given situation, often has little effect on subjects attributions about the causes of a particular target individual's behavior. When told that most people behaved in the same way as the target, subjects shift little or not at all in the direction of assuming that it was situational forces, rather than the target's personal dispositions or traits, that explain the target's behavior.

It is noticed that subjects use prior probabilities correctly when they have no other information. However, prior probabilities are effectively ignored when a description is introduced, even when this description is totally uninformative. Evidently, people respond differently when given no evidence and when given worthless evidence. When no specific evidence is given, prior probabilities are ignored.^[7]

Insensitivity to sample size:

To evaluate the probability of obtaining a particular result in a sample drawn from a specified population, people typically apply the representativeness heuristic. That is, they assess the likelihood of a sample result by the similarity of this result to the corresponding parameter The similarity of a sample statistic to a population parameter does not depend on the size of the sample. Consequently, if probabilities are assessed by representativeness, then the judged probability of a sample statistic will be essentially independent of sample size. Indeed, when subjects assessed the distributions of the sample results for samples of various sizes, they produced identical distributions . A similar insensitivity to sample size has been reported in judgments of posterior probability, that is, of the probability that a sample has been drawn from one population rather than from another. Here again, intuitive judgments are dominated by the sample proportion and are essentially unaffected by the size of the sample, which plays a crucial role in the determination of the actual posterior odds ^[8]. In addition, intuitive estimates of posterior odds are far less extreme than the correct values. The underestimation of the impact of evidence has been observed repeatedly in problems of this type.^[9] It has been labeled "conservatism."

Misconceptions of chance:

People expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short. Thus, people expect that the essential characteristics of the process will be represented, not only globally in the entire sequence, but also locally in each of its parts. A locally representative sequence, how-ever, deviates systematically from chance expectation: it contains too many alternations and too few runs. Another consequence of the belief in local representativeness is the well-known gambler's fallacy. Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not "corrected" as a chance process unfolds, they are merely diluted. Misconceptions of chance are not limited to naive subjects. A study of the statistical intuitions of experienced research psychologists^[10] revealed a lingering belief in what may be called the "law of small numbers," according to which even small samples are highly representative of the populations from which they are drawn. The responses of these investigators reflected the expectation that a valid hypothesis about a population will be represented by a statistically significant result in a sample with little regard for its size. As a consequence, the researchers put too much faith in the results of small samples and grossly overestimated the replicability of such results. In the actual conduct of research, this bias leads to the selection of samples of inadequate size and to overinterpretation of findings.

Insensitivity to predictability: People are sometimes called upon to make such numerical predictions as the future value of a stock, the demand for a commodity, or the outcome of a football game. Such predictions are often made by representativeness. The degree to which the description is favorable is unaffected by the reliability of that description or by the degree to which it permits accurate prediction. Hence, if people predict solely in terms of the favorableness of the description, their predictions will be insensitive to the reliability of the evidence and to the expected accuracy of the prediction demonstrated that intuitive predictions violate this rule, and that subjects show little or no regard for considerations of predictability ^[11]

That is, the prediction of a remote criterion was identical to the evaluation of the information on which the prediction was based The students who made these predictions were undoubtedly aware of the limited predictability never-theless, their predictions were as ex-treme as their evaluations.

This mode of judgment violates the normative statistical theory in which the extremeness and the range of predictions are controlled by considerations of predictability. When predictability is nil, the same prediction should be made in all cases If predictability is perfect, of course, the values predicted will match the actual values and the range of predic-tions will equal the range of outcomes. In general, the higher the predictability, the wider the range of predicted values. Several studies of numerical prediction have

The illusion of validity:

As we have seen, people often predict by selecting the outcome (for example, an occupation) that is most representative of the input (for example, the description of a person). The confidence they have in their prediction depends primarily on the degree of representativeness (that is, on the quality of the match between the selected outcome and the input) with little or no regard for the factors that limit predictive accuracy The unwarranted confidence which is produced by a good fit between the predicted outcome and the input information may be called the illusion of validity. This illusion persists even when the judge is aware of the factors that limit the accuracy of his predictions.

The internal consistency of a pattern of inputs is a major determinant of one's confidence in predictions based on these inputs Highly consistent patterns are most often observed when the input variables are highly redundant or correlated. Hence, people tend to have great con-fidence in predictions based on redundant input variables. However, an elementary result in the statistics of correlation asserts that, given input variables of stated validity, a prediction based on several such inputs can achieve higher accuracy when they are independent of each other than when they are redundant or correlated. Thus, redundancy among inputs decreases accuracy even as it increases confidence, and people are often confident in predictions that are quite likely to be off the mark^[12]

Regression to the mean:

 Regression to the mean- involves moving closer to the average than the earlier value of the variable observed. Also regression to the mean has an explanation, but does not have a cause.^[13]

An important principle of skill training: rewards for improved performance work better than punishment of mistakes. This proposition is supported by much evidence from research.

