There have been studies that asked people to make bets. Here’s an example. It makes no difference—subjects still arrive at fallacious conclusions. That study also goes some way towards answering your concern about ambiguity in the question. The conjunction fallacy is a pretty robust phenomenon.
I’ve just read the example beyond it’s abstract. Typical psychology: the actual finding was that there were fewer errors with the bet (even though the expected winning was very tiny, and the sample sizes were small so the difference was only marginally significant), and also approximately half of the questions were answered correctly, and the high prevalence of “conjunction fallacy” was attained by considering at least one error over many questions.
How is it a “robust phenomenon” if it is negated by using strings of larger length difference in the head-tail example or by asking people to answer in the N out of 100 format?
I am thinking that people have to learn reasoning to answer questions correctly, including questions about probability, for which the feedback they receive from the world is fairly noisy. And consequently they learn that fairly badly, or mislearn it all-together due to how more detailed accounts are more frequently the correct ones in their “training dataset” (which consists of detailed correct accounts of actual facts and fuzzy speculations).
edit:
Let’s say, the notion that people are just generally not accounting for conjunction is sort of like Newtonian mechanics. In a hard science—physics—Newtonian mechanics was done for as a fundamental account of reality once conditions were found where it did not work. Didn’t matter any how “robust” it was. In a soft science—psychology—an approximate notion persists in spite of this, as if it should be decided by some sort of game of tug between experiments in favour and against that notion. If we were doing physics like this, we would never have moved beyond Newtonian mechanics.
Framing the problem in terms of frequencies mitigates a number of probabilistic fallacies, not just the conjunction fallacy. It also mitigates, for instance, base rate neglect. So whatever explanation you have for the difference between the probability and frequency framings shouldn’t rely on peculiarities of the conjunction fallacy case. A plausible hypothesis is that presenting frequency information simply makes algorithmic calculation of the result easier, and so subjects are no longer reliant on fallible heuristics in order to arrive at the conclusion.
The claim of the heuristics and biases program is that the conjunction fallacy is a manifestation of the representativeness heuristic. One does not need to suppose that there is a misunderstanding about the word “probability” involved (if there is, how do you account for the betting experiments?). The difference in the frequency framing is not that it makes it clear what the experimenter means by “probability”, it’s that the ease of algorithmic reasoning in that case reduces reliance on the representativeness heuristic. Further evidence for this is that the fallacy is also mitigated if the question is framed in terms of single-case probabilities, but with a diagram clarifying the relationship between properties in the problem. If the effect were merely due to a misunderstanding about what is meant by “probability”, why would there be a mitigation of the fallacy in this case? Does the diagram somehow make it clear what the experimenter means by “probability”?
In response to your Newtonian physics example, it’s simply not true that scientists abandoned Newtonian mechanics as soon as they found conditions under which it appeared not to work. Rather, they tried to find alternative explanations that preserved Newtonian mechanics, such as positing the existence of Uranus to account for discrepancies in planetary orbits. It was only once there was a better theory available that Newtonian mechanics was abandoned. Is there currently a better account of probabilistic fallacies than that offered by the heuristics and biases program? And do you think that there is anything about the conjunction fallacy research that makes it impossible to fit the effect within the framework of the heuristics and biases program?
I’m not familiar with the effect of variable string length difference, and quick Googling isn’t helping. If you could direct me to some research on this, I’d appreciate it.
A plausible hypothesis is that presenting frequency information simply makes algorithmic calculation of the result easier, and so subjects are no longer reliant on fallible heuristics in order to arrive at the conclusion.
There’s only room for making it easier when the word “probable” is not synonymous with “larger N out of 100“. So I maintain that alternate understanding of the word “probable” (and perhaps also an invalid idea of what one should bet on) are relevant. edit: to clarify, I can easily imagine an alternate cultural context where “blerg” is always, universally, invariably, a shorthand for “N out of 100”. In such context, asking about “N out of 100” or about “blerg” should produce nearly identical results.
Also, in your study, about half of the questions were answered correctly.
The claim of the heuristics and biases program is that the conjunction fallacy is a manifestation of the representativeness heuristic.
I guess that’s fair enough, albeit its not clear how that works on Linda-like examples.
In my opinion its just that through their life people are exposed to a training dataset which consists of
Detailed accounts of real events.
Speculative guesses.
and (1) is much more commonly correct than (2) even though (1) is more conjunctive. So people get mis-trained through a biased training set. A very wide class of learning AIs would get mis-trained by this sort of thing too.
