Monday, 24 December 2012

Shortcuts in decisions-some features...

Certain interesting features regarding the study of heuristics and biases in the writings of Tversky and Kahneman: Munish Alagh.


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  three 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. This discussion below is based broadly on writings by Kahneman and Tversky, the following heuristics and the biases they lead to are discussed:


Ø  Representativeness.

Ø  Adjustment and Anchoring.




Judging probability by representativeness has important virtues: the intuitive impressions that it produces are often-indeed, usually-more accurate than chance guesses would be.[2]


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.


Certain interesting features regarding the errors which result from representativeness are:

Insensitivity to prior probability of outcomes: 

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.[3]


Insensitivity to sample size:

Subjects failed to appreciate the role of sample size even when it was emphasized in the formulation of the problem 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 [4]. 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[5] It has been labeled "conservatism."

Misconceptions of chance:

Misconceptions of chance are not limited to naive subjects. A study of the statistical intuitions of experienced research psychologists[6] 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 illusion of validity:


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 vari-ables 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 vari-ables 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 pre-dictions that are quite likely to be off the mark[7]


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.[8]


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.


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, dis-junctive 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.


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] Amos Tversky and Daniel Kahneman, Judgement under Uncertainty: Heuristics and Biases, (1974).
[2]  Daniel Kahneman, Thinking, Fast and Slow  (2011).
[3] Tversky and Kahneman, “On the Psychology of Prediction.” (1973)
[4] D Kahneman and A Tversky, “Subjective Probability: A Judgment of Representativeness,” Cognitive Psychology 3(1972);430-54
[5] W Edwards,Conservatism in Human Information Processing, 1968
[6] Kahneman and Tversky,1972.
[7] Ibid.
[8] Kahneman, 2011-chapter 17

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