Regression to the mean, involves that poor performance is typically followed by improvement and good performance by deterioration, without any help from either praise or punishment.

The feedback to which life exposes us is perverse. Because we tend to be nice to other people when they please us and nasty when they do not, we are statistically punished for being nice and rewarded for being nasty.

Regression does not have a causal explanation. Regression effects are ubiquitous, and so are misguided casual stories to explain them. The point to remember is that the change from the first to the second occurrence does not need a causal explanation. It is a mathematically inevitable consequence of the fact that luck played a role in the outcome of the first occurence.

Regression inevitably occurs when the correlation between two measures is less than perfect.

The correlation coefficient between two measures, which varies between 0 and 1, is a measure of the relative weight of the factors they share.

Correlation and regression are not two concepts-they are different perspectives on the same concept. The general rule is straightforward but has surprising consequences: whenever the correlation between two scores is imperfect, there will be regression to the mean.

Our mind is strongly biased toward causal explanations and does not deal well with “mere statistics.” When our attention is called to an event, associative memory will look for its cause, more precisely, activation will automatically spread to any cause that is already stored in memory. Causal explanations will be evoked when regression is detected, but they will be wrong because the truth is that regression to the mean has an explanation but does not have a cause.

Regression effects are a common source of trouble in research, and experienced scientists develop a healthy fear of the trap of unwarranted causal inference.

Statistics can be used, but is often not used in intuitive thinking:

Even when judgments are based on the representativeness heuristic, there may be an underlying stratum of probabilistic thinking. In many of the problems studied by Kahneman and Tversky, people probably conceive of the underlying process as random, but they lack a means of making use of their intuitions about randomness and they fall back on representativeness.

Adjustment and Anchoring:

Biases in the evaluation of compound events are particularly significant in the context of planning. The successful completion of an undertaking, such as the development of a new product, typically has a conjunctive character: for the undertaking to succeed, each of a series of events must occur. Even when each of these events is very likely, the overall probability of success can be quite low if the number of events is large. The general tendency to overestimate the probability of conjunctive events leads to unwarranted optimism in the evaluation of the likelihood that a plan will succeed or that a project will be completed on time. Conversely, disjunctive structures are typically encountered in the evaluation of risks. A complex system, such as a nuclear reactor or a human body, will malfunction if any of its essential components fails. Even when the likelihood of failure in each component is slight, the probability of an overall failure can be high if many components are involved. Because of anchoring, people will tend to underestimate the probabilities of failure in complex systems.

The subjects state overly narrow confidence intervals which reflect more certainty than is justified by their knowledge about the assessed quantities.

Anchoring in the assessment of subjective probability distributions.: the subjects state overly narrow confidence intervals which reflect more certainty than is justified by their knowledge about the assessed quantities

it is natural to begin by thinking about one's best estimate of the parameter and to adjust this value upward. If this adjustment like most others is insufficient, then the upper value of the distribution will not be sufficiently extreme. A similar anchoring effect will occur in the selection of the lower value of the distribution, which is presumably obtained by adjusting one's best estimate downward. Consequently, the confidence interval between the lower and upper values of the distribution will be too narrow, and the assessed probability distribution will be too tight.

Availability:

Availability which is discussed above, is affected by various factors which are not related to actual frequency. If the availability heuristic is applied, then such factors will affect the perceived frequency of classes and the subjective probability of events. Consequently, not only does the use of the availability heuristic leads to systematic biases, there are also effects on the statistical picture which is pictured by us as a result.

“Errors” in probabilistic reasoning are in fact not violations of probability

Most so-called “errors” in probabilistic reasoning are in fact not violations of probability theory. Examples of such “errors” include overconfidence bias, conjunction fallacy, and base-rate neglect.[14]

Over-confidence bias-systematic discrepancy between confidence and relative frequency is termed “overconfidence.”

Has probability theory been violated if one’s degree of belief (confidence) in a single event (i.e., that a particular answer is correct) is different from the relative frequency of correct answers one generates in the long run? The answer is “no.” It is in fact not a violation according to several interpretations of probability. According to the frequentists, probability theory is about frequencies, not about single events. To compare the two means comparing apples with oranges. According to subjectivists a discrepancy between confidence and relative frequency is not a “bias,” albeit for diff erent reasons. For a subjectivist, probability is about single events, but rationality is identified with the internal consistency of subjective probabilities. So, in conclusion, a discrepancy between confidence in single events and relative frequencies in the long run is not an error or a violation of probability theory from many experts’ points of view. It only looks so from a narrow interpretation of probability that blurs the distinction between single events and frequencies fundamental to probability theory. [15]

Conjunction fallacy-

The original demonstration of the “Conjunction fallacy” was with problems involving matching a description of a lady, with a) her profession and b) her profession and an activity she was involved in. Subjects were asked which of two alternatives was more probable. Tversky and Kahneman, however, argued that the “correct” answer is a), because the probability of a conjunction of two events, such as b), can never be greater than that of one of its constituents. They explained this “fallacy” as induced by the representativeness heuristic. They assumed that judgments were based on the match (similarity, representativeness) between the description of the lady and the

two alternatives. That is, since the lady was described based on her activity and b)

contains her activity people believe that b)is more probable.

