Tversky & Kahnemann

## TVERSKY and KAHNEMANN: On Anchoring with Variation

We are all taught how we should think. How do people think, really, no matter what they are supposed to do ? Tversky and Kahnemann addressed this issue through the study of how people solved calculation problems that were beyod their capacity in a limited period of time. They concluded that people rely on heuristics — rules of estimation that provide good but not perfect answers to hard questions. Of the three they discuss, representativeness, availability, and adjustment and anchoring, these citations focus on the last — which I consider the most important.

In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, ADJUSTMENTS ARE TYPICALLY INSUFFICIENT. That is, different starting points yield different estimates, which are biased toward the initial value. We call this phenomenon ANCHORING.

In a demonstration of the anchoring effect, subjects were asked to estimate various quantities, stated in percentages (for example, the percentage of African countries in the United Nations). For each quantity, a number between 0 and 100 was determined by spinning a wheel of fortune in the subjects’ presence. The subjects were instructed to indicate first whether that number was higher or lower than the value of the quantity, and then to estimate the value of the quantity by moving upward or downward from the given number. Different groups were given different numbers for each quantity, and these arbitrary numbers had a marked effect on estimates. For example, the median estimates of the percentage of African countries in the United Nations were 25 and 45 for groups that received 10 and 65, respectively, as starting points. Payoffs for accuracy did not reduce the anchoring effect.

Anchoring occurs not only when the starting point is given to the subject, but also when the subject bases his estimate on the result of some incomplete computation….

BIASES IN THE EVALUATION OF CONJUNCTIVE AND DISJUNCTIVE EVENTS:
Studies of choice among gambles and of judgments of probability indicate that people tend to overestimate the probability of conjunctive events and to underestimate the probability of disjunctive events. These biases are readily explained as the effects of anchoring. The stated probability of the elementary event (success at any one stage) provides a natural starting point for the estimation of the probabilities of both conjunctive and disjunctive events. Since adjustment from the starting point is typically insufficient, the final estimates remain too close to the probabilities of the elementary events in both cases. Note that the probability of a conjunctive event is lower than the probability of each elementary event, whereas the overall probability of a disjunctive event is higher than the probability of each elementary event. As a consequence of anchoring, the overall probability will be overestimated in conjunctive problems and underestimated in disjunctive problems.

By collecting subjective probability distributions for many different quantities, it is possible to test the judge for proper calibration…. Several investigators have obtained probability distributions for many quantities from a large number of judges. These distributions indicated large and systematic departures from proper calibration. In most studies, the actual values of the assesed quantites are either smaller than X(01) or greater than X(99) for about 30% of the problems. That is, the subjects state overly narrow confidence intervals which reflect more certainty than is justified by their knowledge about the assessed quantities. This bias is common to naive and sophisticated subjects and is not eliminated by introducing proper scoring rules…. The reliance on heuristics and the prevalence of biases are not restricted to laymen. Experienced researchers are also prone to the same biases — when they think intuitively. For example, the tendency to predict the outcome that best represents the data, with insufficient regard for prior probability, has been observed in the intuitive judgments of individuals who have had extensive training in statistics. Although the statistically sophisticated avoid elementary errors, such as the gambler’s fallacy,
FOOT The gambler’s fallacy is the expectation that preceding events affect what are in fact independent probabilities.
their intuitive judgments are liable to similar fallacies in more intricate and less transparent problems.

If, as Goodman suggests, worlds differ not only in categorization (their assignment of what’s what) but also in the relative salience of one element in comparison with another (what’s primary), the observation that anchoring with variation is a common process of thought among both naive and sophisticated problem solvers argues that it is a natural process of thought as well. This process is one I take as a given in my analyses [note 2]. If thought begins or eventually comes down to processing of concrete models of particular past experience, then anchoring with variation and its implications for the characteristic processes of thinking are of central importance in studying learning.

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