And a follow-up on the follow-up. Here is an idea for how to quantify the conjunction fallacy experimentally. Present the subjects with the standard “Linda” story:

Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

But now, instead of asking them to choose the more probable outcome from the two standard options, (1) Linda is a bank teller (2) Linda is a bank teller and is active in the feminist movement, why not ask them to select from a longer list:

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.
3. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college.
4. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college and owns cats.
5. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college and owns cats and is overweight.
6. …

What is the conjunction size at which the subject begins to realize that increasing the specificity of the outcome is making it less likely?

 

Following up, I’m going to hazard a psychological explanation of the conjunction fallacy. When presented the choices, “(1) Linda is a bank teller (2) Linda is a bank teller and is active in the feminist movement”, here is what I think happens in the subject’s mind. Upon encountering (2), I conjecture that the subject re-interprets (1) as “Linda is a bank teller and not active in the feminist movement”. There must be some clever experiment to verify this empirically. If this is what’s actually happening, then whatever is faulty is not the probabilistic reasoning. Of the two (new) conjunctions, (2) could indeed well be more probable.

I suspect that untrained people’s poor performance in probability stems from a more basic incompetence in logic. Ask a random adult, “What’s the opposite of ‘always’?” I’ll bet most people will blurt out, “Never”. Now there’s the issue of how one interprets opposite, which I take to mean logical negation. In that case, the correct answer is not always rather than never. Setting this up as a clean experiment is a bit of a challenge. Using my wording with “opposite” invites criticism on the grounds of ambiguity. Using the more precise “logical negation” might be judged as technical and arcane. If anyone can phrase the question in a way that’s both natural and unambiguous, I’d be curious to know.

In the past, Steve Sailer had done a superb job taking the overrated Malcolm Gladwell down a notch or two. More recently, he’s been aiming his salvos at Daniel Kahneman of the Thinking, Fast and Slow — and of course, Nobel — fame.

Sailer:

Kahneman’s most celebrated shtick is to ask questions that are stupider than people expect him to ask, so they interpret them in a more intelligent fashion than they literally are, and then he says, “Gotcha! I wasn’t asking about the per capita murder rate like you assumed I must be, I was asking a dumber question than that. Burn on you!”

In other words, another wiley Jew is deceiving trusting gentiles with his shtick. How on earth could the notorious Judeophile Sailer stumble upon a pungent trope like that?

There’s also some sniping at the academia in general: “it’s people assuming that the professors wouldn’t be wasting their time with a lot of contrived details simply in order to play a lowbrow trick on them”. In some cases, the criticism is justified. Consider the example of Jack. Perhaps Sailer (or much of his audience) lacks the language to make this precise, so I will. This is a textbook example of confusion between marginal (a priori) probability and conditional probability. If I don’t know anything about Jack, his probability of being an engineer is 30%. As I learn more and more engineery things about him, the probability of him being an engineer conditioned on this additional knowledge increases. I fully agree with Sailer that by providing this additional information, Kahneman and Tversky intentionally prodded the subject toward the latter. [Of course, I would’ve smelled a rat. The only thing we are given hard numbers for is the proportion of engineers; we don’t know anything about the joint distribution of the other engineery properties. For example, it might be the case that everyone in the group satisfies Jack’s engineery description — and then the additional knowledge doesn’t change Jack’s conditional probability of being an engineer at all. This lack of additional quantitative information would have forced me to grudgingly choose the “correct” answer.]

In other cases, Sailer is completely off. A case in point is the “conjunction fallacy,” illustrated by the story of Linda. “Linda is thirty-one years old, single, outspoken, and very bright […] She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.” Question: “Which alternative is more probable? (1) Linda is a bank teller. (2) Linda is a bank teller and is active in the feminist movement.” Sorry Steve, no matter what philosophical approach to probability you happen to subscribe to, it is never the case that the probability of A and B is greater than the probability of A. I think that the conjunction fallacy is completely real, and is simply yet another illustration (out of many) of how ill-suited untrained human intuition is for probability.

We close on a note of J’accuse.

Everybody was amazed to discover from Kahneman that undergrads fall for a bunch of gags that were surefire ways to fool folks in vaudeville days. Why? Because when Dr. Kahneman tells a story contrived to pull the rug out from under psych majors, it is Science.