Is the “conjunction fallacy” a violation of probability theory, as has been claimed in the literature? Has a person who chooses b) as the more probable alternative violated probability theory? Again, the answer is “no.” Choosing b) is not a violation of probability theory, and for the same reason given above. For a frequentist, this problem has nothing to do with probability theory. Subjects are asked for the probability of a single event (that the lady has a particular profession), not for frequencies. Note that problems which are claimed to demonstrate the “conjunction fallacy” are structurally slightly different from “confidence” problems. In the former, subjective probabilities ( a) or b)) are compared with one another; in the latter, they are compared with frequencies. To summarize the normative issue, what is called the “conjunction fallacy” is a violation of some subjective theories of probability. It is not, however, a violation of the major view of probability, the frequentist conception.[16]

The base-rate fallacy

The example is from Casscells, Schoenberger, and Grayboys (1978, p. 999) and presented by Tversky and Kahneman (1982, p. 154) to demonstrate the generality of the phenomenon:

If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?

Sixty students and staff at Harvard Medical School answered this medical diagnosis problem. Almost half of them judged the probability that the person actually had the disease to be 0.95 (modal answer), the average answer was 0.56, and only 18% of participants responded 0.02. The latter is what the authors believed to be the correct answer. Note the enormous variability in judgments.

Little has been achieved in explaining how people make these judgments and why the judgments are so strikingly variable.

But do statistics and probability give one and only one “correct” answer to that problem?

The answer is again “no.” And for the same reason, as the reader will already guess. As in the case of confidence and conjunction judgments, subjects were asked for the probability of a single event, that is, that

“a person found to have a positive result actually has the disease.” If the mind is an intuitive statistician of the frequentist school, such a question has no necessary connection to probability theory.

A more serious difficulty is that the problem does not specify whether or not the person was randomly drawn from the population to which the base rate refers.[17]

Discussion :

Statistical principles are not learned from everyday experience because the relevant in-stances are not coded appropriately.

The lack of an appropriate code also explains why people usually do not detect the biases in their judgments of probability.

The inherently subjective nature of probability has led many students to the belief that coherence, or internal consistency, is the only valid criterion by which judged probabilities should be evaluated. From the standpoint of the formal theory of subjective probability, any set of internally consistent probability judgments is as good as any other. This criterion is not entirely satisfactory, because an internally consistent set of subjective probabilities can be incompatible with other beliefs held by the individual. Consider a person whose subjective probabilities for all possible outcomes of a coin-tossing game reflect the gambler's fallacy. That is, his estimate of the probability of tails on a particular toss increases with the number of consecutive heads that preceded that toss. The judgments of such a person could be internally consistent and therefore acceptable as adequate subjective probabilities according to the criterion of the formal theory. These probabilities, however, are incompatible with the generally held belief that a coin has no memory and is therefore incapable of generating sequential dependencies. For judged probabilities to be considered adequate, or rational, in-ternal consistency is not enough. The judgments must be compatible with the entire web of beliefs held by the individual. Unfortunately, there can be no simple formal procedure for assessing the compatibility of a set of probability judgments with the judge's total system of beliefs.

---

[1] Nisbett, Richard E., Krantz, David H., Jepson, Christopher. And Kunda, Z.(1983, p. 339)

[2] Nisbett, Richard E., Krantz, David H., Jepson, Christopher. And Kunda, Z.(1983, p. 340)

[3]Amos Tversky and Daniel Kahneman, “On the Psychology of Prediction,” (1973).

[4]  Daniel Kahneman, Thinking, Fast and Slow  (2011).

[5] Tversky and Kahneman (1973)

[6] Nisbett, Richard E., Krantz, David H., Jepson, Christopher. And Kunda, Z.(1983, p. 341)

[7] Tversky and Kahneman, “On the Psychology of Prediction.” (1973)

[8] D Kahneman and A Tversky, “Subjective Probability: A Judgment of Representativeness,” Cognitive Psychology 3(1972);430-54

[9] W Edwards,Conservatism in Human Information Processing, 1968

[10] Kahneman and Tversky,1972.

[11] Kahneman and Tversky,On the Psychology of Prediction, 1973

[12] Ibid.

[13] Kahneman, 2011-chapter 17

[14] Gigerenzer Gerd (1991,p.83)

[15] Gigerenzer Gerd (1991,p.88)

[16] Gigerenzer Gerd (1991,p.91)

[17] Gigerenzer Gerd (1991,p.92)

A new book by a noble-winning economist-a detailed,comprehensive and expanded summary of the section on heuristics and biases approach

Heuristics and Biases

Many decisions are based on beliefs concerning the likelihood of uncertain events.

