Fascinating Bryan! I do wonder about some specific differences between Kahneman & Tversky and your experiment, though...
K&T forced on the same group of people two choices which clearly prove the fallacy: since p(bank teller) = p(bank teller & feminist) + p(bank teller & non-feminist), there's no way that p(bank teller & feminist) > p(bank teller)
In your question there's the possibility that the responders are different (plus all other weird human factors such as answering before or after lunch etc), but more interesting to me is the looseness of language and associated interpretations.
Let's say that in general people don't interpret "inappropriate things" as "all and any inappropriate things, no matter which type," and/or also that "always" is not interpreted as "absolute 100% with no rounding", but instead something like "95% of the time or above"
Then if "sexual inappropriate things" is seen as a small-size sub-segment of "inappropriate things" with stricter control agreement whereas "non-sexual inappropriate things" is a much-larger sub-segment with much looser censorship support, that might provide an alternative logical explanation. (edit: by way of weighted averages)
Not that I think that's the most likely reasoning path! Probably the emotional / gut-feeling path is the winning explanation. But just something to consider.
Love reading your blog, thanks for the continuing intellectual challenges!
You make some great points. I'm reminded of a scene in the US version of The Office.
G: "What kind of music are you into?"
P: "Oh, I like all kinds."
G: "Really, all kinds? So you like songs of hate written by the white knights of the Ku Klux Klan?"
You'd have to be pretty silly to think Gabe is making a valid logical deduction from Peter's answer, rather than wilfully misrepresenting what was said.
Thirded. I can very easily imagine folks that are prudish or hyper-concerned about sex/gender or harassment being against *specific* “inappropriate things”, but possibly not being concerned about others. That isn’t probative, but it offers a way out that doesn’t point to errors in statistical thinking.
As a counter to the counter, though, why would you mentally list anything as “inappropriate” if you don’t care about it? The bigger issue is the imprecision and the variability in definitions that it allows.
Also note that the first question naturally suggests a law that would impose penalties on the inappropriate speaker. Because of sexual harassment law the second question naturally suggests laws that demand the buisness not tolerate employees being sexually inappropriate.
While I suspect Bryan sees those similarly many people see the later as substantially less coercive.
I think, to some extent, a large part of the issue with these questions is that people are answering the question *they think you are asking*, not the question *you think you are asking*. In order to answer the question, first they have to figure out which of the various interpretations of the question you might be asking, which involves building a model of you, and asking what information you are trying to ascertain - and critically, here, the answers are information used in building that model.
So, in the Linda example, that you have provided additional information in choice B gives additional information about A. They are not considered in isolation, because the first task a person's brain has to deal with, in interpreting the question, is figuring out who you are and what you are trying to ask. Since social justice comes up in the question, and feminist comes up in one of the answers, they guess that you're asking whether or not Linda is likely to be a feminist, -not- whether Linda is likely to be a bank teller. So they kind of mentally add an implicit "... and is not a feminist" to answer A, in order to make sense of the bizarre question you are asking. Once they do this, the question makes sense to them, and so they can complete the question by answering it. (In a sense, the two "bank teller" pieces of information in the answers cancel out as red herrings; unless you're familiar with formal logic, you have no experience with these kinds of questions, and so cannot understand what is being asked without spending a lot of time thinking about it.)
Remember: A person answering your question does not know what you are asking, they have to figure that out. The first step in answering a question must be figuring out what is being asked, and this additional pivot point creates a lot of apparent chaos in the final answer.
If you include this process in interpreting polls like this, a lot of them will make a lot more sense. The freedom case, for example, kind of trivially washes out: A lot of people are not, in fact, interpreting the second question in a sense that makes it a subset of their interpretation of the first question. In particular you likely have some group of people who are interpreting your answers in a temporal fashion (look at all the temporal words in your question and your answers - you've literally asked "when", when you meant something like "Under what set of circumstances"). Similarly, you probably have a group of people who are answering with a particular notion of "inappropriate" which may not be a proper superset of "sexually inappropriate" - and some other group of people, who may be interpreting "inappropriate" in the manner you expect, may be interpreting "sexually inappropriate" in a manner you -don't- expect.
