Conjunction Controversy (Or, How They Nail It Down)

Science is smarter than scientists. That's why if an experiment is both important, and still accepted after 20 years, you should suspect there's followup experiments shoring it up. (If not, there's something wrong, bigtime, with that whole field.)

[+]Brian18y-60

[-]Felix218y50

Arrrr. Shiver me timbers. I shore be curious what the rank be of "Linda is active in the feminist movement and is a bank teller" would be, seeing as how its meanin' is so far diff'rent from the larboard one aloft.

A tip 'o the cap to the swabbies what found a more accurate definition of "probability" (I be meanin' "representation".) than what logicians assert the meaning o' "probability" be. Does that mean, at a score of one to zero, all psychologists are better lexicographers than all logicians?

[-]Raemon14y10

I read this comment, predicted the day it was posted, then looked up at the date. I was off by one.

[-]J_Thomas18y80

....people may try to dismiss (not defy) the experimental data. Most commonly, by questioning whether the subjects interpreted the experimental instructions in some unexpected fashion - perhaps they misunderstood what you meant by "more probable".

Which in fact turned out to be the case.

This was done - see Kahneman and Frederick (2002) - and the correlation between representativeness and probability was nearly perfect. 0.99, in fact.

So there's no reason to look for other interpretations about what people meant by "more probable". Anything else they might mean will correlate 0.99 with this, operationally it will be almost the same thing.

So this is what the public means by "more probable". And it's often what people mean in practice by "more probable" even when they've had training in probability theory and statistics.

"An additional group of 24 physicians, mostly residents at Stanford Hospital, participated in a group discussion in which they were confronted with their conjunction fallacies in the same questionnaire. The respondents did not defend their answers, although some references were made to 'the nature of clinical experience.' Most participants appeared surprised and dismayed to have made an elementary error of reasoning."

They interpreted the question the standard way, and then later they remembered they were supposed to use probability.

Probability theory is still new. Most of it is newer than calculus. People consistently make gambling mistakes like the Monty Hall problem. The general belief is that you have to be real smart to get those things right. Just like you have to be real smart to learn calculus.

Is the word "representativeness" standard jargon? It's such an ugly word, but if it's well-established we can't replace it with a better one.

So. People interpret "more probable" as "less surprising". And most of the population does it, enough that this can be exploited reliably. This is potentially a very very profitable discussion.

[-]Senthil18y00

The experiment was bad and felt that way since I first came across the same. But I didn't have any idea that it's the single most questioned experiment or something like that. Recently, I skimmed a book called 'Gut feelings' by Gerd something (not sure about the second name) at the bookshop. There was a blurb by Steven Pinker saying that the book was good. A chapter had a good description on where this experiment is mistaken and said how reframing it in different words made people give the correct answer. What Kahneman says here is a fallacy which people may be encounter in some circumstances. That point can be taken but we need to imagine a good experiment which reflects the point well.

[-]Bob318y00

Interesting that Senthil brings up this book (http://www.amazon.com/Gut-Feelings-Intelligence-Gerd-Gigerenzer/dp/0670038636) because Eliezer's recent posts have gotten me thinking whether there are any good rules for when to trust/doubt intuition. Much of the discussion about bias suggests we should question, and often reject, our instincts but at some point this hits diminishing returns and in others (e.g., the planning fallacy) could be a mistake. If Eliezer or any other contributors has thoughts about good rules of thumb for when it's reasonable (safe? better?) to use rules of thumb, I would be eager to hear them.

[-]J_Thomas18y20

The experiment was bad and felt that way since I first came across the same.

What's bad about it? It looks like it gets reproducible results.

It looks to me like people often read "probable" to mean "plausible".

And we know they do that in actual betting situations like the Monty Haul problem.

People can be trained to think in terms of probability, but the general culture trains them to think otherwise. Perhaps its our evolutionary background, or perhaps its our culture. But somehow the culture trains people to be stupid in this particular way.

