Talk:Conjunction fallacy

Currently, this is confused:

(a) I assume it should read 85% choose 2, or there is no point here (b) the later wording 'people get this problem' is ambiguous - could mean people do see the point.

Charles Matthews 18:01, 17 Jun 2004 (UTC)

Yes, yes I fixed these after re-reading. --Taak 18:28, 17 Jun 2004 (UTC)

Remove Assumption of Independence

$Pr(A\land B)=Pr(A)Pr(B|A)\leq Pr(A)$ I didn't post it properly merely because I don't know if this is the right place for it. If you all want it, there it is. "Pr(B|A)" is read "The probability of B given A". Mo Anabre 17:43, 2 May 2007 (UTC)

Where most people go wrong

I think the example given doesn't really demonstrate a fallacy so much as the way wording can confuse an issue. Clearly, from a probability standpoint, "Linda is a bank teller" must be more probable than "Linda is a bank teller and is active in the feminist movement". However, when presented with the two choices, people may assume that the first option, "Linda is a bank teller", is meant to be "Linda is just a bank teller" (i.e., Linda is a bank teller but is not involved with the feminist movement). In other words, the real fallacy may not be one of conjunction but one of reading too much into the way it's worded. - furrykef (Talk at me) 01:40, 4 February 2006 (UTC)

This is EXACTLY the problem. ---Dagme (talk) 17:38, 7 February 2013 (UTC)

Wording confuses the issue BECAUSE people are prone to the conjunction fallacy. Hanxu9 (talk) 12:58, 23 June 2012 (UTC)

I read about this objection before, and I've seen that studies have been made to show that even eliminating the possibility of that error didn't prevent people from committing the fallacy. When I find the specific info I'll add it to the article, if it's appropriate. Rbarreira 12:20, 1 August 2006 (UTC)

The example given in the article Re. the soviet invasion of poland already demonstrates that there is no ambiguity, in my opinion. Jimhsu77479 (talk) 20:28, 25 January 2009 (UTC)

In other words, 85% of people believe both in the "researchers don't ask stupid questions" fallacy (and so assume that option 1 implies that Linda doesn't actively participate in the feminist movement) and that Linda is more likely to be both a bank teller and a feminist than a bank teller and not a feminist.

I think what may be happening here is that people are simply not answering the question "which is more probable?" - rather, they're picking the "best" answer, where "best" is an admittedly vague notion but has more relevance in the real world.

For example, imagine you're investigating a case which depends on you finding out whatever you can about Linda. You've got a bunch of data suggesting she's a feminist; you've got very little data suggesting she's a bank teller - you're going to go with the option that includes her being a feminist - if that option also includes her being a bank teller, so be it. If it turns out later that she's not actually a bank teller at all, no problem, you'll just discard that part of the option you chose earlier. Yes, I realize this means people are not technically following the rules of the experiment, but after all, the intention is to find out how people think, right? So I don't think it's so much a logical fallacy but rather that people make an unspoken assumption about the intent behind analyzing the data and choose their answer based on that. Branchc (talk) 19:39, 20 June 2012 (UTC)

You're right that it's how people think, and you want to keep in mind that cognitive biases (a/k/a rules of thumb) are usually correct in our day-to-day lives. It's only rarely that they are incorrect, as in the Linda example. That's what makes them so interesting to study. Hanxu9 (talk) 12:57, 23 June 2012 (UTC)

But the reasoning you've set out here - "You've got a bunch of data suggesting she's a feminist; you've got very little data suggesting she's a bank teller - you're going to go with the option that includes her being a feminist - if that option also includes her being a bank teller, so be it." is the conjunction fallacy. The demonstrated fact that this line of reasoning appeals to people is the phenomenon of interest. MartinPoulter (talk) 13:18, 24 June 2012 (UTC)

I agree that what you've quoted is technically the fallacy, but I'm saying more than that this line of reasoning appeals to people - I'm saying that it really is the best line of reasoning in most real-world scenarios, sort of like Hanxu9 said. So the phenomenon of interest applies only to these precisely framed examples. And the conclusion is pretty clear - our mental faculties evolved to deal with real-world scenarios, and we've only recently begun applying them to things like pure logic and thought experiments. Branchc (talk) 19:55, 24 June 2012 (UTC)

Please correct me if I'm wrong, but this seems to be the experiment conducted by Tversky and Kahneman:

     Linda is a feminist. Please tell us which is more probable:
        1) Linda is a bank teller.
        2) Linda is a bank teller and a feminist.

If the problem is in the definition of the word "feminist", then this was a badly designed test. (EveningStarNM) 16:07, 28 November 2015 (UTC)

The question could have been framed as:

what is more probable?

a. Linda is a feminist and

b. Linda is a feminist and a bank teller.