Occasionally, beliefs concerning uncertain events are expressed in numerical form as odds or subjective probabilities. The subjective assessment of probability involve judgements based on data of limited validity, which are processed according to heuristic rules. However, the reliance on this rule leads to systematic errors. Such biases are also found in the intuitive judgement of probability. Kahneman and Tversky[1]describe  heuristics that are employed to assess probabilities and to predict values. Biases to which these heuristics lead are enumerated, and the applied and theoretical implications of these observations are discussed.

Ø      Law of Small Numbers.

Ø      Anchors.

Ø      Availability.

Ø      Affect Heuristic.

Ø      Representativeness.

Ø      Conjuctive fallacy.

Ø      Stereotyping.

Ø      Regression to the mean.

Ø      Substitution.

Kahneman[2] starts with the notion that our minds contain two interactive modes of

thinking:

One part of our mind (which he calls System 1) operates automatically and quickly, with little or no effort and no sense of voluntary control.

The other part of our mind (which he calls System 2) allocates attention to the effortful mental activities that demand it, including complex computations. The operations of System 2 are often associated with the subjective experience of agency, choice, and concentration.[3]

In other words, System 1 is unconscious, intuitive thought (automatic pilot), while slower System 2 is conscious, rational thinking (effortful system).

When we are awake, most of our actions are controlled automatically by System 1. The

mind cannot consciously perform the thousands of complex tasks per day that human functioning requires. System 2 is normally in a low-effort mode. System 2 activates when System 1 cannot deal with a task–when more detailed processing is needed; only System 2 can construct thoughts in a step-by-step fashion. In addition, it continuously monitors human behavior. The interactions of Systems 1 and 2 are usually highly efficient. However, System 1 is prone to biases and errors, and System 2 is often lazy.

System 2 requires effort and acts of self-control in which the intuitions and impulses of System 1 are overcome. Attention and Effort requires the lazy system 2 to act.[4]

System 2 is by its nature lazy.[5]

System 1 works in a process called associative activation: ideas that have been evoked trigger connected coherent ideas.[6]

System 2 is required when cognitive strain comes up due to unmet demands of the situation which require the system 2 to focus.[7]

Our system 1 develops our image of what is normal and associative ideas are formed which represent the structure of events in our life and represent the structure of events in our life and interpretation of the present as well as expectation of the future.[8]

System 1 is a kind of machine which jumps to conclusions, which can lead to intuitive errors, which may be prevented by a deliberate intervention of System 2.[9]

System 1 forms basic assesments by continuously monitoring what is going on inside and outside the mind, and continuously generating assessments of various aspects of the situation without specific intention and with little or no effort. These basic assessments are easily substituted for more difficult questions.[10]

We first define Heuristics–“a simple procedure that helps find adequate, though

often imperfect, answers to difficult questions.”[11] Heuristics, allow humans to act fast, but they can also lead to wrong conclusions (biases) because they sometimes substitute an easier question for the one asked. A type of heuristic is the halo effect–“the tendency to like (or dislike) everything about a person–including things you have not observed. ..”[12] A simple example is rating a baseball player as good at pitching because he is handsome and athletic.

We first discuss the law of small numbers which basically states that researchers who pick too small a sample leave themselves at the mercy of sampling luck.[13]

Random events by definition do not behave in a systematic fashion, but collection of random events do behave in a highly regular fashion. This can lead to an illusion of causation.

Predicting results is based on the following facts:

Results of large samples deserve more trust than smaller samples, we know this as the law of large numbers.

But also, more significantly, the following two statements mean exactly the same thing:

·        large samples are more precise than small samples.

·        Small samples yield extreme results more often than large samples do.

Let us repeat the following result: “researchers who pick too small a sample leave themselves at the mercy of sampling luck”, traditionally psychologists do not use calculations to decide on  sample size. They use their judgement, which is commonly flawed.

People are not adequately sensitive to sample-size. The automatic part of our mind is not prone to doubt. It suppresses ambiguity and spontaneously constructs stories that are as coherent as possible. The effortful part of our mind is capable of doubt, because it can maintain incompatible possibilities at the same time.

The strong bias toward believing that small samples closely resemble the population from which they are drawn is also part of a larger story: we are prone to exaggerate the consistency and coherence of what we see.

Our prelidiction for causal thinking exposes us to serious mistakes in evaluating the randomness of truly random events. We are pattern seekers, believers in a coherent world, in which regularities appear not by accident but as a result of mechanical causality or of someone’s intention. We do not expect to see regularity produced by a random process, and when we detect what appears to be a rule, we quickly reject the idea that the process is truly random. Random processes produce many sequences that  convince people that the process is not random after all.

The law of small numbers is part of two larger stories about the workings of the mind.

·        The exaggerated faith in small samples is only one example of a more general illusion-we pay more attention to the content of messages than to information about their reliability.

·        Statistics produce many observations that appear to beg for causal explanations but do not lend themselves to such explanations. Many facts of the world are due to chance, including accidents of sampling. Causal explanations of chance events are inevitably wrong.

