Related to: The Conjunction Fallacy, Conjunction Controversy

The heuristics and biases research program in psychology has discovered many different ways that humans fail to reason correctly under uncertainty.  In experiment after experiment, they show that we use heuristics to approximate probabilities rather than making the appropriate calculation, and that these heuristics are systematically biased. However, a tweak in the experiment protocols seems to remove the biases altogether and shed doubt on whether we are actually using heuristics. Instead, it appears that the errors are simply an artifact of how our brains internally store information about uncertainty. Theoretical considerations support this view.

EDIT: The view presented here is controversial in the heuristics and biases literature; see Unnamed's comment on this post below.

EDIT 2: The author no longer holds the views presented in this post. See this comment.

A common example of the failure of humans to reason correctly under uncertainty is the conjunction fallacy. Consider the following question:

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

What is the probability that Linda is:

(a) a bank teller

(b) a bank teller and active in the feminist movement

In a replication by Gigerenzer, 91% of subjects rank (b) as more probable than (a), saying that it is more likely that Linda is active in the feminist movement AND a bank teller than that Linda is simply a bank teller (1993). The conjunction rule of probability states that the probability of two things being true is less than or equal to the probability of one of those things being true. Formally, P(A & B) ≤ P(A). So this experiment shows that people violate the conjunction rule, and thus fail to reason correctly under uncertainty. The representative heuristic has been proposed as an explanation for this phenomenon. To use this heuristic, you evaluate the probability of a hypothesis by comparing how "alike" it is to the data. Someone using the representative heuristic looks at the Linda question and sees that Linda's characteristics resemble those of a feminist bank teller much more closely than that of just a bank teller, and so they conclude that Linda is more likely to be a feminist bank teller than a bank teller.

This is the standard story, but are people really using the representative heuristic in the Linda problem? Consider the following rewording of the question:

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

There are 100 people who fit the description above. How many of them are:

(a) bank tellers

(b) bank tellers and active in the feminist movement

Notice that the question is now strictly in terms of frequencies. Under this version, only 22% of subjects rank (b) as more probable than (a) (Gigerenzer, 1993). The only thing that changed is the question that is asked; the description of Linda (and the 100 people) remains unchanged, so the representativeness of the description for the two groups should remain unchanged. Thus people are not using the representative heuristic - at least not in general.