cursed comments on Open Thread, Jul. 6 - Jul. 12, 2015 - Less Wrong

5 Post author: MrMind 06 July 2015 07:31AM

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Comment author: cursed 07 July 2015 05:31:59AM 2 points [-]

Whenever the conjunction fallacy is brought up, it always irks me, because it doesn't seem like a real fallacy. In the example given by Rationality A to Z, "[...] found that experimental subjects consdiered it less likely that a strong tennis player would lose the first set than he would lose the first set but win the match."

There's two valid interpretations of this statement here:

1) The fallacious interpretation: P(Lose First Set) < P(Lose First Set and Win Match)

2) P(Lose First Set) < P(Win Match | Lose First Set), which is a valid and not necessarily fallacious reasoning, given the context that the tennis player is considered strong. Another possible phrasing of "he would lose the first set but win the match" is "given that he lost his first set, what's the chance of him winning the match?"

Has this been addressed before?

Comment author: lfghjkl 07 July 2015 06:04:41AM 9 points [-]

Looks like it has been addressed in Conjunction Controversy (Or, How They Nail It Down):

A further experiment is also discussed in Tversky and Kahneman (1983) in which 93 subjects rated the probability that Bjorn Borg, a strong tennis player, would in the Wimbledon finals "win the match", "lose the first set", "lose the first set but win the match", and "win the first set but lose the match". The conjunction fallacy was expressed: "lose the first set but win the match" was ranked more probable than"lose the first set". Subjects were also asked to verify whether various strings of wins and losses would count as an extensional example of each case, and indeed, subjects were interpreting the cases as conjuncts which were satisfied iff both constituents were satisfied, and not interpreting them as material implications, conditional statements, or disjunctions; also, constituent B was not interpreted to exclude constituent A. The genius of this experiment was that researchers could directly test what subjects thought was the meaning of each proposition, ruling out a very large class of misunderstandings.

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