Another example of a heuristic bias is when judgments are influenced by an uninformative number (an anchor), which results from an associative activation in System 1. People are influenced when they consider a particular value for an unknown number before estimating that number. The estimate for a number then stays close to the anchor. For example, two groups estimated Gandhi’s age when he died. The first group were initially asked whether he was more than 114; a second group was asked whether he was 35 or older. The first group then estimated a higher number for when he died than the second one.[14]

Two different mechanisms produce anchoring effects-one for each system. There is a form of anchoring that occurs in a deliberate process of adjustment, an operation of System 2. And there is anchoring that occurs by a priming effect, an automatic manifestation of System 1.

Insufficient adjustment neatly explains why you are likely to drive too fast when you come off the highway into city streets-especially if you are talking with someone as you drive.

Adjustment is a deliberate attempt to find reasons to move away from the anchor: people who are instructed to shake their head when they hear the anchor, as if they rejected it, move farther from the anchor, and people who nod their head show enhanced anchoring.

Adjustment is an effortful operation. People adjust less (stay closer to the anchor) when their mental resources are depleted, either because their memory is loaded with digits or because they are slightly drunk. Insufficient adjustment is a failure of a weak or lazy System 2.

Suggestion is a priming effect, which selectively evokes compatible evidence. System 1 understands sentences by trying to make them true, and the selective activation of compatible thoughts produces a family of systematic errors that make us gullible and prone to believe too strongly whatever we believe.

A process that resembles suggestion is indeed at work in many situations: System 1 tries its best to construct a world in which the anchor is the true number.

Suggestion and anchoring are both explained by the same automatic operation of System 1.

A key finding of anchoring research is that anchors that are obviously random can be just as effective as potentially informative anchors. Anchors clearly do not have their effects because people believe they are informative.

Anchoring effects-sometimes due to priming, sometimes to insufficient adjustment-are everywhere. The psychological mechanisms that produce anchoring make us far more suggestible than most of us would want to be. And of course there are quite a few people who are willing and able to exploit our gullibility.

A strategy of deliberately “thinking the opposite” may be a good defense against anchoring effects, because it negates the biased recruitment of thoughts that produces these effects.

System 2 is susceptible to the biasing influence of anchors that make some information easier to retrieve.

A message, unless it is immediately rejected as a lie, will have the same effect on the associative system regardless of its reliability. The gist of the message is the story, which is based on whatever information is available, even if the quantity of of the information is slight and its quality is poor.

Anchoring results from associative activation. Whether the story is true, or believable, matters little, if at all. The powerful effect of random anchors is an extreme case of this phenomenon, because a random anchor obviously provides no information at all.

The main moral of priming research is that our thoughts and our behaviour are influenced, much more than we know or want, by the environment of the moment.

The concept of availability is the process of judging frequency by “ the ease with which instances come to mind.”, this heuristic is known to be both a deliberate problem solving strategy and an automatic operation.[15]

A question considered early was how many instances must be retrieved to get an impression of the ease with which they come to mind. We now know the answer: none.

The availability heuristic, like other heuristics of judgement, substitutes one question for another: you wish to estimate the size of a category or the frequency of an event, but you report an impression of the ease with which instances come to mind. Substitution of questions inevitably produces systematic errors.:

·        A salient event that attracts your attention will be easily retrieved from memory.

·        A dramatic event temporarily increases the availability of its category.

·        Personal experiences, pictures, and vivid examples are more available than incidents that happened to others, or mere words, or statistics.

Resisting this large collection of potential availability biases is possible, but tiresome.

One of the best-known studies of availability suggests that awareness of your own biases can contribute to peace in marriages, and probably in other joint projects.

The ease with which instances comes to mind is a System 1 heuristic, which is replaced by a focus on content when System 2 is more engaged.

People who let themselves be guided by System 1 are more strongly susceptible to availability biases than others who are in a higher state of vigilance. The following are some conditions in which people “go with the flow” and are affected more strongly by ease of retrieval than by the content they retrieved:

·        When they are engaged in another effortful task.

·        When they are in a good mood.

·        If they are depressed.

·        If they are knowledgeable novices.

·        Faith in intuition.

·        Are or made to feel powerful.

The concept of an affect heuristic is one in which people make judgements and decisions by consulting their emotions, a particularly important concept is: the availability cascade, the importance of an idea is often judged by the fluency (and emotional charge ) with which that idea comes to mind, this has impacts on public policy, particularly with reference to the effect of the media.[16]

Availability effects help explain the pattern of insurance purchases and protective action after disasters. Victims and near victims are very concerned after a disaster. However, the memories of the disaster dim over time, and so do worry and diligence.

Protective actions, whether by individuals or governments, are usually designed to be adequate to the worst disaster actually experienced.

Esimates of causes of death are warped by media coverage. The coverage is itself biased towards novelty and poignancy. The media do not just shape what the public is interested in, but are also shaped by it.