For example, "Sleep with me or you're fired" - is this strictly speech, or is it something more? I'm not sure whether or not it would be included in "saying inappropriate things" by your definition, but it does seem like it could plausibly be included in "saying sexually inappropriate things" to a much greater degree, and I'm more confident in it being placed in that bucket than I am in it being placed in the theoretical superset. There's some kind of uncertainty principle in language, where greater specificity on one axis can force less specificity on another.
I think you are spot on here. When I read the Linda question and the two possible options, my first gut instinct is to compare the answers against each other, so she's a bank teller in either case and the only question is whether or not she is a feminist. In other words, the way the answers are intended to be read is "A: Linda is possibly a bank teller, or B: Linda is possibly a bank teller and possibly a feminist." but how my not so normal brain parses the answers are "A: Linda is ONLY a bank teller, or B: Linda is a bank teller and a feminist." Since the question strongly hints that Linda is almost certainly a feminist, and in fact I think it is more likely that she is a feminist than a bank teller, that answer seems more likely. In a sense, my brain is asking which answer is more likely correct, given that apparently bank teller is a given and the only question is whether she is a feminist.
Now, if I stop and think I recognize that it is a conjunction question, but it takes stopping because the answers provided give information about what the question meant. The specifics get in the way because we forget "we don't know whether or not she is a bank teller" when we are given two possible states of the world that both contain bank teller, making it feel like a True/False or other dichotomy. I wonder how many people would get it right if there was a third option "C: Linda is a bank teller, a feminist and a world class pastry chef", or something similar.
I want to defend the inerrant rationality of my fellow man from the attacks of Bryan, experimental psychologists, and philosophers.
(1 - Linda) If you read the article Bryan linked to, we see that humans are not committing the conjunctivist fallacy, but simply intuiting that option [1] should actually read "Linda is a bank teller *and only a bank teller (not a feminist)*." Incidentally, this makes perfect sense: nobody in real life (except an expiremental psychologist who is trying to trick you) ever asks you to make inane confirmations about the basic laws of probabilities; they ask you interesting things like whether someone with a certain set of characteristics is likely to be a feminist or not.
The subjects of Tversky and Kahneman graciously ascribed to the question, and to their questioners, a basic notion of common sense and decency, and their reward for this was being labeled "irrational."
(2 - Workplace) There is zero contradiction in answering "always" in poll #1 and "not always" in poll #2. If you answer "always" to poll #1, you are not committing to the position that it should "always" be legal to say *all* inappropriate things, just that it should always be legal to say *some* inappropriate things. You can therefore be perfectly justified in saying that it should "not always" be legal to say sexually inappropriate things.
To show that I'm not merely being pedantic, suppose you answered "always" to both polls. Now suppose I said to you, since you answered "always" to poll #2, I suppose you want to abolish slander laws in this country, since you think it should always be legal to say *all* sexually inappropriate (and potentially slanderous) things. But this is absurd. When you answer "always" to poll #2, you are clearly answering that it should "always" be legal to say *some* sexually inappropriate things.
(3 - Free Speech) "the right to speak freely about whatever you want" is a garbage elicitation of preferences because you can interpret it as whatever *I* want to speak about, not whatever *anyone* might wish to speak about. So there is no contradiction in answering that "the right to speak freely about whatever you [I] want" is super important, and then agreeing with a ban of any type of speech that *I* don't want to speak about.
I dislike this whole exercise of getting people to agree with some vague description of a notion, then getting them to agree with a specific example that goes against said notion, and using the whole game to declare that people are irrational rubes or victims of SDB or something. Maybe they simply agree with some notions *in general, but not in all cases*.
I think it's mostly social, responding to a specific prompt. If you say "Lovely and brisk today!" versus "Wow, it's bloody freezing!" you'll get different responses, and no-one thinks this is a puzzle about people's genuine opinions about the weather.
"Should people be able to say what they like?" is heard as an invitation to support free speech, so people take it. "Should people be able to say sexually inappropriate things in the workplace?" is heard (on the margin) as an invitation to condemn sexual harassment, so people take it.
