There usually is.
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The title of this post contains the false statement fallacy. You cannot avoid this “conjunction fallacy” because it is no fallacy. Regarding Kahnemann and Twersky, they committed fallacy of definition.
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"Linda is a bank teller or Linda is a bank teller AND is active in the feminist movement?”
The reason people get this wrong is that for the standard math to apply, the first possibility has to be read as “Linda is a bank teller (feminist affinities not specified).” However, in the context of the second option, the socially normal way to interpret the first possibility is "Linda is a bank teller AND is not active in the feminist movement.” Understood that way, both possibilities require multiplication. The problem is not that people don’t understand about the multiplication–it’s that they read the first statement as conveying information that it formally does not. This isn’t really an error in most everyday communication. This is because if someone meant the first option, they’d say something like, “The only thing I know about Linda these days is that she’s a bank teller.”
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[quote=“GulliverFoyle, post:15, topic:84178”]
Only if there is more than one of Linda. As long as there is only one of Linda, there is no such thing as a probability for what she is. Which is to say that probability only has meaning when there is more than one example of an outcome. When you flip a coin once, you don’t have an even chance of getting heads or tails, you have an absolute chance of getting the one and only outcome you get. You have to flip the coin at least twice to show a probabilistic distribution.[/quote]
Uh, this is really arguable along a number of lines. I don’t think a Bayesian would have any trouble calling this a probability. But maybe less obscurely, if I flip a coin, I can say I have an (approximately) equal chance if I consider the distribution of (e.g.) all coin flips that have ever happened or something similar – coins have been flipped before. And in Linda’s case, she is not the first to either be or not be a bank teller and or a feminist, so we can compare the likelihood of Linda being one or the other to the distribution of whether people in general fall into one or the other.
By having considered the problem before, my snarky friend.
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You’re being rational. That will never do.
That’s a rather odd way of looking at it.
I’m reminded of watching poker on TV (my mother likes watching the “Score Channel” which often shows poker).
In the bottom-right corner, it shows what each person’s hand is, and the probability each person will have the best hand if the hand makes it all of the way to the River. If you look at it your way, the channel (which isn’t showing the tournament live) should show “100%” on the person who is going to have the best hand, and “0%” on everyone else, because that’s what the actual probability of that person winning is.
Or, to take what you’re saying a step further, if you look at the universe through a deterministic point of view, there’s no such thing as probability. If I shuffle a deck, it has a 100% probability of ending up in whatever order it ends up, because the mechanism for shuffling is a function of the state that the universe was in when I started shuffling, and the laws of physics, with no randomness at all. You can have statistics, but not probability.
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As a programmer, when I hear a weatherman say it’ll snow “north and west of the city” I think that means “northwest”. The alternative is they mean “not southeast”.
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While I was in graduate school, a famous probabilist spent his last day of lecture (after an intensely technical introduction to his research) talking exactly about this. As pathological as these fallacies can be, a world without them would basically require some form of telepathy. Assumptions are necessary as long as we have to flap our gums to talk (world record for English speed-talking is ~650wpm, and English words have ~12 bits of entropy, so that’s 130bps compressed. sad!), and our limited attention spans don’t help either.
Back to the subject, the probabilist’s example was asking a politician whether crime has gone up or down. If the politician responds “Violent crime has gone down,” then logically you can infer either nothing, or that overall crime has gone down if you have more information (such as the overall proportion of violent crime to non-violent crime). However, most attentive listeners would at least begin to suspect that crime has, actually, increased, since otherwise the politician wouldn’t need to reframe the question. His opinion was that this is a legitimate problem for mathematical probability to work on; I’m not sure I agree with that, but it is haunting.
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in some sense this is correct, but fake probability sure does act a lot like real probability sometimes. there are practical and theoretical systems wherein it is impossible (or at least ridiculously difficult) to tell “truly random” apart from “the output of a deterministic but extremely complex procedure”.
that is, determinism alone would not be enough to make the universe boring; you would also need to be omniscient and capable of infinitely fast computation.
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TE;DR (no summary, just don’t read it, you’ve been warned (the E is for epistemological))
I disagree. Which is true, that I made it to work this morning (full stop) or that I made it to work this morning but I also died on the way, it’s just that I died with small enough probability that it isn’t worth worrying about in practical terms? The former is “true” according to a best-evidence idea of truth (I could easily test the hypothesis that I’m alive), and it’s unknowable according to a classical idea of truth (just like everything else is unknowable because that idea of truth has never been workable despite being the one that most people still appeal to) but could we use a probabilistic model of truth and would it be better than either of those?
I think a probabilistic idea of truth, which is process focused rather than outcome focused, is probably better at generating generalizable or predictive results. It’s the truth that says going all in on your 7-2 off was wrong even though you won. So whether a specific individual has a probability of being things or not depends on what function you’d like facts/truth to play.
No, I think the question is designed to trick people into misunderstanding the question. People don’t understand probability or what it means, and even if we asked them the question with an explicit spelling out of the first option, many would still get it wrong.