This passage prompted me to go ahead order the book. Actually, I didn’t have to; it’s right there in the Introduction (use Amazon’s “look inside” option):

We prepared a survey that included realistic scenarios of statistical issues that arise in research. Amos (Tversky) collected the responses of a group of expert participants in a meeting of the Society of Mathematical Psychology, including the authors of two statistical textbooks. As expected, we found that our expert colleagues, like us, greatly exaggerated the likelihood that the original result of an experiment would be successfully replicated even with a small sample. They also gave very poor advice to a fictitious graduate student about the number of observations she needed to collect. Even statisticians were not good intuitive statisticians.

So Sailer’s characterization of Kahneman and Tversky’s research as “undergrads fall for a bunch of gags” is scandalously, libelously wrong. Such gross misrepresentation is out of character for the normally factually careful Steve Sailer; I expect him to retract that claim and issue a correction.

Like all publications on the right side of history, Scientific American can’t get enough of diversity. You wouldn’t know it from their recent spate of Trump-derangement hysteria — Donald Trump’s Lack of Respect for Science Is Alarming (September 1, 2016); What Trump’s Surprise Victory Could Mean for Science (November 9, 2016); Science and the Trump Presidency (November 27, 2016), etc.

I’m not for a moment suggesting any sort of intellectual diversity — certainly not, Heaven forbid, soliciting a pro-Trump scientist’s viewpoint. But how about some diversity in the headlines, folks?

Our beef is actually with an older piece, from the blissful pre-Trump era, titled “How Diversity Makes Us Smarter”. It starts with the usual slight-of-hand conflating diversity of expertise with the more vibrant kind:

It seems obvious that a group of people with diverse individual expertise would be better than a homogeneous group at solving complex, nonroutine problems. It is less obvious that social diversity should work in the same way—yet the science shows that it does.

Why yes, it does seem obvious. A team of scientists struggling to cure cancer would be wise to cast a wide net of knowledge: recruit physicists, chemists, maybe even mathematicians. They’ll at the very least do no harm and might just provide that missing link.

How this extends to racial, gender and all-the-other-kinds-of bean-counting is far less obvious. Scientific American is happy to educate us that in fact it does:

Racial diversity can deliver the same kinds of benefits. In a study conducted in 2003, Orlando Richard, a professor of management at the University of Texas at Dallas, and his colleagues surveyed executives at 177 national banks in the U.S., then put together a database comparing financial performance, racial diversity and the emphasis the bank presidents put on innovation. For innovation-focused banks, increases in racial diversity were clearly related to enhanced financial performance.

Who are we to argue with Science?! And yet this diversity-as-a-boon claim
fails the PTT diffusion gradient™ test. Look, if there’s one thing bankers understand, it’s how to make a profit. If racial diversity indeed provided a financial advantage — even a slight one — I am fully confident that the Wall Street sharks would have (1) discovered this decades ago (2) leveraged this knowledge like crazy in hiring. Anytime we need to be told (over and over again) how beneficial something is despite all evidence to the contrary, wethinks the lady doth protest too much.

And evidence to the contrary there is aplenty. You can read John Derbyshire’s fascinating account of social scientist Robert Putnam‘s reluctant  discoveries concerning the deleterious social effects of diversity. Not a word about any of that in Scientific American’s cheery article, of course. Science is swell, but trust me comrade, you do not want to end up on the wrong side of history.

Just in time for New Year’s. Aww:

One man has spent years befriending KKK members and persuaded 200 of them to leave the hate group

The real question is, where did this guy manage to find 200 actual KKKlansmen? Would he mind sharing some with the producers of this fake cancelled documentary?

KKK Leaders Allege Producers Paid Them to Fake Scenes in Canceled A&E Documentary

There’s a whole genre out there of videos purporting to “document” street “harassment” of women by random men. The dubious terms are put in quotation marks since (1) these things tend to reek of being staged and (2) most of the harassment is of the unwanted compliment type, which is setting a pretty low bar. The latest specimen to show up on my social media is this one. The comments were (but of course) nothing but you-go-girl, and an informal survey of the commentators confirms once again that the women most outraged by street compliments from strangers are precisely in the lowest-risk group of receiving them.

Here at PTT we try to resist the temptation to paint our opponents as idiots. It’s usually a weak man’s cop-out to impugn the character or intelligence of his opponent rather than attack his ideas. Still, in light of this WaPo grudging admission that Trump is shaping up to be a sensible, competent executive, methinks the time is ripe to call out the hysterical spaz-cases — who’d chosen to howl at an imaginary toothbrush moustache rather than discuss Trump’s very real flaws — for what they are: idiots. And here’s a prediction you can take to the bank: not one of these wretched souls will have the integrity to walk back their embarrassing hysteria.