“Linda is single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with the issue of discrimination and social justice. Which of the following is more probable: Linda participates in Neonazi rallies, or Linda participates in Neonazi rallies as a undercover mole?
Clearly when phrased that way, it seems to imply that the first half of the conjunction refers to participating in Neonazi rallies not as a mole, even though the logician says “Bwa ha, that’s not what I said!”
i meant the ontological fact that a female bank teller is going to be a few % more likely to be-or-not-be a feminist, than people on average.
the sentence structure is also important. for the record, i also hate things like this unless they’re explicitly presented as puzzles (i.e. meant to be smart-ass bullshit for smart-ass bullshitters, which is just fine imho).
however much of a fallacy this may or may not be, it seems more fallacious to take people’s poor performance on these “tests” as meaningful evidence about anything apart from these tests themselves.
I still wouldn’t make that mistake. But I guess that explains this:
During federally mandated yearly training, we are supposed to take all the tests over and over again until we get everything right.
So: a certain service is available 24 hours a day, 365 days a year, to all employees. The related test question is “This certain service is available 8am to 9pm Monday through Friday. True or False?”
The correct answer is obviously True, as per dictum de omnia, anything which is true of ALL hours and days is also true of ANY hours or days.
But the test software is programmed to only accept an answer of False. I assumed this was just due to a typographic error by the test administrator, and sent her a polite email warning that there was a bug in the test (I recommended strategically inserting the word “ONLY” into the question).
The test administrator bounced my email to the Director of Human Resources (a company Vice President who does not like me) who insisted that I was wrong, and the correct answer is False (presumably because if she buys kippers it will not rain, trout live in trees, and I do not love her any more).
This started an email exchange that ended with me refusing to answer the question incorrectly, and providing copious documentation referencing Aristotle, Boole, Kleene and the laws of thought and reason.
Eventually my boss did an end run around both of us, and somehow got the requirement for a perfect score on the test waived, and I posted the email exchange on my office door, where’s it’s been a year or so now.
I dated Linda and she can’t count money for shit so the bank thing is out. I think she’s down at City Hall doing something for Social Services or whatnot. She was a good cook, though.
Totally agree. And thus, 80% of people got the question right. It was the researchers who got the question wrong. Perhaps there should be an article about the “tricky superiority” fallacy or the “smug researcher” fallacy.
When I was a kid (like 4 or something) I drew some lines on a page in a pattern and then I drew over the lines with a different pattern and then I took it to my dad and said “tell me what the pattern is.” He of course told me the visible, topmost pattern, and I told him he was wrong. That’s what the researchers are doing here. They intentionally used language to obfuscate the answer, and in the process, ended up changing the question so much that they themselves were wrong.
Exactly, “is the store open -” is a common way to ask “are the store hours -”. It is less clear but widely used. If you take the question literally it would be easy to misinform someone by just saying yes.
I mean in a purely abstract logical sense, a sample group of one has only a single outcome. It will either be 100% heads or 100% tails. Probability only has meaning in the wider context of multiple flips. True you don’t know ahead of time the outcome of a single flip, but it’s still definitely going to be all one outcome. Bayesian probability applies only to distributions of events. It says nothing about a single event. It says that in a sample group of infinite coin tosses, the distribution of heads and tails will be 50/50, and so all finite sample group distributions of two tosses or more approaches that ratio. But a single toss has no distribution, it simply is whatever outcome it is. So it’s not exactly accurate to say one event has an outcome of a certain probability unless you mean compared to a wider sample group. More directly stated, a sample group of one has no ratio of outcomes.
Exactly! But that’s not how the thought experiment used to illustrate the fallacy is traditionally presented. It’s asking for the probability of her outcome, not her and her fellow tellers and/or feminists. As I said before, the fallacy is quite real, but the way the example is perpetuates a common misunderstanding about what a probability actually is. I admit, it’s a minor point, but that was the one I was making.
Actually I was thinking about Schrödinger’s cat and how most people misunderstand that thought experiment. Erwin Schrödinger presented that thought experiment as a way to illustrate how different Heisenberg’s quantum uncertainty principle was to the behavior of macroscopic objects. You see, if you really tried the Schrödinger’s cat experiment (and it’s worth nothing that experimental physicists have tried versions of it that didn’t involve risk to our feline overlords), decoherence would collapse the uncertainty of the uranium-sample decay before it ever influenced the observable outcome of the cat’s safety (whether or not that decoherence goes another way in a parallel universe is a separate debate).
there aren’t that many strict frequentists these days, but apparently there’s at least one.
the way that this question “should” be interpreted is something like “Assuming that one Linda is selected at uniform random from the population of all Americans named Linda and referred to as ‘her’, is it more likely…”
i’m not sure that single events are meaningless. mathematically, they are definitely well-defined. pragmatically, well, if an airline’s maiden flight crashes due to maintenance failure, i’m probably going to not plan on taking that airline.
Although my little digression towards stupidity was good reminder that P(x) is only known to be greater than or equal to P(x and y). If I change the question to “Is Linda more likely to be the Sun, or be the Sun and a feminist” then people are probably going to get the question right. In fact, the assumption that there is at least one bank teller is the fallacy from the very next episode, apparently:
Just remember when you accuse someone of a logical fallacy that assuming there is a bank teller is a logical fallacy (stating that there is a bank teller as an assumption is not and pointing out logical fallacies that can be remedied by adding assumptions that everyone agrees on is a dickheaded waste of time, but still, this is how logical fallacies work). People commit a lot of logical fallacies and get things right anyway (which goes back to my earlier statement that if logical were bridge engineering I’d stay off of bridges).
I understand that the authors of the Linda thought experiment meant her as a place holder for a set of many. The problem is that when I first heard that example as a student, and a lot of other examples in applied probability, I didn’t understand the functional difference between a set of one and a set of many, and sloppily worded examples like the Linda thought experiment reinforced my mistaken impression that one event outcome can have a probabilistic distribution. The main reason I think it matters is because it leads people to start thinking of probability as a force that can effect one event, rather than what it really is, a simple observation of how multiple outcomes will distribute under the influence of the complex forces shaping them.
yeah, statistics pedagogy is a festering cesspit. i’m sorry for your experience. there are genuine difficulties in that it’s really hard to always be precise and have textbooks be less than 3,000 pages long, but really we could be doing much better. part of the problem is that the people who do bother to speak precisely tend to become mathematicians and promptly lock themselves away in attics.
In context, it seems heavily implied that we’re supposed to judge the likelihood of Linda’s being a feminist bank teller relative to that of the background population.
Sorry, your nitpick seems predicated on an incredibly uncharitable reading of the problem. @anon50609448’s nitpick is more on point, IMO.
But beyond the problem of interpretation, your nitpick seems to give intuitively strange results. It seems like it prevents us from making any predictions about Linda’s behavior – whatever she does is what she does with no action being more probable than any other. But again, in context it seems intuitively more likely that she might eat breakfast and then commute to work than to put on a matador costume and bait neighborhood dogs with a red cape.
Humans are theoretically capable of undertaking many actions that they essentially have never and never will actually undertake – as a matter of fact, human behavior is heavily constrained, and our cognition in general relies on these constraints to make sense of the behavior of other human beings in general.
Demanding that people treat the behavior and/or identity of a particular human being (even in a hypothetical) as not being subject to probabilities for some obscure technical reason is contrary to human nature and all useful forms of reasoning about those topics.
