Of course the mathematical probability of a given statement decreases by adding an additional condition. But the average person uses common sense and basic social skills—not formal probability—in the Linda example.
If someone approaches you and spouts unsolicited information about some lady you don’t know and then asks you which of several statements about her is most probably true, then the average person assumes they are being asked to make their best guess at choosing the statement that contains the most truth.
There probably (ha) is some large % of the population that is ignorant of even basic formal mathematic probability (I’m one of them) and will choose the wrong statement however the question is phrased...
But the average Joe isn’t doing the math anyway when they are asked about Linda. In polite society, if we are asked what we think about a matter of trivial consequence, we give it our best shot using the all the data we have.
If someone tells us a bunch of stuff about Linda that indicates she might have the desire and capability to be active in a social movement, we might guess the conjunction statement to be the one containing more truth. Or we might grab a calculator and ask the person to restate the question (more slowly this time, please) so we can arrive at the answer that would score highly on a math test.
If you tend to do the latter, no one will talk to you after a while. Thus, using formal probability in situations like this is not very rational.
I acknowledged “some large % of the population that is ignorant of even basic formal mathematic probability (I’m one of them) and will choose the wrong statement however the question is phrased...”
In EY’s post, among lots of other stuff, he says research shows the incidence of the conjunction fallacy is reduced by taking measures to ensure those asked about Linda realize they are being asked for the formal mathematical probability and there is some incentive to get the correct answer.
My point was that in real life, especially in matter of trivial significance, people make quick decisions using the context and clues they are presented with. Of course this leads to mistakes, and I therefore do not deny or dismiss the conjunction fallacy exists… but treating every social situation like a math problem is a sure fire way to make sure you are not taken seriously outside of the math classroom.
In real life, the Linda example might go something like this:
Random Person: “Hey you! Linda is all these awesome things. Do you think she is a bank teller? Or do you think she is a bank teller who is also doing some awesome things that other awesome people do? Which one?
Me: “Um. Who are you? And who is Linda?”
RP: “Just answer.”
Me: “Um. Okay. I don’t know, and I’m not sure why you are asking me. But from what you said, it sounds like Linda is probably a bank teller who is doing some awesome things.”
RP: “Nope!! You are wrong. Conjunction fallacy. It is more probable that Linda is just a bank teller. Ha!”
Me: “Wow. I guess you really got me there. I’ve no idea why you asked, no reason to believe anything you said about Linda was true and no incentive to provide anything other than my inkling about what seemed to be the most true scenario given all that. Of course, if you would have presented this as a question about the formal probabilities of each statement, assured me all the data was accurate and this wasn’t some kind of trick question, and then provided even the slightest incentive to answer correctly beyond just wanting to end this horribly awkward interaction, then I posit my response would have been significantly more likely to be correct. Though I suck at math, so you still might have...erm...won. If your point is that the conjunction fallacy it real, you are preaching to the converted, and you’re doing it in a pretty off-putting way. Have a nice day.”
RP: {yelling as I walk away} “Conjunction fallacy. You can’t deny it! Eliezer wrote a massive post, so...”
The conjunction fallacy is a great reason to take time to closely examine the probabilities of important life decisions. It exists. It is limited when the question is framed so that it is clearly a math problem.
I think this is part of what is going on.
Of course the mathematical probability of a given statement decreases by adding an additional condition. But the average person uses common sense and basic social skills—not formal probability—in the Linda example.
If someone approaches you and spouts unsolicited information about some lady you don’t know and then asks you which of several statements about her is most probably true, then the average person assumes they are being asked to make their best guess at choosing the statement that contains the most truth.
There probably (ha) is some large % of the population that is ignorant of even basic formal mathematic probability (I’m one of them) and will choose the wrong statement however the question is phrased...
But the average Joe isn’t doing the math anyway when they are asked about Linda. In polite society, if we are asked what we think about a matter of trivial consequence, we give it our best shot using the all the data we have.
If someone tells us a bunch of stuff about Linda that indicates she might have the desire and capability to be active in a social movement, we might guess the conjunction statement to be the one containing more truth. Or we might grab a calculator and ask the person to restate the question (more slowly this time, please) so we can arrive at the answer that would score highly on a math test.
If you tend to do the latter, no one will talk to you after a while. Thus, using formal probability in situations like this is not very rational.
Did you read the post Viliam_Bur and I both linked to?
Yes. Did you read my post?
I acknowledged “some large % of the population that is ignorant of even basic formal mathematic probability (I’m one of them) and will choose the wrong statement however the question is phrased...”
In EY’s post, among lots of other stuff, he says research shows the incidence of the conjunction fallacy is reduced by taking measures to ensure those asked about Linda realize they are being asked for the formal mathematical probability and there is some incentive to get the correct answer.
My point was that in real life, especially in matter of trivial significance, people make quick decisions using the context and clues they are presented with. Of course this leads to mistakes, and I therefore do not deny or dismiss the conjunction fallacy exists… but treating every social situation like a math problem is a sure fire way to make sure you are not taken seriously outside of the math classroom.
In real life, the Linda example might go something like this:
Random Person: “Hey you! Linda is all these awesome things. Do you think she is a bank teller? Or do you think she is a bank teller who is also doing some awesome things that other awesome people do? Which one?
Me: “Um. Who are you? And who is Linda?”
RP: “Just answer.”
Me: “Um. Okay. I don’t know, and I’m not sure why you are asking me. But from what you said, it sounds like Linda is probably a bank teller who is doing some awesome things.”
RP: “Nope!! You are wrong. Conjunction fallacy. It is more probable that Linda is just a bank teller. Ha!”
Me: “Wow. I guess you really got me there. I’ve no idea why you asked, no reason to believe anything you said about Linda was true and no incentive to provide anything other than my inkling about what seemed to be the most true scenario given all that. Of course, if you would have presented this as a question about the formal probabilities of each statement, assured me all the data was accurate and this wasn’t some kind of trick question, and then provided even the slightest incentive to answer correctly beyond just wanting to end this horribly awkward interaction, then I posit my response would have been significantly more likely to be correct. Though I suck at math, so you still might have...erm...won. If your point is that the conjunction fallacy it real, you are preaching to the converted, and you’re doing it in a pretty off-putting way. Have a nice day.”
RP: {yelling as I walk away} “Conjunction fallacy. You can’t deny it! Eliezer wrote a massive post, so...”
The conjunction fallacy is a great reason to take time to closely examine the probabilities of important life decisions. It exists. It is limited when the question is framed so that it is clearly a math problem.