Error in Human Reasoning
Although humans are the only animals that reason, we do not follow probability theory, a normative model, very closely in our everyday reasoning. The conjunction fallacy is one of the major errors that humans commit when dealing with problems that involve probability. Exemplified by Linda the feminist bank teller, this problem occurs when we assume that a conjunction of two premises is more likely than one or more of the premises alone. According to probability, the conjunction of two premises can never be more probable than either of the premises alone. In the Linda problem, the subjects are given a brief biographical description of Linda, followed by several statements about Linda's current occupation or activities. The subjects are then asked to rank the statements in order of most likely to least likely. The majority of the subjects choose "Linda is a bank teller and a feminist" (T and F) as more likely than "Linda is a bank teller." (F) (Barron, pg. 138)
According to the laws of probability, T must be more probable than the combination of T and F. Thus, the question arises as to why we reason this way. As Professor Kellman explained in his lectures, we commit this fallacy because of our association of the word "feminist" with the biographical description of Linda. Apparently, we ignore the most basic laws of probability, and rely on our ability to associate certain characteristics with likely careers and hobbies of an individual.
Ever since the original study by Tversky and Kahnerman in 1983, it has been assumed that human reasoning prefers association of terms in lieu of mathematical probabilities in these situations. There is debate, however, as to whether this is a fallacy in human reasoning or not. The original authors of the study argue that Linda's biographical description is irrelevant. Only the words "probability" and "and" are important. (Hertwig and Gigerenzer, pg. 276) Hertwig and Gigerenzer, however, argue that this is not necessarily the case. They argue that a content-blind normative model is not a proper means of assessing human reasoning, i.e. (P & Q) is never * (P v Q). Hertwig and Gigerenzer place a greater emphasis on natural language and our understanding of the term probability in this problem. Their study is a "step toward integrating content, context, and representation of information." (Hertwig and Gigerenzer, pg. 276)
Hertwig and Gigerenzer believe the word "probable" is the key to the Linda problem. In their opinion, when people read the problem as presented by Tversky and Kahneman, they did not infer the mathematical definition of the word "probable." Rather, a more casual interpretation of the word was taken, i.e. strength of argument or intensity of belief. Under this definition it is very reasonable for people to say that T and F is more probable than T. The selection of T and F to be more probable than T "creates a story." That is, they wanted to...