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The engineer/lawyer problem explanation (spoilers) is only correct in a world where lawyers and engineers have all the same characteristics. That the sampled

by Uhhrrr 15y ago

The engineer/lawyer problem explanation (spoilers) is only correct in a world where lawyers and engineers have all the same characteristics. That the sampled individual is a man will skew things all by itself. Of the lawyers, approximately 40% will be women, whereas only 11% of the engineers. So our samplee could be one of 27 engineers or 42 lawyers - we've already bumped Peng from .3 to .39! That he likes math puzzles easily takes Peng to over .4, meaning the answer can't be A).

nostromo 15y ago
They didn't do a good job representing that particular heuristic. Here's a better example: http://en.wikipedia.org/wiki/Representativeness_heuristic#The_Taxicab_problem http://en.wikipedia.org/wiki/Representativeness_heuristic#Th... A better way to explain the common response to question #2 would be "quiz questions usually only give me information relavant to their answers" heuristic.
deleted 15y ago
[deleted]
gburt 15y ago
The author of this quiz seems to have completely misunderstood the relevant research. Either he has to assume that all individuals are identical (in which case, the little story is irrelevant) or he needs to apply Bayes rule according to the probabilities associated with the factors expressed in the personality exposition. Either way, the article's explanation for that particular question is wrong.
- diego 15y ago
  Exactly. Here's the example used in Kahneman's book: "Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. This description was intended to convey no information relevant to the question of whether Dick is an engineer or a lawyer." The description in the quiz is very different.
  - elnerdo 15y ago
    This still conveys a lot of information. Engineering is more male-heavy than lawyering.
    - diego 15y ago
      Yes, there's more to it. The experiment was done with 70/30 and 30/70 ratios for different subjects. The book doesn't say whether they specified they were all males, my guess would be that they did.
      - jfoutz 15y ago
        a frequentist would take issue with the two sons, one born on a tuesday problem. you can actually count up the permutations. let's say we have 10 engineers, 9 of them are male. we also have 10 lawyers, 6 of them are male. Let's say one in 10 people likes doing math on the weekend. There are 90 out of 100 ways to have a group of male engineers, one of which who likes math, but only 60 out of 100 ways to do the same with a male lawyer. furthermore, if we add in the four kids as another 1 in 10 thing, the situation gets even worse. This isn't bayesian, this is just counting boxes on a permutation table.
        screwt 15y ago
        > This isn't bayesian, this is just counting boxes on a permutation table. It's the same thing. Bayes' theorem allows you to shortcut straight to the answer without having to draw out a full probability tree / permutation table. But the underlying math is the same - in each case you have a different probability of B given A, versus B given (not A).
        wizzard 15y ago
        Personally I wouldn't call it "Bayesian" so much as just "a conditional probability." The question doesn't ask what the probability is that a randomly selected participant is an engineer, it asks what the probability is that a participant is an engineer given that he has "typical" engineer-like traits. But then yes, ideally you could use Bayes' Rule to find that probability.
amireza 15y ago
I think it still depends which school do you belong, Bayesian or frequentists. A real frequntist may not assign a probability to a single instance of society! he is either an engineer or not!
bfung 15y ago
30 engineers, 70 lawyers, the probability of being an engineer is 30%. What Jack likes to do is irrelevant. Why can't a lawyer like math and dislike politics (winning a case framed by certain rules is just a puzzle/game to hack)?
- Jach 15y ago
  What Uhrrr is saying is that prob(Person is an engineer | Named Jack and has Jack's description and initial 30/70 ratio) > prob(Person is an engineer | 30/70 ratio)=30%. I think the article goofed on that question too. I'd rather have seen an illustration of the conjunction bias, which is similar. Given Jack's description, what's more probable: Jack is a lawyer, or Jack is a lawyer who likes classical music. (The first one, but people overwhelmingly pick the second one.)
- prof_hobart 15y ago
  It's not that a lawyer can't like maths or dislike politics. The issue is whether they are less likely to on average. From my personal experience of knowing several of both groups, I would say that on average the lawyers I know are less interested in maths than the engineers and more interested in politics than them. It doesn't apply universally (some of the engineers I know are obsessed by politics, just not all of them and not as many of them as lawyers). It's possible that there may be research that demonstrates this doesn't hold when you look at the sum total of lawyers and engineers, but that's not what the author is trying to rely on. Assuming that there is a skew of preferences, then this info isn't irrelevant you can perfectly reasonably use this to help identify the likelihood of this person being in one group or another. It doesn't guarantee that you're right, but it will improve your chances.
  - condiment 15y ago
    I think the point that many are missing is that is not known for certain that an engineer is more likely to enjoy certain hobbies over others. People use their personal experience to develop a heuristic which this test is designed to reveal. Getting hung up over the specificity of the hobbies and interests and the likelihood of those hobbies and interests representing either or a lawyer or an engineer is irrelevant, because the only factual data that was provided by the questioner is that 30% of the participants were engineers, and 70% were lawyers.
ubernostrum 15y ago
I'm just gonna quote what I said when this was on Metafilter a few months back: "Anyway, yes, the fundamental problem in these questions is not how people think -- it's that the question they want the respondent to think they're asking, and the question they claim they're actually asking, are two different things. The lawyer/engineer one is a classic example of this; what they hope is that you will read it as "how likely is it that these personality traits correlate to an engineer", so that they can then swoop in and say "what we were really asking is the mathematical definition of a percentage!" Which ultimately tells us very little about the respondents and quite a bit about the people conducting the quiz..."
nevinera 15y ago
It's worse than that - the probability is biased as you say if the sample were chosen randomly, but they did not claim that. Given that the only distinguishing characteristic mentioned is a boolean (engineer or lawyer), and that they only chose one sample, the probability might just as well be 50% - the probability of the person picking the sample deciding one way or the other.
mjwalshe 15y ago
And the killer mistake in # 2 is that he "He shows no interest in political and social issues" Now Law is inherently political (both big and small P's) even more so in the USA where Judges etc are elected. I would bet good money that hes more likely an engineer than a lawyer.

