Editing Conjunction fallacy (section)

==Other examples==

While the Linda problem is the best-known example, researchers have developed dozens of problems that reliably elicit the conjunction fallacy. 

=== Tversky & Kahneman (1981)  ===

The original report by Tversky & Kahneman<ref name="tk81"/> (later republished as a book chapter<ref name="Tversky & Kahneman 1982"/>) described four problems that elicited the conjunction fallacy, including the Linda problem. 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. They rated it on average as having a 4% probability of occurring. 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. They gave it an average probability of only 1%.

In an experiment conducted in 1980, respondents were asked the following:

<blockquote>Suppose [[Björn Borg]] reaches the [[The Championships, Wimbledon|Wimbledon]] finals in 1981. Please rank order the following outcomes from most to least likely.
* Borg will win the match
* Borg will lose the first set
* Borg will lose the first set but win the match
* Borg will win the first set but lose the match</blockquote>

On average, participants rated "Borg will lose the first set but win the match" more likely than "Borg will lose the first set". However, winning the match is only one of several potential eventual outcomes after having lost the first set. The first and the second outcome are thus more likely (as they only contain one condition) than the third and fourth outcome (which depend on two conditions).

===  Tversky & Kahneman (1983) ===

Tversky and Kahneman followed up their original findings with a 1983 paper<ref name="tk83"/> that looked at dozens of new problems, most of these with multiple variations. The following are a couple of examples.

<blockquote>Consider a regular six-sided die with four green faces and two red faces. The die will be rolled 20 times and the sequence of greens (G) and reds (R) will be recorded. You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you choose appears on successive rolls of the die.

# RGRRR
# GRGRRR
# GRRRRR</blockquote>

65% of participants chose the second sequence, though option 1 is contained within it and is shorter than the other options. In a version where the $25 bet was only hypothetical the results did not significantly differ. Tversky and Kahneman argued that sequence 2 appears "representative" of a chance sequence<ref name="tk83"/> (compare to the ''[[clustering illusion]]'').

<blockquote> 
A health survey was conducted in a representative sample of adult males in British Columbia of all ages and occupations.
    
Mr. F. was included in the sample. He was selected by chance from the list of participants.

Which of the following statements is more probable? (check one)

# Mr. F. has had one or more heart attacks.
# Mr. F. has had one or more heart attacks and he is over 55 years old.</blockquote>

The probability of the conjunctions is never greater than that of its conjuncts. Therefore, the first choice is more probable.