Almost, everyone should answer the question correctly. Because people think of it as a probability question. The one actually asked was more of a "leading question" to prove the so called "conjunction fallacy". Human brain discards a lot of garbage in communication. The "banker" option was more of a "garbage discarded" than a "miscalculated probability". — Preceding unsigned comment added by 182.70.12.154 (talk) 16:08, 23 June 2016 (UTC)

No Paradox here

There is no reason to call this a paradox, as the material requirements for a paradox do not occur. While it is true that people would not expect that each representative (but less than certain) conjunction would reduce the probability; the fact that the probability itself is diminished is not paradoxical, as demonstrated easily in the example given on this page. In the mathematical proof of the example, it is explicitly demonstrated that no such paradox occurs.

Just because something violates the expectations of the reader does not make it a paradox, but rather sets it up closer to irony, than a paradox. --Puellanivis 04:42, 30 July 2006 (UTC)

'...this inequality...'

Is it just me, or does the inequality 'Pr(A) > Pr(A^B) < Pr(B)' look un-mathematical, due to the conflicting directions of the inequalities? When you write 'A<B<C', this is valid because A<B, B<C, and A<C all hold simultaneously; but in a form like 'A>B<C', what implication does that make for A and C? I think the statement should be changed to read that the probability of the conjunction is less than or equal to the MINIMUM of the set {P(A), P(B)}.

There's another problem too. Just before the formula, the article links to Boole's_inequality, which describes a completely different (albeit similar sounding) concept.129.2.167.219 (talk) 23:41, 3 November 2009 (UTC)

Okay so I just rewrote the inequality using two different formula, and removed the link, hopefully the meaning is still clear. This article could use some extra cleaning up, but I don't know *anything* about the quantum stuff that is written below the break. I'm not sure what someone could do to make it fit in better with the rest of the article.129.2.167.219 (talk) 23:53, 3 November 2009 (UTC)

Pr(Linda is just a bank teller and not involved in feminism|Linda was a philosophy major)

It seems as if this fallacy is wrong, and I wonder if this criticism has come up: people are assuming that they are asking what the probability is that Linda is just a bank teller given that she majored in philosophy and is concerned about issues. Also, that "and" or "or" misunderstanding is likely as well. I'd like to see some studies cited, because clearly there's a lot of room for criticism here. It's likely that if you looked at female philosophy majors, the probability that these women are involved in feminism is higher than the probability that they are not. OptimistBen | talk - contribs 19:24, 25 April 2008 (UTC)

• see [1] and [2] --Taak (talk) 16:13, 26 April 2008 (UTC)

"However, mathematically, the probability of two events occurring together (in "conjunction") will always be less than or equal to the probability of either one occurring alone."

I don't think it's necessarily true that the conjunction of two events is always less/equal to the probability of either occuring alone. For instance, which is more likely:

a) I get struck in the stomach very hard.
b) I get struck in the stomach very hard and my stomach hurts.

the problem with this analogy is that a is related to b. i agree with you, but the analogy is a false analogy. make a unrelated to b and then test your argument.

Clearly, b) is more likely, right? I understand the import of the experiment, I was just confused by this sentence. Or is a) not meant to imply that my stomach doesn't hurt? —Preceding unsigned comment added by 204.69.190.75 (talk) 21:00, 1 February 2009 (UTC)

premise- i only eat candy canes

which is more probable

"i am a banker whether or not i am unhealthy"

" i am a banker and i am unhealthy."

it seems to me that the whole experiment suffers from the fallacy of contradiction(on 2 levels), the fallacy of complex question, the exploitation of the problem of vacuous truth, the non-sequitur, and incoherence.

contradiction 1- the first statement is not a cunjunctive statement and is a conjunctive statement simultaneously.

contradiction 2- in the first statement "I am unhealthy" is permenently irrelevant while simultameously being asked what its probobality is.

complex question- yes or no=> banker/unhealthy-irrelevant vs banker/unhealthy-certain?

vacuous truth-"whether or not" assumes you're not allowed to include the probability that i am not unhealthy. in what reality is that rule plausible?

non-sequitur- i am a banker

incoherence-(i am a banker whether or not i am unhealthy)=P and (i am a banker)=P. both do not equal p unless statement 2 can be "i am a banker whether or not i am unhealthy and i am unhealthy." both do not equal p unless statement 1 can be "i am a banker whether or not i am unhealthy and i am not unhealthy" what if we know for a fact that i am a banker? now what? the first statement is irrational because (whether or not) has no value. what is the probability that i am a banker and i am unhealthy when i am a banker is known to be true? Either i'm healthy, or i'm not healthy-but i'm never "whether or not". the problem is that 85% of people are trying to give a rational answer to an irrational question. The math is crude because it can't take into account the "whether or not" statement. —Preceding unsigned comment added by 76.15.29.209 (talk) 05:52, 2 July 2009 (UTC)

premise- i am a one legged duck

"i have no feathers whether or not i swim in circles"

"i have no feathers and i swim in circles"

of course i swim in circles! we know i swim in circles! "whether or not i swim in circles"? what? it's like saying the negative square root. did you just make a rule that i have to pretend; in statement one; that i can't beg the question, "do i swim in circles?" when i already know that i do swim in circles? simultaneously you're expecting me to beg the question in statement 2. i'm not allowed to beg the question in statement 1 and must beg the question in statement 2, all while working out the probability of statement 2 vs the unknown quantity in statement 1.

which has a greater probability?