Notion of an affect heuristic was developed in which people make judgements and decisions by consulting their emotions: Do I like it? Do I hate it? How strongly do I feel about it?

“The emotional tail wags the rational dog.” The affect heuristic simplifies our lives by creating a world that is much tidier than reality. In the real world, of course, we often face painful trade-offs between benefits and costs.

Availability cascades are real and they undoubtedly distort priorities in the allocation of public resources. One perspective is offered by Cass Sunstein who would seek mechanisms that insulate decision makers from public pressures, letting the allocation of resourcesa be determined by impartial experts who have a broad view of all risks and of the resources available to reduce them. Paul Slovic on the other hand trusts the experts much less and the public somewhat more than Sunstein does, and he points out that insulating the experts from the emotions of the public produces policies that the public will reject-an impossible situation in a democracy.

People who are asked to assess probability are not stumped, because they do not try to judge probability as statisticians and philosophers use the word. A question about probability or likelihood activates a mental shotgun, evoking answers to easier questions. Judging probability by representativeness has important virtues: the intuitive impressions that it produces are often-indeed, usually-more accurate than chance guesses would be.[17]

In the absence of specific information about a subject, you will go by the base rates.

Activation of association with a stereotype, is an automatic activity of System1.

Representativeness involves ignoring both the base rates and the doubts about the veracity of the description. This is a serious mistake, because judgements of similarity and probability are not constrained by the same logical rules. It is entirely acceptable for judgements of similarity to be unaffected by the base rates and also by the possibility that the description was inaccurate, but anyone who ignores base rates and the quality of evidence in probability assessments will certainly make mistakes.

Logicians and statisticians have developed competing definitions of probability, all very precise.

In contrast people who are asked to assess probability are not stumped, because they do not try to judge probability as statisticians and philosophers use the word. A question about probability or likelihood activates a mental shotgun, evoking answers to easier questions.

Although it is common, prediction by representativeness is not statistically optimal.

Judging probability by representativeness has important virtues: the intuitive impressions that it produces are often-indeed, usually-more accurate than chance guesses would be.

In other situations, the stereotypes are false and the representativeness heuristic will mislead, especially if it causes people to neglect base-rate information that points in another direction.

One sin of representativeness is an excessive willingness to predict the occurrence of unlikely (low base-rate) events.

People without training in statistics are quite capable of using base rates in predictions under some conditions.

Instructing people to “think like a statistician” enhanced the use of base rate information, while the instruction to “think like a clinician” had the opposite effect.

Some people ignore base rates because they believe them to be irrelevant in the presence of individual information. Others make the same mistake because they are not focussed on the task.

The second sin of representativeness is insensitivity to the quality of evidence.

To be useful your beliefs should be constrained by the logic of probability.

The relevant “rules” for such cases are provided by Bayesian Statistics: the logic of how people should change their mind in the light of evidence.

There are two ideas to keep in mind about Bayesian reasoning and how we tend to mess it up. The first is that base rates matter, even in the presence of evidence about the case at hand. This is often not intuitively obvious. The second is that intuitive impressions of the diagnosity of evidence are often exaggerated.

A conjunction fallacy is one which people commit when they judge a conjunction of two events to be more probable than one of the events in a direct comparision.[18]

When you specify a possible event in greater detail you can only lower its probability. So, there is a conflict between the intuition of representativeness and the logic of probability.

The word fallacy is used, in general, when people fail to apply a logical rule that is obviously relevant. Amos and I introduced the idea of a conjunction fallacy, which people commit when they judge a conjunction of two events to be more probable than one of the events in a direct comparision.

The fallacy remains attractive even when you recognise it for what it is.

The uncritical substitution of plausibility for probability has pernicious effects on judgements when scenarios are used as tools of forecasting.

Adding detail to scenarios makes them more persuasive, but less likely to come true.

Less is more:sometimes even in joint evaluation: the scenario that is judged more probable is unquestionably more plausible, a more coherent fit with all that is known.

A reference to a number of individuals brings a spatial representation to mind.

The frequency representation, as it is known, makes it easy to appreciate that one group is wholly included in the other. The solution to the puzzle appears to be that  a question phrased as “how many?’ makes you think of individuals, but the same question phrased as “ what percentage?” does not.

The laziness of System 2 is an important fact of life, and the observation that representativeness can block the application of an obvious logical rule is also of some interest.

Intuition governs judgments in the between-subjects condition:logic rules in joint evaluation. In other problems, in contrast, intuition often overcame logic even in joint evaluation, although we identified some conditions in which logic prevails.

The blatant violations of the logic of probability that we had observed in transparent problems were interesting.

Causes trump statistics, in the sense that statistical base rates are generally underweighted and causal base rates are considered as information about the individual.[19]

This chapter considers a standard problem of Bayesian inference. There are two items of information: a base rate and the imperfectly reliable testimony of a witness.

You can probably guess what people do when faced wth this problem: they ignore the base rate and go with the witness.