So even if you aren't susceptible to that yourself, you need to deal with it carefully. On the defensive side, when you try to persuade people, don't ever depend on probability arguments that don't sound plausible because people won't believe them.

And on the offensive side, you can carefully use this generalised stupidity to exploit people, if you choose to.

[-]Senthil18y00

What's bad about it? It looks like it gets reproducible results.

Thomas, I'm not sure why it's bad. That's the problem. I was unable to put my finger on it. I don't remember what I answered. But even after the explanation was given, I felt that it wasn't quite convincing that this would be a problem. It sure is getting reproducible results. But what may be causing the result may not be the bias.

I think you've answered why it's bad when you said that it's because of our culture, and particularly the way we use the word 'probable' to mean something than what the dictionary says it should. If that's the case, it doesn't throw any light on the conjunction fallacy per se. Even if the problem is framed differently, people should fall for the fallacy. But if you're able to check the section in 'Gut Feelings', you'll see that most people would answer it perfectly well. There would be no fallacy involved.

Thanks, Bob, for the Amazon link.

[-]Eliezer Yudkowsky18y200

Senthil, Gigerenzer is one of the primary critics of this experiment, but my understanding is that in the larger field his critiques are widely considered to have been refuted by further experiments.

More than half the subjects still committed the conjunction fallacy when they were asked to bet. If people are betting on similarities instead of probabilities, if doctors are treating similarities instead of probabilities, that is not a "misunderstanding" that explains away the experimental result. It IS the representativeness heuristic and conjunction fallacy!

Also, the conjunction fallacy has been replicated in many different formats besides the Linda experiment, as discussed today and yesterday. Why are people just ignoring this? Do they feel that if they come up with some arguable critique of the Linda experiment, that excuses them from any further work? That they don't have to explain all the other experiments?

I'm starting to get that feeling of frustration again. It doesn't excuse the subjects if they "misinterpreted" the experimental instructions, because they are misinterpreting real life the same way. More than half of them bet on the conjunction fallacy. Understanding exactly how someone makes a mistake does not mean it is not a mistake. They still lose the bet. The patient still dies. Am I making sense here?

[-]Ed218y00

I certainly don't have any problem with the experiments and as important as the conjunction bias is, I think its just as important to ask and assess why this bias exists. Once we can nail that down, it becomes easier to teach yourself and others how not to fall into that bias trap.

So the sympathy towards the subjects is part of the explanation. Same with the commments discussing the use of language and framing of the questions.

My opinion on this is that the reason the poor reasoning occurs is simply because we are comforted by one of the fitted answers sitting in conjunction with one of the unfit answers rather than an unfit answer by itself.

There may not be an easy way to teach this to a layman or ourselves so we see the correct reasoning easily but its a start.

[-]Keith_Elis18y40

Do people commit the conjunction fallacy even after having been warned of the conjunction fallacy?

[-]Eliezer Yudkowsky18y50

Keith, of course they do. The smart ones won't commit it deliberately.

I'm sure I do it accidentally. It's hard to debias this one.

[-]Senthil18y10

Eliezer, thanks for the explanation. I'm sorry that you're getting frustrated to explain this again. I agree with you and understand what you're trying to explain. It makes perfect sense. But it's difficult to make the explanation clear and easy for lay people. Also, maybe I didn't make myself clear in the above post.

I was referring only to the particular experiment. I'm not at all denying that the fallacy exists. I meant that the fallacy doesn't exist in the context of that experiment alone. I just felt that there could be a better thought out experiment demonstrate it.

I can compare this with reading a good detective story and a bad one. A good one is where you were shown the evidence and you could've predicted the murderer but didn't. A bad one introduces a character relatively late in the story or make one who wasn't talked about much the murderer. I feel the experiments demonstrating the fallacy to be similar to the latter type of stories, kind of contrived and unnatural.

[-]J_Thomas18y30

What would be the opposite mistake?

