I am particularly fond of this example [the Linda problem] because I know that the [conjoint] statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me—"but she can't just be a bank teller; read the description."
As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more "representative" of Linda from the description of her, even though it is clearly mathematically less likely.
In other words, one group of participants is asked to rank-order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank-order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without "Linda is a bank teller" as an option).
There was also a similar problem about a man named Bill (a good fit for the stereotype of an accountant — "intelligent, but unimaginative, compulsive, and generally lifeless" — but not a good fit for the stereotype of a jazz player), and two problems where participants were asked to make predictions for events that could occur in 1981.
Policy experts were asked to rate the probability that the Soviet Union would invade Poland, and the United States would break off diplomatic relations, all in the following year.
Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year.
In an experiment conducted in 1980, respondents were asked the following: Suppose Björn Borg reaches the Wimbledon finals in 1981.
Tversky and Kahneman followed up their original findings with a 1983 paper[4] that looked at dozens of new problems, most of these with multiple variations.
A health survey was conducted in a representative sample of adult males in British Columbia of all ages and occupations.
[4] If the first option is changed to obey conversational relevance, i.e., "Linda is a bank teller whether or not she is active in the feminist movement" the effect is decreased, but the majority (57%) of the respondents still commit the conjunction error.
If the probability is changed to frequency format (see debiasing section below) the effect is reduced or eliminated.
However, studies exist in which indistinguishable conjunction fallacy rates have been observed with stimuli framed in terms of probabilities versus frequencies.
[6][9][13] In an incentivized experimental study, it has been shown that the conjunction fallacy decreased in those with greater cognitive ability, though it did not disappear.
[15] Still, the conjunction fallacy occurs even when people are asked to make bets with real money,[16] and when they solve intuitive physics problems of various designs.
[17] Drawing attention to set relationships, using frequencies instead of probabilities, and/or thinking diagrammatically sharply reduce the error in some forms of the conjunction fallacy.