Now consider a variation of the same story, in which only the presentation of the base rate has been altered.

The two versions of the problem are mathematically indistinguishable, but they are psychologically quite different. People who read the first version do not know how to use the base rate and often ignore it. In contrast, people who see the second version give considerable weight to the base rate, and their average judgment is not too far from the Bayesian solution. Why?

In the first version, the base rate is a statistical fact. A mind that is hungry for causal stories finds nothing to chew on.

In the second version, in contrast, you formed a stereotype, which you apply to unknown individual observations. The stereotype is easily fitted into a causal story. In this version, there are two causal stories that need to be combined or reconciled. The inferences from the two stories are contradictory and approximately cancel each other. The Bayesian estimate is 41%, reflecting the fact that the base rate is a little more extreme than the reliability of the witness.

The example illustrates two types of base rates. Statistical base rates are facts about a population to which a case belongs, but they are not relevant to the individual case. Causal base rates change your view of how the individual case came to be. The two types of base-rate information are treated differently:

Statistical base rates are generally underweighted, and sometimes neglected altogether, when specific information about the case at hand is available.

Causal base rates are treated as information about the individual case and are easily combined with other case-specific information.

The causal version of the cab problem had the form of a stereotype: Stereotypes are statements about the group that are (at least tentatively) accepted as facts about every member.

These statements are readily interpreted as setting up a propensity in individual members of the group, and they fit in a causal story.

Stereotyping is a bad word in our culture, but in the authors usage it is neutral. One of the bsic characteristics of System 1 is that it represents categories as norms and prototypical examplars; we hold in memory a representation of one or more “normal” members of each of these categories. When the categories are social, these representations are called stereotypes. Some stereotypes are perniciously wrong, and hostile stereotyping can have dreadful consequences, but the psychological facts cannot be avoided: stereotypes, both correct and false, are how we think of categories.

You may note the irony. In the context of the  problem, the neglect of base-rate information is a cognitive flaw, a failure of Bayesian reasoning, and the reliance on causal base rates is desireable. Stereotyping improves the accuracy of judgement. In other contexts, however, there is a strong social norm against stereotyping, which is also embedded in the law.

The social norm against stereotyping, including the opposition to profiling, has been highly been highly beneficial in creating a more civilised and more equal society. It is useful to remember, however, that neglecting valid stereotypes inevitably results in suboptimal judgements.

The explicitly stated base rates had some effects on judgment, but they had much less impact than the statistically equivalent causal base rates. System 1 can deal with stories in which the elements are causally linked, but it is weak in statistical reasoning. For a Bayesian thinker, of course, the versions are equivalent. It is tempting to conclude that we have reached a satisfactory conclusion:causal base rates are used; merely statistical facts are more or less neglected. The next study, however, shows that the situation is rather more complex.

Individuals feel relieved of responsibility when they know that others can take responsibility.

Even normal, decent people do not rush to help when they expect others to take on the unpleasantness of dealing with a seizure.

Respondents “quietly exempt themselves” (and their friends and acquaintances) from the conclusions of experiments that surprise them.

To teach students any psychology they did not know before, you must surprise them. But which surprise will do? When respondents were presented with a surprising statistical fact they managed to learn nothing at all. But when the students were surprised by individual cases-two nice people who had not helped-they immediately made the generalisation and inferred that helping is more difficult than they had thought.

This is a profoundly important conclusion. People who are taught surprising statistical facts about human behaviour may be impressed to the point of telling their friends about what they have heard, but this does not mean that their understanding of the world has really changed. The test of learning psychology is whether your understanding of situations you encounter has changed, not whether you have learned a new fact. There is a deep gap between our thinking about statistics and our thinking about individual cases. Statistical results with a causal interpretation have a stronger effect on our thinking than noncausal information. But even compelling causal statistics will not change long-held beliefs or beliefs rooted in personal experience. On the other hand, surprising individual cases have a powerful impact and are a more effective tool for teaching psychology because the incongruity must be resolved and embedded in a causal story.

Regression to the mean involves moving closer to the average than the earlier value of the variable observed. Also regression to the mean has an explanation, but does not have a cause.[20]

An important principle of skill training:rewards for improved performance work better than punishment of mistakes. This proposition is supported by much evidence from research.

Regression to the mean, involves that poor performance is typically followed by improvement and good performance by deterioration, without any help from either praise or punishment.

The feedback to which life exposes us is perverse. Because we tend to be nice to other people when they please us and nasty when they do not, we are statistically punished for being nice and rewarded for being nasty.

Regression does not have a causal explanation. Regression effects are ubiquitous, and so are misguided casual stories to explain them. The point to remember is that the change from the first to the second occurrence does not need a causal explanation. It is a mathematically inevitable consequence of the fact that luck played a role in the outcome of the first occurence.

Regression inevitably occurs when the correlation between two measures is less than perfect.

The correlation coefficient between two measures, which varies between 0 and 1, is a measure of the relative weight of the factors they share.