I’m not familiar with the effect of variable string length difference, and quick Googling isn’t helping. If you could direct me to some research on this, I’d appreciate it.
The point is that you can’t pull the representativeness trick with e.g. R vs RGGRRGRRRGG . All research I ever seen had strings with small % difference in their length. I am assuming that the research is strongly biased towards researching something un-obvious, while it is fairly obvious that R is more probable than RGGRRGRRRGG and frankly we do not expect to find anyone who thinks that RGGRRGRRRGG is more probable than R.
There’s only room for making it easier when the word “probable” is not synonymous with “larger N out of 100″. So I maintain that alternate understanding of the word “probable” (and perhaps also an invalid idea of what one should bet on) are relevant.
Maybe a misunderstanding about the word is relevant, but it clearly isn’t entirely responsible for the effect. Like I said, the conjunction fallacy is much less common if the structure of the question is made clear to the subject using a diagram (e.g. if it is made obvious that feminist bank tellers are a proper subset of bank tellers). It seems implausible that providing this extra information will change the subject’s judgment about what the experimenter means by “probable”.
I guess that’s fair enough, albeit its not clear how that works on Linda-like examples.
The description given of Linda in the problem statement (outspoken philosophy major, social justice activist) is much more representative of feminist bank tellers than it is of bank tellers.
Maybe a misunderstanding about the word is relevant, but it clearly isn’t entirely responsible for the effect.
In the study you quoted, a bit less than half of the answers were wrong, in sharp contrast to the Linda example, where 90% of the answers were wrong. It implies that at least 40% of the failures were a result of misunderstanding. This only leaves 60% for fallacies. Of that 60%, some people have other misunderstandings and other errors of reasoning, and some people are plain stupid (10% are the dumbest people out of 10, i.e. have an IQ of 80 or less), leaving easily less than 50% for the actual conjunction fallacy.
It seems implausible that providing this extra information will change the subject’s judgment about what the experimenter means by “probable”.
Why so? If the word “probable” is fairly ill defined (as well as the whole concept of probability), then it will or will not acquire specific meaning depending on the context.
The description given of Linda in the problem statement (outspoken philosophy major, social justice activist) is much more representative of feminist bank tellers than it is of bank tellers.
Then the representativeness works in the opposite direction from what’s commonly assumed of the dice example.
Speaking of which, “is” is sometimes used to describe traits for identification purposes, e.g. “in general, an alligator is shorter and less aggressive than a crocodile” is more correct than “in general, an alligator is shorter than a crocodile”. If you were to compile traits for finding Linda, you’d pick the most descriptive answer. People know they need to do something with what they are told, they don’t necessarily understand correctly what they need to do.
There have been studies that asked people to make bets. Here’s an example. It makes no difference—subjects still arrive at fallacious conclusions. That study also goes some way towards answering your concern about ambiguity in the question. The conjunction fallacy is a pretty robust phenomenon.
I’ve just read the example beyond it’s abstract. Typical psychology: the actual finding was that there were fewer errors with the bet (even though the expected winning was very tiny, and the sample sizes were small so the difference was only marginally significant), and also approximately half of the questions were answered correctly, and the high prevalence of “conjunction fallacy” was attained by considering at least one error over many questions.
How is it a “robust phenomenon” if it is negated by using strings of larger length difference in the head-tail example or by asking people to answer in the N out of 100 format?
I am thinking that people have to learn reasoning to answer questions correctly, including questions about probability, for which the feedback they receive from the world is fairly noisy. And consequently they learn that fairly badly, or mislearn it all-together due to how more detailed accounts are more frequently the correct ones in their “training dataset” (which consists of detailed correct accounts of actual facts and fuzzy speculations).
edit: Let’s say, the notion that people are just generally not accounting for conjunction is sort of like Newtonian mechanics. In a hard science—physics—Newtonian mechanics was done for as a fundamental account of reality once conditions were found where it did not work. Didn’t matter any how “robust” it was. In a soft science—psychology—an approximate notion persists in spite of this, as if it should be decided by some sort of game of tug between experiments in favour and against that notion. If we were doing physics like this, we would never have moved beyond Newtonian mechanics.
