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)

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.

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)