It’s not that haunting. Here’s a quick quote from the wikipedia on the conjunction fallacy:
For example, even choosing a very low probability of Linda 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 independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller). [Emphasis mine]
In reality virtually nothing (maybe literally nothing) is independent. What if being a feminist makes it more likely that Linda is a bank teller? It’s almost impossible to believe it doesn’t make it either more or less likely. Our intuition tells us that it shouldn’t make it so much more or less likely as to affect the outcome of the question, but that’s admitting that we can’t speculate about the answer to the question without employing intuition about the real world. There is no definitive fallacy. ETA: This is stupid stupidity, see @retchdog below.
In the case of the politician, our intuition about the world tells us that the reframing of the question is far from independent of the statistics. ETA: This is where the lack of independence of things matters.
Mathematics and logic do lots of work, but logic is actually really shitty at being a form of truth engineering for reality. If bridges collapsed as often as logic got us the wrong answer I would never set foot on a bridge. ETA: This is still very true.
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yes, there is a fallacy. independence is not necessary to construct it, though it does allow you to have concrete numbers, so it’s often used to teach the concept to the uneducated (note, uneducated does not mean stupid; it just means you haven’t recently taken a lot of math classes).
in more general form, note that Pr(Linda is a bank teller) = Pr(Linda is a bank teller and a feminist) + Pr(Linda is a bank teller and not a feminist). it doesn’t matter what dependence structure there is between “bank teller” and “feminist”. since probabilities are non-negative, Pr(Linda is a bank teller) is necessarily going to be at least as large as Pr(Linda is a bank teller and a feminist).
of course, this does assume that one cannot at the same time be both a feminist and not a feminist, but that’s a much weaker assumption than independence. i’m not being snarky to feminists in particular; the same concerns would be true for MRAs or whatever.
like, if i said “yeah, i smoke cigarettes, but i’m not a smoker,” or “i drink alcohol, but i’m not a drinker”, you’d probably understand what i meant. similarly, people say “yeah i’m a feminist, but i’m not a feminist”.
// not mansplaining; i just find this stuff interesting and am getting sucked into my own aspie bubble.
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Yup, don’t know what was going on in my head. At best the probability that Linda is a bank teller and a feminist is equal to the probability she is a bank teller and equality seems extremely unlikely (unless we work with an epistemology in which both are either 0 or 1 because they are settled facts about a specific case).
The politician thing with the crime rate is a very different question.
Depressingly, I find myself suspecting that part of the problem is that a lot of people simply do not really understand the difference between “and” and “or” at a deep level. They hear feminist and bank teller and the and is heard as additive without any relation to the actual conjunction.
The sentence structure matters for understanding what you’re answering.
Consider the (different!) question “do you think she has a cat, or a cat and a dog?”
I’d read that as the alternatives being “cat-only” and “cat+dog”.
Now with that in mind, consider “do you think it’s more likely that she has a cat, or that she has a cat and a dog”. I get how the technically correct parsing is that the former means exactly “has a cat”, but to read it like that instead of like “only has a cat” I’d need the proper context - like a statistics quiz.
Of course, I haven’t heard the episode yet, so maybe they address this. Besides, I don’t think this invalidates the fallacy described or the research done, it’s just a small niggle I’d like to see acknowledged. 
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Yeah, I’d go so far as to say that there it is not “technically” correct to read it as “has a cat” and not as “has only a cat”. Is the technically correct reading of “it’s raining cats and dogs” that cats and dogs are falling from the sky? Natural language just isn’t technical, there is no technical reading of it. I think it’s entirely fair to say, if asked, “Is it more likely she is a bank teller or a bank teller and a feminist” that the question means “Is it more likely she is bank teller and not a feminist or that she is bank teller and a feminist,” even over the objection of the person who asked it.
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It’s less well known than it’s Schoolhouse Rock counterpart; but I’ve always found securing a conjunction injunction to be a good way of stopping people from committing that fallacy. They also lose the ability to form sentences; but you can’t make a omelette without killing a few people, right?
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[quote=“theodore604, post:8, topic:84178”]
You really need that much info to explain why people get this wrong?[/quote]
Well, possibly. I mean, I don’t think I could ever natively model the structure of a mind that would get this wrong, since it’s so inutterably alien to my own.
Having the error explained to me is sort of interesting, although I have to take on faith that the explanation is correct, since I don’t see anything I’d call a valid proof.
It truly astounds me that the answer is not obvious to anyone minimally capable of functioning as a human adult. Seriously, I had no idea. I also write a lot of code, though, so maybe it’s my mind that’s abnormal.
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Northwest would be the resultant vector if you take north and west as components.
It’s the difference between a literal reading and “what would a person typically mean when saying these things”. If someone tells you a story with a lot of stereotypical descriptions, then it’s most likely either true or the setup for a joke. If someone asks you “a or a+b”, they typically mean “only a or a+b”. Going along with conversational standards makes communication easier, so it takes some conscious effort to break out and answer the literal question.
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Do they actually make it all the time, or just when asked these kinds of questions?
What examples are there of people actually committing this fallacy in real life.
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