Correlation and regression are not two concepts-they are different perspectives on the same concept. The general rule is straightforward but has surprising consequences: whenever the correlation between two scores is imperfect, there will be regression to the mean.

Our mind is strongly biased toward causal explanations and does not deal well with “mere statistics.” When our attention is called to an event, associative memory will look for its cause-more precisely, activation will automatically spread to any cause that is already stored in memory. Causal explanations will be evoked when regression is detected, but they will be wrong because the truth is that regression to the mean has an explanation but does not have a cause.

System 2 finds it difficult to understand and learn. This is due in part to the insistent demand for causal interpritations, which is a feature of System 1.

Regression effects are a common source of trouble in research, and experienced scientists develop a healthy fear of the trap of unwarranted causal inference.

Intuitive predictions need to be corrected because they are not based on regression to the mean and are therefore biased. Correcting intuitive predictions are a task for system 2.[21]

Life presents us with many occasions to forecast. Some predictive judgments, rely largely on precise calculations. Others involve intuition and System 1 in two main varieties. Some intuitions draw primarily on skill and expertise acquired by repeated experience.

Other intuitions, which are sometimes subjectively indistinguishable from the first, arise from the operation of heuristics that often substitute an easy question for the harder one that was asked. Of course, many judgements, especially in the professional domain, are influenced by a combination of analysis and intuition.

We are capable of rejecting information as irrelevant or false, but adjusting for smaller weaknesses in the evidence is not something that system 1 can do. As a result intuitive predictions are almost completely insensitive to the actual predictive quality of the evidence. When a link is found, what you see is all there is applies:your associative memory quickly and automatically constructs the best possible story from the information available.

Next the evidence is evaluated in relation to a relevant norm.

The next step involves substitution and intensity matching.

The final step is a translation from an impression of the relative position  of the candidates performation to the result.

Intensity matching yields predictions that are as extreme as the evidence on which they are based. By now you should realise that all these operations are features of system 1. You should imagine a process of spreading activation that is initially prompted by the evidence and the question, feeds back upon itself, and eventually settles on the most coherent solution possible.

The prediction of the future is not distinguished from an evaluation of current evidence-prediction matches evaluation.

This is perhaps the best evidence we have for the role of substitution. People are asked for a prediction but they substitute an evaluation of the evidence, without noticing that the question they answer is not the one they were asked. This process is guaranteed to generate predictions that are systematically biased; they completely ignore regression to the mean.

Intuitive predictions need to be corrected because they are not regressive and are therefore are biased.

The corrected intuitive predictions eliminate these biases, so that predictions (both high and low) are about equally likely to overestimate and to underestimate the true value. You will still make errors when your predictions are unbiased, but the errors are smaller and do not favour either high or low outcomes.

Correcting your intuitive predictions is a task for System 2. Significant effort is required to find the relevant reference category, estimate the baseline prediction, and evaluate the quality of the evidence. The effort is justified only when the stakes are high and when you are particularly keen not to make mistakes.

The objections to the principle of moderating intuitive predictions must be taken seriously, because absence of bias is not always what matters most. A preference for unbiased predictions is justified if all errors of prediction are treated alike, regardless of their direction. But there are situations in which one type of error is much worse than another.

For a rational person, predictions that are unbiased and moderate should not present a problem.

Extreme predictions and a willingness to predict rare events from weak evidence are both manifestations of System1. It is natural for the associative machinery to match the extremeness of predictions to the perceived extremeness of evidence on which it is based-this is how substitution works. And it is natural for System1 to generate overconfident judgements, because confidence, as we have seen, is determined by the coherence of the best story you can tell from the evidence at hand. Be warned: your intuitions will deliver predictions that are too extreme and you will be inclined to put far too much faith in them.

Regression is also a problem for System 2. The very idea of regression is alien and difficult to communicate and comprehend.

Matching predictions to the evidence is not only something we do intuitively; it also seems a reasonable thing to do. We will not learn to understand regression from experience. Even when a regression is identified, it will be given a causal interpretation that is almost always wrong.

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[1] Amos Tversky and Daniel Kahneman, Judgement under Uncertainty: Heuristics and Biases, 1974.

[2] Daniel Kahneman, Thinking, Fast and Slow  (2011).

[3] Ibid-page 21

[4] Ibid-chapter 2

[5] Ibid-chapter 3

[6] Ibid-chapter 4

[7] Ibid-chapter 5

[8] Ibid-chapter 6

[9] Ibid-chapter 7

[10] Ibid-chapter 8

[11] Ibid-page 98

[12] Ibid-page 82

[13] Ibid-chapter 10

[14] Ibid-chapter 11.

[15] Ibid-chapter 12.

[16] Ibid-chapter 13.

[17] Ibid-chapter 14.

[18] Ibid-chapter 15

[19] Ibid-chapter 16

[20] Ibid-chapter 17

[21] Ibid-chapter 18.