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 strengthen their beliefs about Linda’s biography.
They did this by selecting T & F (an activist with a respectable job) to be more probable than T (a mundane bank teller) alone. (Hertwig and Gigerenzer, pg. 277-79) Hertwig and Gigerenzer conducted three studies to illustrate their argument that a nonmathematical meaning of “probability” is inferred in the original Linda problem. In the first experiment, after posing the Linda problem, they asked the participants to paraphrase the word “probability” in the. Then they asked them to check off their understood definition of the word “probability” as used in the problem from a list of definitions.
As expected, there was a high rate of the conjunction fallacy. Most of the subjects, however, indicated that they understood “probability” to have a nonmathematical meaning. In the second experiment, the subjects were first asked of the typicality of the choices, then of the probability. The occurrence of the conjunction fallacy decreased in this experiment. The participants used the supplied information about Linda in the “typicality” phase, while inferring a more mathematical meaning in the “probability” phase. In the third experiment, the word probability was replaced altogether with frequency.
This produced the least number of conjunction fallacies. Most of the subjects understood frequency to be a mathematical term. Thus they approached the problem in like manner. The experimenters conclude that the responses given to the original problem are completely reasonable given that a nonmathematical meaning is attached to “probability. ” (Hertwig and Gigerenzer, pgs. 279-88) This is certainly true in everyday life. Whenever we make inferences about people we do not attach mathematical meanings to these. For example, what is the probability that our next president will be well educated?
Insert George W. joke here) According to Tversky and Khanerman’s method, anyone that guesses a high number is committing the conjunction fallacy. It is less likely to be president and well educated than president alone. Life simply does not work this way. We automatically assume that there are certain characteristics that one must meet in order to become president. Since the president is not selected at random, we assign high priority to the qualifications of the office. Therefore, education, a good one at that, is considered very important to a president.
The prediction that our next president will be well educated is a very reasonable assumption. The above example may seem a far stretch to the Linda problem. A simple rearrangement will, however, make it very similar to the Linda problem. Given various biographies of individuals, if subjects are asked to rate the biographies from most probable to least probable of being that of the next President of the United States, then we would have a scenario that is very similar to the Linda problem. This experiment would hit the core of the Linda problem: base rates.
Although a different subject altogether, base rates are inseparable from the Linda problem. (We ignore the high base rate of bank tellers versus bank tellers and feminists. ) Most subjects would choose a biography that included significant leadership experience, political offices, education at a university, probably an Ivy League level school, etc. , not a biography of a middle class white-collar worker. They would ignore the fact that there are more of the latter than the former in the general population because the president is not selected at random from the population. Similarly, Linda is not a random individual.
We have certain information about her that leads us to think of her in a way that eventually violates the conjunction rule. We do not see Linda as a bank teller who has forgotten her days of social activism. We want to believe that she is still an activist. Therefore, we ignore the probabilities of randomness, and make the selection that is most compatible with the biographical sketch. As Hertwig and Gigerenzer have pointed out in their study, we do not infer mathematical probabilities when asked to make judgments about characters of individuals, most notably, Linda, the feminist banker.