불확실성속에서의 판단.. 휴리스틱 오류...

[문형철]

Many decisions are based on beliefs concerning the likelihood of uncertain events such as the outcome of an election, the guilt of a defendant, or the future value of the dollar. These beliefs are usually expressed in statements such as "I think that . . . ," "chances are . . . ," "it is unlikely that . . . ," and so forth. Occasionally, beliefs concerning iuncertain events are expressed in numerical form as odds or subjective probabilities.

What determines such beliefs?

How do people assess the probability of an uncertain event or the value of an uncertain quantity?

This article shows that people rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities and predicting values to simpler judgmental operations. In general, these heuristics are quite useful, but sometimes they lead to severe and systematic errors. The subjective assessment of probability resembles the subjective assessment of physical quantities such as distance or size. These judgments are all based on data of limited validity, which are processed according to heuristic rules. For example, the apparent distance of an object is determined in part by its clarity. The more sharply the object is seen, the closer it appears to be. This rule has some validity, hecaust: in any given scene the more distant objects are seen less sharply than nearer objects. However, the reliance on this rule leads to systematic errors in the estimation of distance. Specifically, distances are often overestimated when visibility is poor because the contours of objects are blurred. On the other hand, distances are often underestimated when visibility is good because the objects are seen sharply. Thus, the reliance on clarity as an indication of distance leads to common biases. Such biases are also found in the intuitive judgment of probability. This article describes 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 observation5 are discussed.

많은 결정은 

선거 결과, 

피고인의 유죄 여부 또는 

달러의 미래 가치와 같은 

불확실한 사건의 가능성에 대한 믿음에 근거합니다. 

이러한 신념은 

일반적으로 “나는 ... . ,” ”가능성이 ... . ,” ”그럴 가능성은 ... . .” 등과 같은 식으로 표현됩니다. 

간혹 불확실한 사건에 대한 믿음이 

확률이나 주관적인 확률로 수치로 표현되는 경우도 있습니다. 

무엇이 그러한 믿음을 결정할까요? 

사람들은 불확실한 사건의 확률이나 불확실한 수량의 가치를 어떻게 평가할까요? 

이 글에서는 

사람들이 확률을 평가하고 

값을 예측하는 복잡한 작업을 

보다 간단한 판단 작업으로 줄여주는 

제한된 수의 휴리스틱 원칙에 의존한다는 사실을 보여줍니다. 

일반적으로 이러한 휴리스틱은 매우 유용하지만 때로는 심각하고 체계적인 오류로 이어지기도 합니다. 확률에 대한 주관적인 평가는 거리나 크기와 같은 물리적 양에 대한 주관적인 평가와 유사합니다. 이러한 판단은 모두 휴리스틱 규칙에 따라 처리되는 제한된 유효성의 데이터를 기반으로 합니다. 예를 들어, 물체의 겉보기 거리는 부분적으로 선명도에 따라 결정됩니다. 물체가 선명하게 보일수록 더 가까이 있는 것처럼 보입니다. 이 규칙은 어느 정도 타당성이 있습니다. 어떤 장면에서든 멀리 있는 물체는 가까이 있는 물체보다 덜 선명하게 보입니다. 그러나 이 규칙에 의존하면 거리 추정에서 체계적인 오류가 발생합니다. 특히 물체의 윤곽이 흐려져 시야가 좋지 않은 경우 거리가 과대평가되는 경우가 많습니다. 반면에 가시성이 좋을 때는 물체가 선명하게 보이기 때문에 거리가 과소평가되는 경우가 많습니다. 따라서 거리를 나타내는 선명도에 대한 의존은 일반적인 편견으로 이어집니다. 이러한 편향은 확률에 대한 직관적인 판단에서도 발견됩니다. 이 문서에서는 확률을 평가하고 값을 예측하는 데 사용되는 세 가지 휴리스틱에 대해 설명합니다. 이러한 휴리스틱이 이끄는 편향이 열거되고 이러한 관찰의 적용 및 이론적 함의5가 논의됩니다.