"i have no feathers and ?"

"i have no feathers and i swim in circles"

participants shall not account for "?" in statement 1, and the equation will also not account for "?" (because we don't know how, so we just leave it blank). —Preceding unsigned comment added by 76.15.29.209 (talk) 06:23, 2 July 2009 (UTC)

I'm not sure what to make of the above dialog, but yes, it's always true. It should be easy to see why it's always at least equal. If someone is "a banker, and X" then clearly they must also be "a banker." It's not the same as comparing "a banker and X" to "a banker and not X," which is a separate question entirely. 129.2.167.219 (talk) 23:59, 3 November 2009 (UTC)

OR?

Does the section on Quantum ... qualify as OR? I see that, in the page's history, a user who shares a name with the author of the arxiv reference has added that section. Besides, it doesn't appear to add anything beyond the original mathematical discussion. I say this from the point of view of someone who has taken graduate classes in both areas (probability, quantum mechanics). 99.155.53.151 (talk) 09:21, 1 August 2009 (UTC)

Seems that it contradicts the mainstream treatment of the effect, is based on a WP:SPS and violates WP:COI. It needs to go. A more mainstream explanation would invoke Attribute substitution. MartinPoulter (talk) 12:18, 31 May 2010 (UTC)

Soviet Relations Example Not an Example

Simply put, the two possibilities are not independent. The Soviet Union invading Poland modifies the likelihood of the United States breaking off relationship with the Soviet Union. Suppose the unmodified chance of the United States breaking off ties with the Soviet Union to be 1%, while the chance of the Soviet Union invading Poland to be 50%, and the chance of the United States breaking relations with the Soviet Union given that the Soviet Union invaded Poland to be 90%. 90% x 50% is 45%, much higher than the unmodified chance. — Preceding unsigned comment added by 75.129.102.8 (talk) 08:16, 16 July 2011 (UTC)

the "given that" is not part of the logic of the question. it says breaking off relations "and" an invasion of poland. It's a conjunction, not a conditional. Taak (talk) 08:32, 6 March 2012 (UTC)

Taak has it right here. The wording in the article is correct. Going by all the comments in this Talk page, it looks like there is a major obstacle to people understanding the conjunction fallacy, which is the conjunction fallacy itself: we show people examples of fallacious reasoning, but they don't see the problem because that's the way they're used to thinking. MartinPoulter (talk) 13:32, 24 June 2012 (UTC)

formal or informal fallacy?

The page List of Fallacies categorizes the Conjunction fallacy a formal fallacy while here it is listed as an informal fallacy. Which one is it? 155.105.7.43 (talk) 18:30, 11 December 2012 (UTC)

Merger discussion

Base rate fallacy is not the same thing as conjunction fallacy, though base rate fallacy may be one explanation for conjunction fallacy. Conjunction fallacy involves saying that A&B is more likely than A but this is not part of the definition of base rate fallacy. MartinPoulter (talk) 10:33, 2 September 2013 (UTC)

Other possibility

"Linda is a bank teller and activist" is chosen because being an activist is important and actually relates to one's opinion of her whereas being a bank teller or not is sort of irrelevant to just about any discussion about Linda; a lot less relevant than her other info. The bank teller stuff is just ignored because it's boring. — Preceding unsigned comment added by Benvhoff (talk • contribs) 10:29, 21 August 2016 (UTC)

Error in section Other demonstrations?

Currently it states "The die will be rolled 20 times". This conflicts with the presented series of length 5 or length 6. I suggest to reword to "The die will be rolled several times". --tomaschwutz (talk) 07:13, 10 August 2017 (UTC)

"Huang's theory of conditions"

@Sanketio31: Can you explain this edit? User:Deuteroscopy found what seems to be vandalism and removed it. You not only undid that edit; you posted a vandalism warning on the user's Talk page. Removing vandalism isn't "unconstructive editing". Have you any evidence that the term "Huang's theory of conditions" isn't an invention by the anonymous editor who added it? @Deuteroscopy: thanks for taking action to improve the article. MartinPoulter (talk) 14:40, 12 April 2021 (UTC)