by Uhhrrr 15y ago

nostromo 15y ago

They didn't do a good job representing that particular heuristic. Here's a better example: http://en.wikipedia.org/wiki/Representativeness_heuristic#The_Taxicab_problem http://en.wikipedia.org/wiki/Representativeness_heuristic#Th... A better way to explain the common response to question #2 would be "quiz questions usually only give me information relavant to their answers" heuristic.

deleted 15y ago

[deleted]

gburt 15y ago

The author of this quiz seems to have completely misunderstood the relevant research. Either he has to assume that all individuals are identical (in which case, the little story is irrelevant) or he needs to apply Bayes rule according to the probabilities associated with the factors expressed in the personality exposition. Either way, the article's explanation for that particular question is wrong.

diego 15y ago
Exactly. Here's the example used in Kahneman's book: "Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. This description was intended to convey no information relevant to the question of whether Dick is an engineer or a lawyer." The description in the quiz is very different.
- elnerdo 15y ago
  This still conveys a lot of information. Engineering is more male-heavy than lawyering.
  - diego 15y ago
    Yes, there's more to it. The experiment was done with 70/30 and 30/70 ratios for different subjects. The book doesn't say whether they specified they were all males, my guess would be that they did.
    - jfoutz 15y ago
      a frequentist would take issue with the two sons, one born on a tuesday problem. you can actually count up the permutations. let's say we have 10 engineers, 9 of them are male. we also have 10 lawyers, 6 of them are male. Let's say one in 10 people likes doing math on the weekend. There are 90 out of 100 ways to have a group of male engineers, one of which who likes math, but only 60 out of 100 ways to do the same with a male lawyer. furthermore, if we add in the four kids as another 1 in 10 thing, the situation gets even worse. This isn't bayesian, this is just counting boxes on a permutation table.
      - screwt 15y ago
        > This isn't bayesian, this is just counting boxes on a permutation table. It's the same thing. Bayes' theorem allows you to shortcut straight to the answer without having to draw out a full probability tree / permutation table. But the underlying math is the same - in each case you have a different probability of B given A, versus B given (not A).
        wizzard 15y ago
        Personally I wouldn't call it "Bayesian" so much as just "a conditional probability." The question doesn't ask what the probability is that a randomly selected participant is an engineer, it asks what the probability is that a participant is an engineer given that he has "typical" engineer-like traits. But then yes, ideally you could use Bayes' Rule to find that probability.