In the Linda case, I think people are just confusing absolute and conditional probabilities. The extra information does imply that Linda is more likely to be a feminist, just not in relation to being a bank teller.
I fear another aspect may be at issue in your polls. When you ask if it should be always legal to say inappropriate things at work a natural interpretation is: should any individual face criminal/civil penalities for saying inappropriate things at work.
When you ask if it should always be legal to say sexually inappropriate things at work the salient law is sexual harassment law which imposes torts **on the company** for tolerating sexually inappropriate remarks. Thus, respondents may be expressing their belief that such laws shouldn't be repealed which is consistent with the other outcome.
On Linda the bank teller... Is there philosophical term --perhaps pedantry-- for those that want to trick and belittle people about logic by pretending you are a real person. The two sentence context before the question sets one up for a discussion on Linda as a feminist. There was no hint that we were in a philosophy department classroom.
Altruism is about sacrificing the people who create jobs, not helping the people who want jobs, thus the evasion of long-range, indirect, unintended effects. When jobs decrease, minimum wage advocates will say that their intentions are moral, ie, "helping" people, thus the destructive effect is unfortunate but morally correct.
Economics was, in a more rational culture, recognized as a moral science, the study of rational choices in a market. IF man want material values, he SHOULD use reason to guide production. Reason is basically for man's life as end, not reason serving irrational ends.
Agree re most people typically just pick the thing that sounds good or that fits the common social truth in their social circle. I would add people also don't think through second order effects. They aren't thinking "...well if I accept this position then I should accept x and y and z also." They also arent thinking "if x happens then people will react with y." There is also some fear of other people's freedom going on with this kind of thing, you want to be free to speak your mind on what you think is edgy but you don't want to hear something that you find offensive. For me personally it's normal that in a workplace your behavior is going to be constrained in exchange for money. If you are going around upsetting other employees that will hurt the firms ability to work on projects and keep and retain talent. Even if it were not a legal issue I think many firms would still fire people for certain kinds of speech for that reason.
I'm not sure the Twitter poll results are illogical. There's a difference between inappropriate and illegal.
"Inappropriate speech," without further qualification, is likely assumed by most readers to be legal speech. Sexually inappropriate speech, on the other hand, could very well be illegal and your audience knows this. At minimum, it could need adjudicating in court.
The response profile you got thus appears pretty logical.
The respondent to the psychology questionnaire thinks first: how likely is it that LInda would be a bank teller. This is not especially likely, but far from impossible; say, 1%. Next he thinks: how likely is it that Linda, now known to be a bank teller, is active in the feminist movement. That's very likely; say 50%. 50% > 1%; so . . . .
The first question is unclear and user interpretation affects the results. Does "say inappropriate things" mean SOME things or ALL things? In the response options, is it the speech we are varying or the context?
While "sexually inappropriate things" is certainly a subset of "inappropriate things", I suspect that if you were to make a list of all inappropriate things ranked in order of severity, the sexual ones would be biased towards the top.
Polite society tends to think sexual misdeeds are a special kind of perfidy, and I also suspect that most people, if given the two questions side by side, would think "when should it be legal to say things with an average badness of 3/10" vs. "when should it be legal to say things with an average badness of "6/10"?
Put another way I think Bryan might appreciate, yes, sexual inappropriate comments are a subset of inappropriate comments. But if x = the probability that a particular inappropriate comment crosses the line from boorish and cringe to actively bad, then Pr(x | sexual) is probably going to be higher than Pr(x | any comment).
The conjunction fallacy itself seems like a fallacy. Aren't there are a lot of different things that frequently but not always occur in conjunction with one another? Like...not all heavy rains cause flooding and not all flooding is caused by heavy rain, but still, it'd be weird to say that the probably of each one occurring independently is higher than the two occurring together.
Fascinating Bryan! I do wonder about some specific differences between Kahneman & Tversky and your experiment, though...
K&T forced on the same group of people two choices which clearly prove the fallacy: since p(bank teller) = p(bank teller & feminist) + p(bank teller & non-feminist), there's no way that p(bank teller & feminist) > p(bank teller)
In your question there's the possibility that the responders are different (plus all other weird human factors such as answering before or after lunch etc), but more interesting to me is the looseness of language and associated interpretations.