I came close to committing it. When I guessed the order I ignored the description almost completely. I first estimated how many school teachers there were compared to bank tellers. I thought there were mor school teachers. And how many psychiatric social workers? More bank tellers. Lots of insurance salesmen, more than bank tellers. And so on. I pretty much ignored Linda's description and just looked at my guesses about the numbers of people. Lisa could have fallen into any of those categories entirely apart from those little scraps of information about her.

I did it wrong -- I didn't consider that more women than men tend to be schoolteachers, feminists, and members of the League of Women Voters and bank tellers, but not insurance salesmen. But my guesses about how many there were of each type were probably way off anyway.

I remembered from a college summer job -- when people know a few random facts about somebody else they tend to put too much emphasis on those facts. Like, if you are asked to guess whether somebody is going to be a suicide bomber and what's important is being right, then the answer is almost always no. Hardly any arabs are suicide bombers. Hardly any Wahabi arabs are suicide bombers. Hardly any young male wahabi arabs whose girlfriends have jilted them are suicide bombers. The way to bet is almost always no.

But by completely ignoring the information about Linda instead of ignoring the (guessed at) statistics about numbers of each category, haven't I made the opposite mistake? There ought to be some best amount of weight to give that information. I assumed none of it was worth anything, and actually I even ignored that Linda was a woman though I obviously shouldn't have. To do it right, wouldn't you know the actual relative numbers of each category (instead of guessing) and also know how much weight to put on the individual information about Linda?

If you knew everything you could answer the question without bias.

[-]bigjeff515y10

The key mistake was not the probability numbers (though that certainly could be a mistake in real life), it was ranking bank-teller/feminist higher than bank-teller.

I think the point to bear in mind on this is that any time you add two criteria together the probabilities plummet.

When you did it yourself, you should have evaluated the bank teller and feminist part of the BT/F question separately (however you chose to evaluate it), and then examined the likelihood that both would be true. That way you should clearly see that the combination could not possibly have higher probabilities than either individual criteria.

It's certainly a hard thing to do, I'm going to have to look out for this one because I'd wager I do it a ton.

[-]komponisto14y10

What would be the opposite mistake?

Being confused by the Gettier problem.

[-]Eliezer Yudkowsky18y00

J Thomas, I would guess that in real life your method would work well in this specific case, because I'm guessing the prior odds are more extreme than the likelihoods. But you're correct that, in general, it is equally fallacious to ignore evidence as to ignore priors. :)

[-]J_Thomas18y00

So how do we correctly blend our knowledge of comparative numbers versus the way specific circumstances bias the odds?

Mix in too much of either sort of knowledge and you have a bias. But how can you know how much of each to include? Usually you'd have to guess.

[-]MoreOn15y20

Maybe the experimenters missed <yet another brilliant idea proven wrong in the last century>? Just kidding. What I ask instead is, Do people ever not suffer from conjunction bias?

I read about this experiment a couple years ago, about logic and intuition. (I’m writing from memory here, so it’s likely I screwed something up). People were given logical rules, and asked to find violations. Something like:

(Rule) If you are under 21, you can’t buy alcohol.

Bob is 24 and buys alcohol. (That’s not a violation)

Tom is 18 and buys alcohol. (Most people spotted this violation).

(Rule) If you go to France, you can’t drive a car.

Bob goes to France and takes a subway. (Not a violation).

Tom goes to France and drives. (Fewer people spotted this violation).

Of course it wasn’t easy like here, with a rule and a violation right next to each other. The rules were phrased more cleverly, too.

Anyway, people were better at logic when the situation was more intuitive. I wonder if any experiments have been done in which (untrained) people demonstrated a likewise absence of conjunction bias?

Maybe something like below would work, when you’re pointing out that (T) and (F) are occurring together.

Linda is 31 years old…

Please rank…

(F) Linda is active in the feminist movement.

(T) Linda is a bank teller.

(L) Both (T) and (F)

And if that doesn’t work… well, maybe better minds than mine had ALREADY done an experiment. Any suggestions for further reading, anyone? Summaries greatly appreciated.