Representativeness

Many of the probabilistic questions with which people are concerned belong to one of the following types: 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 R w~ll generate event A? In answering such questions, people typically rely on the representativeness heuristic, in 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 ib 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. For an illustration of judgment by representativeness, consider an individual who has been described by a former neighbor as follows: "Steve is very shy and withdrawn, invariably helpful, but with little interest in people, or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail." How do people assess the probability that Steve is engaged in a particular occupation from a list of possibilities (for example, farmer, salesman, airline pilot, librarian, or physician)? How do people order these occupat~oas from most to least likely? In the representativenes> heuristic, the probability that Steve is a I~brarian, for example, IS assessed by the degree to which he is representative of, or similar to, the stereotype of a librarian. Indeed, research with problems of this type has shown that people order the occupations by probability and by similarity in exactly the same way (I). This approach to the ji~dg~~ient of probability leads to serious errors, because similarity, or representativeness, is not 1t1- fluenced by several factors that should affect judgments of probability. l1zrer7ritivity to prior probability of outcomer. One of the factors that have no effect on representat~veness but should have a major effect on probabil- ~ty isthe prior probability, or base-rate frequency, of the outcomes. In the 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 probabil~ty that Steve is a librarian rather than a farmer. Considerations of base-rate frequency, however, do not affect the similarity of Steve to the stereotypes of librarians and farmers. If people eval‎uate probability by representativeness, therefore, prior probabilities will be neglected. This hypothesis was tested in an experiment where prior probabilities were manipulated (I). Subjects were shown brief personality descriptions of several individuals, allegedly sampled at random from a group of 100 professionals-engineers and lawyers. The subjects were askcd to assess, for each description, the probability that it belonged to an engineer rather than to a lawyer. In one experimental condition, subjects were told that the group from which the descriptions had been drawn consisted of 70 engineers and 30 lawyers. Tn another condition, subjects were told that the group consisted of 30 engineers and 70 lawyers. The odds that any particular description belongs to an engineer rather than to a lawyer should be higher in the first condition, where there is a majority of engineers, than in the second condition, where there is a majority of lawyers. Specifically, it can be shown by applying Bayes' rule that the ratio of these odds should be (.7/.312, or 5.44, for each description. In a sharp violation of Bayes' rule, the subjects in the two conditions produced essen tially the same probability judgments. Apparently, subjects eval‎uated the likelihood that a particular description belonged to an engineer rather than to a lawyer ,by the degree to which this 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. In the absence of a personality sketch, they judged the probability that an unknown individual is an engineer to be .7 and .3, respectively, in the two base-rate conditions. However, prior probabilities were effectively ignored when a description was introduced, even when this description was totally uninformative. The responses to the following description illustrate this phenomenon: Dick is a 30 year old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. This description was intended to convey no information relevant to the question of whether Dick is an engineer or a lawyer. Consequently, the probability that Dick is an engineer should equal the proportion of engineers in the group, as if no description had been given. The subjects, however, judged the probability of Dick being an engineer to be .5 regardless of whether the stated proportion of engineers in the group was .7 or .3. Evidently, people respond differently when given no evidence and when given worthless evidence. When no specific evidence is given, prior probabilities are properly utilized; when worthless evidence is given, prior probabilities are ignored (1). 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, for example, that the average height in a random sample of ten men will be 6 feet (180 centimeters), by the similarity of this result to the corresponding parameter (that is, to the average height in the population of men). 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 subiects assessed the distributions of average height for samples of various sizes, they produced identical distributions. For example, the probability of obtaining an average height greater than 6 feet was assigned the same value for samples of 1000, 100, and 10 men (2). Moreover, subjects failed to appreciate the role of sample size even when it was emphasized in the formulation of the problem. Consider the following question: A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in $he smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60 percent of the babies born were boys. Which hospital do you think recorded more such days? b The larger hospital (21) b The smaller hospital (21) b A'bout the same (that is, within 5 percent of each other) (53) The values in parentheses are the number of undergraduate students who chose each answer. Most subjects judged the probability of obtaining more than 60 percent boys to be the same in the small and in the large hospital, presumably because these events are described by the same statistic and are therefore equally representative of the general population. In contrast, sampling theory entails that the expected number of days on which more than 60 percent of the babies are boys is much greater in the small hospital than in the large one, because a large sample is less likely to stray from 50 percent. This fundamental notion of statistics is evidently not part of people's repertoire of intuitions. 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. Consider the following example: Imagine an urn filled with balls, of which % are of one color and 1/3 of another. One individual has drawn 5 balls 'from the urn, and found that 4 were red and 1 was white Another individual has drawn 20 balls and found that 12 were red and 8 were white. Which of the two individuals should feel more confident that the urn contains 2/3 red balls and 95 white balls, rather than the opposite? What odds should each individual give? In this problem, the correct posterior odds are 8 to 1 for the 4 : 1 sample and 16 to 1 for the 12 : 8 sample, assuming equal prior probabilities. However, most people feel that the first sample provides much stronger evidence for the hypothesis that the urn is predominantly red, because the proportion of red balls is larger in the first than in the second sample. 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 (2). 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 (3, 4). 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. In considering tosses of a coin for heads or tails, for example, people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T-T-T, which does not appear random, and also more likely than the sequence H-HH-H-T-H, which does not represent the fairness of the coin (2). 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, however, 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. After observing a long run of red on the roulette wheel. for example, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red. 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 (5) revealed a lingering belief in what may be called the "law of small numbers," according to which even small samples are highly