Let's say that in general people don't interpret "inappropriate things" as "all and any inappropriate things, no matter which type," and/or also that "always" is not interpreted as "absolute 100% with no rounding", but instead something like "95% of the time or above"
Then if "sexual inappropriate things" is seen as a small-size sub-segment of "inappropriate things" with stricter control agreement whereas "non-sexual inappropriate things" is a much-larger sub-segment with much looser censorship support, that might provide an alternative logical explanation. (edit: by way of weighted averages)
Not that I think that's the most likely reasoning path! Probably the emotional / gut-feeling path is the winning explanation. But just something to consider.
Love reading your blog, thanks for the continuing intellectual challenges!
You make some great points. I'm reminded of a scene in the US version of The Office.
G: "What kind of music are you into?"
P: "Oh, I like all kinds."
G: "Really, all kinds? So you like songs of hate written by the white knights of the Ku Klux Klan?"
You'd have to be pretty silly to think Gabe is making a valid logical deduction from Peter's answer, rather than wilfully misrepresenting what was said.
Great points! I had the same feeling about “inappropriate things.”
Thirded. I can very easily imagine folks that are prudish or hyper-concerned about sex/gender or harassment being against *specific* “inappropriate things”, but possibly not being concerned about others. That isn’t probative, but it offers a way out that doesn’t point to errors in statistical thinking.
As a counter to the counter, though, why would you mentally list anything as “inappropriate” if you don’t care about it? The bigger issue is the imprecision and the variability in definitions that it allows.
Also note that the first question naturally suggests a law that would impose penalties on the inappropriate speaker. Because of sexual harassment law the second question naturally suggests laws that demand the buisness not tolerate employees being sexually inappropriate.
While I suspect Bryan sees those similarly many people see the later as substantially less coercive.
I think, to some extent, a large part of the issue with these questions is that people are answering the question *they think you are asking*, not the question *you think you are asking*. In order to answer the question, first they have to figure out which of the various interpretations of the question you might be asking, which involves building a model of you, and asking what information you are trying to ascertain - and critically, here, the answers are information used in building that model.
So, in the Linda example, that you have provided additional information in choice B gives additional information about A. They are not considered in isolation, because the first task a person's brain has to deal with, in interpreting the question, is figuring out who you are and what you are trying to ask. Since social justice comes up in the question, and feminist comes up in one of the answers, they guess that you're asking whether or not Linda is likely to be a feminist, -not- whether Linda is likely to be a bank teller. So they kind of mentally add an implicit "... and is not a feminist" to answer A, in order to make sense of the bizarre question you are asking. Once they do this, the question makes sense to them, and so they can complete the question by answering it. (In a sense, the two "bank teller" pieces of information in the answers cancel out as red herrings; unless you're familiar with formal logic, you have no experience with these kinds of questions, and so cannot understand what is being asked without spending a lot of time thinking about it.)
Remember: A person answering your question does not know what you are asking, they have to figure that out. The first step in answering a question must be figuring out what is being asked, and this additional pivot point creates a lot of apparent chaos in the final answer.
If you include this process in interpreting polls like this, a lot of them will make a lot more sense. The freedom case, for example, kind of trivially washes out: A lot of people are not, in fact, interpreting the second question in a sense that makes it a subset of their interpretation of the first question. In particular you likely have some group of people who are interpreting your answers in a temporal fashion (look at all the temporal words in your question and your answers - you've literally asked "when", when you meant something like "Under what set of circumstances"). Similarly, you probably have a group of people who are answering with a particular notion of "inappropriate" which may not be a proper superset of "sexually inappropriate" - and some other group of people, who may be interpreting "inappropriate" in the manner you expect, may be interpreting "sexually inappropriate" in a manner you -don't- expect.
For example, "Sleep with me or you're fired" - is this strictly speech, or is it something more? I'm not sure whether or not it would be included in "saying inappropriate things" by your definition, but it does seem like it could plausibly be included in "saying sexually inappropriate things" to a much greater degree, and I'm more confident in it being placed in that bucket than I am in it being placed in the theoretical superset. There's some kind of uncertainty principle in language, where greater specificity on one axis can force less specificity on another.
