The Linda Problem

Reading a review of Daniel Kahneman's Thinking, Fast and Slow, I ran across this problem which resonated with me: You are asked a simple question about Linda, who you are told is an imaginary woman who as a student was deeply moved by concerns about discrimination and social justice. You are asked which is more probable: A/ Linda is a bank teller B/Linda is a bank teller who is active in the feminist movement.
Of course, the answer is A, because adding the detail can only lower the probability. Any engineer or math major will choose A.
I would have taken B, knowing the answer is A. This is why I could never score 800 on my SAT exams. I would have answered B because: 1/ It is the more interesting answer. 2/ It indicates I can infer something about Linda from the extra information about her, even if what I infer may be wrong, it provides a more interesting working hypothesis. 3/ It shows I was thinking about Linda and wanted to know more about her.

It is also an attempt to spit in the eye of the obvious.

I also got questions wrong like: Does England have a Fourth of July? Now, of course, I knew, England uses the same calendar we do, but when you capitalize the Fourth, then you are talking about our American holiday celebrating what England might not be expected to celebrate, i.e., our independence from England. Answering "no" indicates I have thought beyond the literal to the implied. Would England be celebrating this holiday? Some uneducated American might think they are setting off fire works in England because the Fourth of July must be a holiday everywhere, because this goof ball has never thought past the fireworks to what the holiday is all about. I wanted to show I knew what the holiday celebrates, so I answered no, knowing it is, in a literal sense, wrong.

It's thinking like this which has gotten me into academic trouble my whole life.

People who can force themselves to "Just answer the question," i.e. to think in a certain way, will score high on their SAT's and go to Harvard.

A high school classmate of mine in senior advance placement English completed an assignment, "Trace the use of 'roads' through the Tale of Two Cities," by writing down every time the word "road" appeared in the book. (And this was before computers with word search.) She had a five hundred page list of, "Road appears on page 1," and so forth. And she started to go through this as I (and several of my classmates) sat there, mouths on our chests, astonished. After about three minutes of her cataloguing the appearance of "road" I finally said, "Uh, Martha, I think the point of the question is Dickens uses "road" as an image. He's saying we all travel different roads, with different and divergent paths through life." Martha stared at me, uncomprehending. She scored high on her SAT's and she went to Harvard. Heaven only knows what became of her.

Toward the end of my third year in medical school, a dean pulled me aside and said, "You know you have got honors in every rotation third year, including Neurology, and you were the first student to get honors in Neurology in five years. But you were just below the middle of your class, 51 out of 100 at the end of the second year. What got into you?"

I said, "I didn't change. What changed were the people who were asking the questions."

He had no clue what I was talking about. But the questions on the tests during the first year were of the "Trace the use of Roads" and they meant, literally, recite the page numbers. In third year, you had to infer and use all of the information given you to form meaning.

A different sort of mind excelled in the first two years' setting. My roommate, who used to sit motionless with his microbiology book in his lap, just reading and memorizing, did superlatively his first two years, while I made outlines and tried to fit all the detail into meaningful categories: There must be a reason they separate gram positive bacteria from gram negative bacteria. Perhaps they behave differently when they cause infections. But no, in the second year microbiology course the differences in the diseases caused by the two groups were of no concern. All they wanted you to know was which bug stains gram negative, which gram positive. It was memory without meaning.

It was: Memorize this--NYSE, DJA, WSJ, and so on. So many meaningless letter combinations. I was unable to do this, and I would have to say, "Okay, think of some meaning for these letters. Think of financial pages: New York Stock Exchange. NYSE. Get it? Now you can remember.

When we got to the wards, suddenly I was able to use the information I had learned the first two years. For my room mate, none of it helped. He was barely able to keep his head above water. Nothing on the wards made sense. He had no outlines in his head. He went from a top twenty student to below 50. But he was a star when all he had to do was "answer the question." Don't try to attach a meaning to your answer.

Later, when we applied for internships, the wise men who reviewed our applications said, "Well, Bob is a really intelligent guy. His first two years show that. He just had no personality. Third year grades are all about charm and personality. It's the first two years which tell you how bright medical students are."

I would beg to differ. The questions in the first two years, multiple choice, the answer is right there in front of you; answer A or B, did not allow for inference, attaching meaning. The probability is greatest Linda is a bank teller, not that she is a bank teller with some specific characteristic of feminism. She might, after all have been an impassioned rejector of discrimination and social injustice, but there's a slim chance a woman who was that sort of student is not a feminist now. Strictly speaking, the answer is A.

The person who answers "A" is not any smarter or dumber than the person who picks "B."

The problem is not with either the person or the answer; the problem is with the guy who judges one better, more correct, than the other.

And, as far as I can tell, too many people who have been in a position to judge other people have not understood the limitations of their own thinking. They have seized upon easy formulae because it's easier for them to cling to their beliefs.

These are the same sorts who read US News and World Reports and believe Harvard is a better college than Stanford this year, but last year believed just the reverse, because the US News and World Reports gave the opposite answer last year. Something must have changed over the year. There couldn't be anything wrong with the method of the US News and World Reports.

I'll look forward to reading Thinking, Fast and Slow, because I have been told it explores "systematic errors in thinking of normal people." But if the basis for this analysis is the Linda problem, I may well be concluding the error is not in the thinking of normal people but in the thinking of those narrow minded judges. People answer not the question asked, sometimes, but the more interesting aspect raised by the question, the part that interests them, not the part that interests the questioner. Many people care nothing about probability, especially when the probability is so obvious, so they ignore that and go to the "better" answer.

It reminds me of that wonderful line in Roger Rabbit where Eddie, the detective, explodes at Roger for an answer which was clearly wrong and he asks how Roger could have made such a
obviously wrong statement when the truth was right in front of him and Roger stammers, rather astonished Eddie could not see why he answered that way: "Because," Roger says, "It was funnier that way."

For Roger, it was important to choose the answer he liked better, not the answer the questioner liked better.

I get this every day, when I take a medical history from a patient. I ask a specific question and the patient answers a slightly different question, a question he is more interested in, or a question he knows the answer to rather than the question I asked which he does not recall the answer to.

This is not because he is stupid. It is because he cannot see the underlying reason for my question, because he doesn't have my training. It's up to me to point out how he has answered a different question, and I need the answer to the one I'm interested in. I don't tell him he gets no points for his answer. I just ask the same question again, maybe a different way. Often, it turns out he didn't know the answer.

"What hour of day do you take this drug?" He cannot remember when he takes that drug. All he knows is he takes his drugs when his wife tells him to. So he tells me about how he feels after he takes his bedtime drugs, how he has to get out of bed an hour later and pee after he takes his bedtime drugs. "But do you know whether you take this drug I'm asking you about at bedtime?"

"Hell, doc," I just take those little pills out of that plastic box with the morning, noon, dinner, bedtime compartments. I don't know which drugs are in what compartment."

Okay, now we are getting somewhere. He did not know the answer I'm looking for. But he had his reasons for answering the way he did.