Framing the problem in terms of frequencies mitigates a number of probabilistic fallacies, not just the conjunction fallacy. It also mitigates, for instance, base rate neglect. So whatever explanation you have for the difference between the probability and frequency framings shouldn’t rely on peculiarities of the conjunction fallacy case. A plausible hypothesis is that presenting frequency information simply makes algorithmic calculation of the result easier, and so subjects are no longer reliant on fallible heuristics in order to arrive at the conclusion.
The claim of the heuristics and biases program is that the conjunction fallacy is a manifestation of the representativeness heuristic. One does not need to suppose that there is a misunderstanding about the word “probability” involved (if there is, how do you account for the betting experiments?). The difference in the frequency framing is not that it makes it clear what the experimenter means by “probability”, it’s that the ease of algorithmic reasoning in that case reduces reliance on the representativeness heuristic. Further evidence for this is that the fallacy is also mitigated if the question is framed in terms of single-case probabilities, but with a diagram clarifying the relationship between properties in the problem. If the effect were merely due to a misunderstanding about what is meant by “probability”, why would there be a mitigation of the fallacy in this case? Does the diagram somehow make it clear what the experimenter means by “probability”?
In response to your Newtonian physics example, it’s simply not true that scientists abandoned Newtonian mechanics as soon as they found conditions under which it appeared not to work. Rather, they tried to find alternative explanations that preserved Newtonian mechanics, such as positing the existence of Uranus to account for discrepancies in planetary orbits. It was only once there was a better theory available that Newtonian mechanics was abandoned. Is there currently a better account of probabilistic fallacies than that offered by the heuristics and biases program? And do you think that there is anything about the conjunction fallacy research that makes it impossible to fit the effect within the framework of the heuristics and biases program?
I’m not familiar with the effect of variable string length difference, and quick Googling isn’t helping. If you could direct me to some research on this, I’d appreciate it.
There’s only room for making it easier when the word “probable” is not synonymous with “larger N out of 100“. So I maintain that alternate understanding of the word “probable” (and perhaps also an invalid idea of what one should bet on) are relevant. edit: to clarify, I can easily imagine an alternate cultural context where “blerg” is always, universally, invariably, a shorthand for “N out of 100”. In such context, asking about “N out of 100” or about “blerg” should produce nearly identical results.
Also, in your study, about half of the questions were answered correctly.
I guess that’s fair enough, albeit its not clear how that works on Linda-like examples.
In my opinion its just that through their life people are exposed to a training dataset which consists of
Detailed accounts of real events.
Speculative guesses.
and (1) is much more commonly correct than (2) even though (1) is more conjunctive. So people get mis-trained through a biased training set. A very wide class of learning AIs would get mis-trained by this sort of thing too.
The point is that you can’t pull the representativeness trick with e.g. R vs RGGRRGRRRGG . All research I ever seen had strings with small % difference in their length. I am assuming that the research is strongly biased towards researching something un-obvious, while it is fairly obvious that R is more probable than RGGRRGRRRGG and frankly we do not expect to find anyone who thinks that RGGRRGRRRGG is more probable than R.
Maybe a misunderstanding about the word is relevant, but it clearly isn’t entirely responsible for the effect. Like I said, the conjunction fallacy is much less common if the structure of the question is made clear to the subject using a diagram (e.g. if it is made obvious that feminist bank tellers are a proper subset of bank tellers). It seems implausible that providing this extra information will change the subject’s judgment about what the experimenter means by “probable”.
The description given of Linda in the problem statement (outspoken philosophy major, social justice activist) is much more representative of feminist bank tellers than it is of bank tellers.
In the study you quoted, a bit less than half of the answers were wrong, in sharp contrast to the Linda example, where 90% of the answers were wrong. It implies that at least 40% of the failures were a result of misunderstanding. This only leaves 60% for fallacies. Of that 60%, some people have other misunderstandings and other errors of reasoning, and some people are plain stupid (10% are the dumbest people out of 10, i.e. have an IQ of 80 or less), leaving easily less than 50% for the actual conjunction fallacy.
Why so? If the word “probable” is fairly ill defined (as well as the whole concept of probability), then it will or will not acquire specific meaning depending on the context.
Then the representativeness works in the opposite direction from what’s commonly assumed of the dice example.
Speaking of which, “is” is sometimes used to describe traits for identification purposes, e.g. “in general, an alligator is shorter and less aggressive than a crocodile” is more correct than “in general, an alligator is shorter than a crocodile”. If you were to compile traits for finding Linda, you’d pick the most descriptive answer. People know they need to do something with what they are told, they don’t necessarily understand correctly what they need to do.