I think you are spot on here. When I read the Linda question and the two possible options, my first gut instinct is to compare the answers against each other, so she's a bank teller in either case and the only question is whether or not she is a feminist. In other words, the way the answers are intended to be read is "A: Linda is possibly a bank teller, or B: Linda is possibly a bank teller and possibly a feminist." but how my not so normal brain parses the answers are "A: Linda is ONLY a bank teller, or B: Linda is a bank teller and a feminist." Since the question strongly hints that Linda is almost certainly a feminist, and in fact I think it is more likely that she is a feminist than a bank teller, that answer seems more likely. In a sense, my brain is asking which answer is more likely correct, given that apparently bank teller is a given and the only question is whether she is a feminist.
Now, if I stop and think I recognize that it is a conjunction question, but it takes stopping because the answers provided give information about what the question meant. The specifics get in the way because we forget "we don't know whether or not she is a bank teller" when we are given two possible states of the world that both contain bank teller, making it feel like a True/False or other dichotomy. I wonder how many people would get it right if there was a third option "C: Linda is a bank teller, a feminist and a world class pastry chef", or something similar.
I want to defend the inerrant rationality of my fellow man from the attacks of Bryan, experimental psychologists, and philosophers.
(1 - Linda) If you read the article Bryan linked to, we see that humans are not committing the conjunctivist fallacy, but simply intuiting that option [1] should actually read "Linda is a bank teller *and only a bank teller (not a feminist)*." Incidentally, this makes perfect sense: nobody in real life (except an expiremental psychologist who is trying to trick you) ever asks you to make inane confirmations about the basic laws of probabilities; they ask you interesting things like whether someone with a certain set of characteristics is likely to be a feminist or not.
The subjects of Tversky and Kahneman graciously ascribed to the question, and to their questioners, a basic notion of common sense and decency, and their reward for this was being labeled "irrational."
(2 - Workplace) There is zero contradiction in answering "always" in poll #1 and "not always" in poll #2. If you answer "always" to poll #1, you are not committing to the position that it should "always" be legal to say *all* inappropriate things, just that it should always be legal to say *some* inappropriate things. You can therefore be perfectly justified in saying that it should "not always" be legal to say sexually inappropriate things.
To show that I'm not merely being pedantic, suppose you answered "always" to both polls. Now suppose I said to you, since you answered "always" to poll #2, I suppose you want to abolish slander laws in this country, since you think it should always be legal to say *all* sexually inappropriate (and potentially slanderous) things. But this is absurd. When you answer "always" to poll #2, you are clearly answering that it should "always" be legal to say *some* sexually inappropriate things.
(3 - Free Speech) "the right to speak freely about whatever you want" is a garbage elicitation of preferences because you can interpret it as whatever *I* want to speak about, not whatever *anyone* might wish to speak about. So there is no contradiction in answering that "the right to speak freely about whatever you [I] want" is super important, and then agreeing with a ban of any type of speech that *I* don't want to speak about.
I dislike this whole exercise of getting people to agree with some vague description of a notion, then getting them to agree with a specific example that goes against said notion, and using the whole game to declare that people are irrational rubes or victims of SDB or something. Maybe they simply agree with some notions *in general, but not in all cases*.
I think it's mostly social, responding to a specific prompt. If you say "Lovely and brisk today!" versus "Wow, it's bloody freezing!" you'll get different responses, and no-one thinks this is a puzzle about people's genuine opinions about the weather.
"Should people be able to say what they like?" is heard as an invitation to support free speech, so people take it. "Should people be able to say sexually inappropriate things in the workplace?" is heard (on the margin) as an invitation to condemn sexual harassment, so people take it.
In the Linda case, I think people are just confusing absolute and conditional probabilities. The extra information does imply that Linda is more likely to be a feminist, just not in relation to being a bank teller.
I fear another aspect may be at issue in your polls. When you ask if it should be always legal to say inappropriate things at work a natural interpretation is: should any individual face criminal/civil penalities for saying inappropriate things at work.
