Cognition and Chance: The Psychology of Probabilistic Reasoning
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Lack of ability to think probabilistically makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naiveté, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, and precludes critical evaluation of likelihood claims. Cognition and Chance presents an overview of the information needed to avoid such pitfalls and to assess and respond to probabilistic situations in a rational way. Dr. Nickerson investigates such questions as how good individuals are at thinking probabilistically and how consistent their reasoning under uncertainty is with principles of mathematical statistics and probability theory. He reviews evidence that has been produced in researchers' attempts to investigate these and similar types of questions. Seven conceptual chapters address such topics as probability, chance, randomness, coincidences, inverse probability, paradoxes, dilemmas, and statistics. The remaining five chapters focus on empirical studies of individuals' abilities and limitations as probabilistic thinkers. Topics include estimation and prediction, perception of covariation, choice under uncertainty, and people as intuitive probabilists.
Cognition and Chance is intended to appeal to researchers and students in the areas of probability, statistics, psychology, business, economics, decision theory, and social dilemmas.
“effects of chance,” noting that this or that event was “due to chance” or “happened by chance.” We refer to many games as “games of chance.” The importance of the concept to mathematics and science is seen in references to the “mathematics of chance,” the “theory of chance,” the “doctrine of chances,” “the science of chance phenomena,” and the, some would say incongruous, term “the laws of chance” Chance is a controversial concept. As I see it, the word has several connotations as used in the
it. In my view, chance is a descriptive concept and never an explanation. We may say that under specified conditions, certain events are best described as chance events—that the various possibilities have equal probability of occurring—and this observation may be very useful, but simply calling it chance does not explain why the behavior is such as it is. The atoms of a radioactive substance are constantly decaying, the rate of decay differing over a very large range from substance to substance.
only one type of mass and it is a consequence of the curvature of space. These cases illustrate that attempting to account in a causal way for what might appear, at first, to be chance coincidences has been a fruitful endeavor in science. But one can find examples of attempting to account for coincidences that are generally considered not to be science at its best. A well-known case in point is that of the attention given, beginning in the mid- 19th century, to the great pyramid of Egypt. Much of
the theoretical relative frequencies as indicative of the momentary probabilities, then the numbers in the matrix associated with Case 4 represent also the probabilities associated with that trial, and the correct answer to the question of the probability that the cab was blue, given that the witness said it was green is .59. Cohen argues that a relativefrequency conception of probability is not appropriate here, that probability in this case is better viewed as a “causal propensity” the judgment
chance 142 the 10-toss game as well, but the differences in probabilities are instructive. Perhaps the most obvious difference in the two probability distributions is the fact that an outcome that deviates from the most likely one (one half heads) by a given percentage is much greater in the 10-toss than in the 100-toss game. The probability of getting 60% or more heads is about .38 in the 10-toss game and less than .03 in the 100-toss one; the probability of getting 70% or more heads is about.