amireza 15y ago

I think it still depends which school do you belong, Bayesian or frequentists. A real frequntist may not assign a probability to a single instance of society! he is either an engineer or not!

bfung 15y ago

30 engineers, 70 lawyers, the probability of being an engineer is 30%. What Jack likes to do is irrelevant. Why can't a lawyer like math and dislike politics (winning a case framed by certain rules is just a puzzle/game to hack)?

Jach 15y ago
What Uhrrr is saying is that prob(Person is an engineer | Named Jack and has Jack's description and initial 30/70 ratio) > prob(Person is an engineer | 30/70 ratio)=30%. I think the article goofed on that question too. I'd rather have seen an illustration of the conjunction bias, which is similar. Given Jack's description, what's more probable: Jack is a lawyer, or Jack is a lawyer who likes classical music. (The first one, but people overwhelmingly pick the second one.)
prof_hobart 15y ago
It's not that a lawyer can't like maths or dislike politics. The issue is whether they are less likely to on average. From my personal experience of knowing several of both groups, I would say that on average the lawyers I know are less interested in maths than the engineers and more interested in politics than them. It doesn't apply universally (some of the engineers I know are obsessed by politics, just not all of them and not as many of them as lawyers). It's possible that there may be research that demonstrates this doesn't hold when you look at the sum total of lawyers and engineers, but that's not what the author is trying to rely on. Assuming that there is a skew of preferences, then this info isn't irrelevant you can perfectly reasonably use this to help identify the likelihood of this person being in one group or another. It doesn't guarantee that you're right, but it will improve your chances.
- condiment 15y ago
  I think the point that many are missing is that is not known for certain that an engineer is more likely to enjoy certain hobbies over others. People use their personal experience to develop a heuristic which this test is designed to reveal. Getting hung up over the specificity of the hobbies and interests and the likelihood of those hobbies and interests representing either or a lawyer or an engineer is irrelevant, because the only factual data that was provided by the questioner is that 30% of the participants were engineers, and 70% were lawyers.

ubernostrum 15y ago

I'm just gonna quote what I said when this was on Metafilter a few months back: "Anyway, yes, the fundamental problem in these questions is not how people think -- it's that the question they want the respondent to think they're asking, and the question they claim they're actually asking, are two different things. The lawyer/engineer one is a classic example of this; what they hope is that you will read it as "how likely is it that these personality traits correlate to an engineer", so that they can then swoop in and say "what we were really asking is the mathematical definition of a percentage!" Which ultimately tells us very little about the respondents and quite a bit about the people conducting the quiz..."

nevinera 15y ago

It's worse than that - the probability is biased as you say if the sample were chosen randomly, but they did not claim that. Given that the only distinguishing characteristic mentioned is a boolean (engineer or lawyer), and that they only chose one sample, the probability might just as well be 50% - the probability of the person picking the sample deciding one way or the other.

mjwalshe 15y ago

And the killer mistake in # 2 is that he "He shows no interest in political and social issues" Now Law is inherently political (both big and small P's) even more so in the USA where Judges etc are elected. I would bet good money that hes more likely an engineer than a lawyer.