When you ask if it should always be legal to say sexually inappropriate things at work the salient law is sexual harassment law which imposes torts **on the company** for tolerating sexually inappropriate remarks. Thus, respondents may be expressing their belief that such laws shouldn't be repealed which is consistent with the other outcome.
I was lucky enough to help with Dr. Kahneman's talk at Google, and part of that was being in the group that had lunch with him.
I asked him, "Dr. Kahneman, you've been writing about thinking for 40 years. Do you think you've had any impact on the way people think?"
He said, "No, not even my own!" He proceeded to relate an anecdote where his daughter had internalized his teachings better than he himself had.
Well, he's changed the way I think, for sure.
I interpreted the two things slightly differently:
"Inappropriate things" => I think women with a big ass are the most attractive
"Sexually inappropriate things" => Hey Linda, I really like your ass! Wanna go to my place after work?
That's not what you meant but that's how I've read the question.
On Linda the bank teller... Is there philosophical term --perhaps pedantry-- for those that want to trick and belittle people about logic by pretending you are a real person. The two sentence context before the question sets one up for a discussion on Linda as a feminist. There was no hint that we were in a philosophy department classroom.
Arrogant pedantry.
>“No, there has to be a minimum wage.”
>“What if this keeps Linda from finding a job?”
Altruism is about sacrificing the people who create jobs, not helping the people who want jobs, thus the evasion of long-range, indirect, unintended effects. When jobs decrease, minimum wage advocates will say that their intentions are moral, ie, "helping" people, thus the destructive effect is unfortunate but morally correct.
Economics was, in a more rational culture, recognized as a moral science, the study of rational choices in a market. IF man want material values, he SHOULD use reason to guide production. Reason is basically for man's life as end, not reason serving irrational ends.
Agree re most people typically just pick the thing that sounds good or that fits the common social truth in their social circle. I would add people also don't think through second order effects. They aren't thinking "...well if I accept this position then I should accept x and y and z also." They also arent thinking "if x happens then people will react with y." There is also some fear of other people's freedom going on with this kind of thing, you want to be free to speak your mind on what you think is edgy but you don't want to hear something that you find offensive. For me personally it's normal that in a workplace your behavior is going to be constrained in exchange for money. If you are going around upsetting other employees that will hurt the firms ability to work on projects and keep and retain talent. Even if it were not a legal issue I think many firms would still fire people for certain kinds of speech for that reason.
I'm not sure the Twitter poll results are illogical. There's a difference between inappropriate and illegal.
"Inappropriate speech," without further qualification, is likely assumed by most readers to be legal speech. Sexually inappropriate speech, on the other hand, could very well be illegal and your audience knows this. At minimum, it could need adjudicating in court.
The response profile you got thus appears pretty logical.
The respondent to the psychology questionnaire thinks first: how likely is it that LInda would be a bank teller. This is not especially likely, but far from impossible; say, 1%. Next he thinks: how likely is it that Linda, now known to be a bank teller, is active in the feminist movement. That's very likely; say 50%. 50% > 1%; so . . . .
The first question is unclear and user interpretation affects the results. Does "say inappropriate things" mean SOME things or ALL things? In the response options, is it the speech we are varying or the context?
While "sexually inappropriate things" is certainly a subset of "inappropriate things", I suspect that if you were to make a list of all inappropriate things ranked in order of severity, the sexual ones would be biased towards the top.
Polite society tends to think sexual misdeeds are a special kind of perfidy, and I also suspect that most people, if given the two questions side by side, would think "when should it be legal to say things with an average badness of 3/10" vs. "when should it be legal to say things with an average badness of "6/10"?
Put another way I think Bryan might appreciate, yes, sexual inappropriate comments are a subset of inappropriate comments. But if x = the probability that a particular inappropriate comment crosses the line from boorish and cringe to actively bad, then Pr(x | sexual) is probably going to be higher than Pr(x | any comment).
The conjunction fallacy itself seems like a fallacy. Aren't there are a lot of different things that frequently but not always occur in conjunction with one another? Like...not all heavy rains cause flooding and not all flooding is caused by heavy rain, but still, it'd be weird to say that the probably of each one occurring independently is higher than the two occurring together.