Editing Conjunction fallacy (section)

==Definition and basic example== 
{{quote box|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."|[[Stephen J. Gould]]<ref name="Gould (1988)">{{cite news|last=Gould|first=Stephen J.|title=The Streak of Streaks|url=http://www.nybooks.com/articles/archives/1988/aug/18/the-streak-of-streaks/?pagination=false|newspaper=The New York Review of Books|year=1988}}</ref>|width=25%|align=right}}

The most often-cited example of this fallacy originated with [[Amos Tversky]] and [[Daniel Kahneman]].<ref name="tk83" /><ref name="tk81">{{cite report |last1=Tversky |first1=Amos |last2=Kahneman |first2=Daniel |year=1981 |title=Judgments of and by representativeness |  publisher  = Stanford University }}</ref><ref name="Tversky & Kahneman 1982">{{cite book |last1=Tversky |first1=A. |last2=Kahneman |first2=D. |year=1982 |chapter=Judgments of and by representativeness |editor-first=D. |editor-last=Kahneman |editor2-first=P. |editor2-last=Slovic |editor3-first=A. |editor3-last=Tversky |title=Judgment under uncertainty: Heuristics and biases |location=Cambridge, UK |publisher=Cambridge University Press |isbn=0-521-28414-7 }}</ref>

<blockquote>''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 anti-nuclear demonstrations.''

Which is more probable?
# Linda is a bank teller.
# Linda is a bank teller and is active in the feminist movement.</blockquote>

The majority of those asked chose option 2. However, this is logically impossible: if Linda is a bank teller active in the feminist movement, then she is a bank teller. Therefore, it is impossible for 2 to be true while 1 is false, so the probabilities are at most equal.

More generally, the [[probability]] of two events occurring together (that is, in conjunction) is always less than or equal to the probability of either one occurring itself. For two events ''A'' and ''B'' this inequality can be written as <math>\Pr(A \land B) \leq \Pr(A)</math>.

For example, even choosing a very low probability of Linda's being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming [[statistical independence|these two facts are independent of each other]], Pr(Linda is a bank teller ''and'' Linda is a feminist)&nbsp;= 0.05&nbsp;×&nbsp;0.95 or&nbsp;0.0475, lower than Pr(Linda is a bank teller).

Tversky and Kahneman argue that most people get this problem wrong because they use a [[heuristics in judgment and decision making|heuristic]] (an easily calculated) procedure called [[representativeness heuristic|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.<ref name="tk83">{{Cite journal |last1=Tversky |first1=Amos |last2=Kahneman |first2=Daniel |date=October 1983 |title=Extension versus intuitive reasoning: The conjunction fallacy in probability judgment |journal=[[Psychological Review]] |volume=90 |issue=4 |pages=293–315 |url=http://content2.apa.org/journals/rev/90/4/293 |archive-url=https://archive.today/20130223193247/http://content2.apa.org/journals/rev/90/4/293 |url-status=dead |archive-date=2013-02-23 |doi=10.1037/0033-295X.90.4.293 |url-access=subscription }}</ref>

In other demonstrations, they argued that a specific scenario seemed more likely because of representativeness, but each added detail would actually make the scenario less and less likely. In this way it could be similar to the [[misleading vividness]] fallacy. More recently, Kahneman has argued that the conjunction fallacy is a type of [[extension neglect]].<ref>{{cite book |last=Kahneman |first=Daniel |year=2000 |chapter=Evaluation by moments, past and future |editor-first=Daniel |editor-last=Kahneman |editor2-first=Amos |editor2-last=Tversky |title=Choices, Values and Frames |publisher=Cambridge University Press |isbn=0-521-62749-4 }}</ref>