Monday, January 30, 2012

In Defense of Critical Thinking

Steve wrote a couple of articles on Daniel Kahneman’s book, Thinking Fast, Thinking Slow:

Most of the experiments recounted in Thinking, Fast and Slow aren’t as prima facie silly, but Kahneman, a literal-minded soul, often seems to miss the fundamental point of why his subjects fall for his little hoaxes so often:

“Steve is very shy and withdrawn, invariably helpful but with little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure and a passion for detail.

“Is Steve more likely to be a librarian or a farmer?”

Wrong! Kahneman scoffs at your intuition: “Did it occur to you that there are more than 20 male farmers for each male librarian in the United States?”

Well, no, actually, I didn’t know.  Come to think of it, nor do I know the measured frequency of the traits listed among either farmers or librarians.  Give me that information, and I can calculate the conditional probabilities.  As it is, though, the only correct answer to the question as written is:  insufficient information.

Steve continues:

Did it occur to Kahneman that anybody who isn’t trying to deceive us would have added, “So, Steve’s just not cut out for his life of slopping hogs” or the like? As con men, conjurors, and comedians demonstrated long before Kahneman, most people trust in the speaker’s good faith. They play along and try to guess what is being implied. So it’s easy to pull the rug out from under us.

Yes, but there is still such a thing a critical thinking.  For instance, here is another Kahneman problem from Michael Lewis’ Vanity Fair review that Steve quotes:

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

Which alternative is more probable?

(1) Linda is a bank teller.
(2) Linda is a bank teller and is active in the feminist movement.

The vast majority—roughly 85 percent—of the people they asked opted for No. 2, even though No. 2 is logically impossible. (If No. 2 is true, so is No. 1.)  The human mind is so wedded to stereotypes and so distracted by vivid descriptions that it will seize upon them, even when they defy logic, rather than upon truly relevant facts. Kahneman and Tversky called this logical error the “conjunction fallacy.”

Well said, and I would add that this is exactly the kind of problem that tests use to measure critical thinking skills.  Unfortunately, Kahneman mixes bogus problems like the first in with true logic challenges like the second in an effort to show that stereotypes are worthless.

7 comments:

samsonsjawbone said...

Which alternative is more probable?

(1) Linda is a bank teller.
(2) Linda is a bank teller and is active in the feminist movement.

The vast majority—roughly 85 percent—of the people they asked opted for No. 2, even though No. 2 is logically impossible. (If No. 2 is true, so is No. 1.)


This is not true (or is phrased *very* poorly). Either Linda is JUST a bank teller, or she is a bank teller AND a feminist. I'm not inspired to read the rest of the article.

Dr. Φ said...

The question is worded correctly. Option 1 is Not "Just a bank teller" as in "a bank teller and not a feminist". The set "bank tellers" necessarily includes both feminist and non-feminist bank tellers.

trumwill said...

For the second question, the issue is whether or not the word "just" can be safely inferred. Am I to wear my LSAT hat or my English As It Is Generally Used hat. There is value in the LSAT hat, of course, though if you try to pull that in an every day conversation, you will likely get a "What the hell is wrong you?" sort of response.

It's only partially an issue of stereotypes. A lot of it is reading the precise wording of the question (Which alternative is more probable vs Which alternative is probably more accurate) and the precise wording of the answers (Linda is a bank teller vs Linda is just a bank teller).

Credit where credit is due: I got it wrong. It's 2am and I wasn't wearing my LSAT hat.

samsonsjawbone said...

The question is worded correctly. Option 1 is Not "Just a bank teller" as in "a bank teller and not a feminist".

Then the question (as the writer acknowledges! Cripes!) "Which alternative is more probable?" is nonsensical. Thus:

For the second question, the issue is whether or not the word "just" can be safely inferred.

Yes, Will, that is exactly the issue, and the answer is, "OF COURSE it can be inferred - not only can, but *should* be, otherwise the question doesn't make sense." When something seems not to make sense, we feel free to make necessary inferences; this is how language WORKS, and only quasi-autistic retards (or people desperate to show off how LSAT-smart they are - sometimes the same people) would think otherwise.

In fact, my reaction shows precisely why it's not a very good trick question: if most readers are going to answer "wrongly" because they see the trick and therefore make a necessary inference, the thing is poorly done.

I think I've had my say.

Dr. Φ said...

I've never taken the LSAT, but this is pretty elementary set theory. Venn diagrams and stuff.

There may be a case to be made that the question requires the reader to discern what particular trick the tester is trying to play, but that case is pretty weak. For instance, reading comprehension questions on standardized tests often ask the test taker to draw inferences from a passage, but to my recollection they ask for inferences pretty specifically. Critical thinking tests, in contrast, usually require knowledge of probability, statistics, and verbal logic.

The main problem with Khanamen's tests questions is that they mix good questions with bogus ones.

samsonsjawbone said...

Wiki offers a *much* better explanation of the mathematics of the problem:

85% of those asked chose option 2.[2] However the probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone—formally, for two events A and B this inequality could be written as [XXXX, and YYYY]

Right. The chance of X event happening is always greater than the chance of X *and* some other event. That is basic statistics.

But it doesn't say what the Vanity Fair article said - that (2) is "logically impossible". And this is where Wiki vindicates me (in my opinion :) ):

Gerd Gigerenzer presents a different take on the conjunction fallacy,[4] and claims that the problem doesn't necessarily lie with the participants, but with the way the question is phrased...

... Readers are sensitive to the different meanings of words, and can understand probabilistic reasoning very well if presented in a more concrete way (like natural frequencies: 1 out of 100 persons instead of 1%). According to Gigerenzer this demonstrates intelligent context-sensitive reasoning.


Right. The confusing part of the VF article is the word "alternative":

a choice limited to one of two or more possibilities... the selection of which precludes any other possibility

If picking an answer precludes the other answer, then my inference *must* be drawn. I've satisfied myself on this, at any rate.

trumwill said...

When I was studying for the LSAT, the thing that jumped out at me was "Read the questions literally and carefully!"

With a conversational hat, if someone says "Pick a whole number between 1 and 3" you have three options.

With the LSAT hat, and the same question, the only answer is 2.

And despite knowing this, I would say 50% of the logics questions I missed on pre-tests were due to an inaccurate reading of the question. Reading "probably the most accurate" rather than "most probable."

None of this is to say that the question, and the line of inquiry, are not valuable. Merely that some of the 85% that got it wrong did so at least partially by assuming a different question than the one asked, or by assuming things of the answer options that weren't there.