Spin Off Logic Problem From Genius-Religion Debate
 

Regardless of the subject, what are we to make of the fact that, lets say, the percentage of people with an IQ of x who believe Y to be true, is x/6? This is a statistic after a survey. Not a scientific formula

Of course we must stipulate that the above statistic is not known to anybody before they come to their conclusion about Y.

Since no one has an IQ of 300, there is no group of people who are better than even money to believe Y. And there is no guarantee that the formula would hold for them anyway. Of the very smartest people alive about 30% believe Y. In other word even among the very smartest people, at least 70% believe Y isn't true. (Remember again that the results of this survey were not known when opinions were first expressed.)

On the other hand there is the unmistakable pattern that the smarter you are, the more likely you are to believe Y.

Armed with this information, but with no information as to what Y is about, are you justified in believing that Y is probably true?

PS To avoid muddying the waters, I will specify that anyone who believes Y to be true does so with the same degree of high certainty. Likewise those who don't believe Y. Perhaps 95%.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

As long as Y is the kind of thing you score points for getting right in an IQ test.

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As long as Y is the kind of thing you score points for getting right in an IQ test.

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Like seeing a multiple choice question, assigning probability's and opting for the most likely you mean?

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As long as Y is the kind of thing you score points for getting right in an IQ test.

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This is far from clear. Notice that if you only surveyed very smart people you would have no reason to bet Y was correct.

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As long as Y is the kind of thing you score points for getting right in an IQ test.

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Like seeing a multiple choice question, assigning probability's and opting for the most likely you mean?

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Yeah, if Y is something like that, then people who score highly on IQ tests are more likely to get it right. I'm not convinced that scoring highly on an IQ test means you're more likely to get any old question right - why would anyone think that?

It's probably true that there are a class of problems for which IQ-successful strategies are not optimal.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

This is an excellent point that invalidates some of the points made in the other thread - namely, the one about geniuses in the 1600s made by Mendacious.

I'd agree with the Y-truth correlation on the stipulation that the subject matter required to form the opinion is broadly understandable and available to all and not highly esoteric. It may also need to be limited to a single culture/country. I can think of some limited domains of knowledge where the smartest experts can get it wrong for reasons of groupthink or similar, where the gut feelings of the less intelligent are more likely to be correct. But that's certainly not the case for religion, evolution, political theories, social theories and so on.

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As long as Y is the kind of thing you score points for getting right in an IQ test.

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This is far from clear. Notice that if you only surveyed very smart people you would have no reason to bet Y was correct.

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Sorry - I read too quickly. Didnt notice that most of them thought it was incorrect. (EDIT: Despite the fact you went out of your way to make it abundantly clear)

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Yeah, if Y is something like that, then people who score highly on IQ tests are more likely to get it right. I'm not convinced that scoring highly on an IQ test means you're more likely to get any old question right - why would anyone think that?

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?

Do you really think that the group of people who can:

- Correctly recognize patterns
- Think quickly and with agility
- Understand mathematical relationships
- Understand logical relationships
- Have good reading comprehension
- Have a solid vocabularly,

are going to be outperformed on questions of fact or considered opinion by the group of people who:

- Can't recognize patterns as well
- Can't think as quickly or with agility
- Don't understand mathematical relationships as well
- Don't understand logical relationships as well
- Don't have as good a reading comprehension
- Don't have as solid a vocubularly

bunny: WTF?

Re: Spin Off Logic Problem From Genius-Religion Debate
 

No I think the first group will outperform the second on a huge number of such questions. I do think there are likely to be questions for which the IQ-maximising strategies are not optimal (similar to the groupthink you mentioned above). In that small subset of questions, high IQ will be a liability.

EDIT: Also the problem with IQ tests is that they test all of those things together. Someone in the second group may be much, much better than me in all of the categories you list except for vocabulary (for example). I will then score a higher IQ than them in a test situation even though they will be more likely to get an IQish question right in non-test conditions (once it was patiently explained to them in simple language)

Re: Spin Off Logic Problem From Genius-Religion Debate
 

Let's hear them.

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In that small subset of questions, high IQ will be a liability.

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I can't imagine a high IQ being a liability in practical terms. Maybe an absurd hypothetical like "in order to get the question right, you must fail to understand it," but in the real world - high IQ a liability?

Re: Spin Off Logic Problem From Genius-Religion Debate
 

See my edit as well for another reason I'm not convinced a higher IQ individual is more likely to solve a problem than a lower IQ individual. Test conditions necessarily impose artificial limitations.

I'll ponder on some examples - I dont have a catalog, I just expect the category exists, since it seems unlikely to me that we have been able to formulate the optimal approach for solving all problems.

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In that small subset of questions, high IQ will be a liability.

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I can't imagine a high IQ being a liability in practical terms. Maybe an absurd hypothetical like "in order to get the question right, you must fail to understand it," but in the real world - high IQ a liability?

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There were no constraints on Y in DS's scenario. I agree with you that a high IQ is a good indicator of problem solving ability in general. I dont think it's right to annoint it as the be-all and end-all though - I suspect a category of (perhaps odd) questions exists which will deceive people who approach problems in the way that scoring highly on an IQ test requires - perhaps Y is one of those questions.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

i'm going to have to go with believing Y is probably true ... but i'll have to think a bit more about this.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

Let's say using independent methods I determine that Y has an n probability of being correct. After recognizing this correlation, I would adjust that upward significantly. The extent would depend on n though - if n is initially .000001, then I might raise go all the way to .05 certainty of Y on this basis. If n is initially .9, then I might go to .95. I don't think I can evaluate the probability of Y being correct solely on the basis of this correlation.

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See my edit as well for another reason I'm not convinced a higher IQ individual is more likely to solve a problem than a lower IQ individual. Test conditions necessarily impose artificial limitations.

I'll ponder on some examples - I dont have a catalog, I just expect the category exists, since it seems unlikely to me that we have been able to formulate the optimal approach for solving all problems.

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Well, this is more about groups than individuals. Of course one individual can have more common sense than another, but I'd like to hear how IQ can bias thinking strongly enough, across the group of smart individuals, that their important advantages in other areas would be wiped out.

The reason I challenged you to come up with examples is because it seems your comments are just coming from a gut feeling. If what you say is true, there should be examples in the world.

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In that small subset of questions, high IQ will be a liability.

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I can't imagine a high IQ being a liability in practical terms. Maybe an absurd hypothetical like "in order to get the question right, you must fail to understand it," but in the real world - high IQ a liability?

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There were no constraints on Y in DS's scenario. I agree with you that a high IQ is a good indicator of problem solving ability in general. I dont think it's right to annoint it as the be-all and end-all though - I suspect a category of (perhaps odd) questions exists which will deceive people who approach problems in the way that scoring highly on an IQ test requires - perhaps Y is one of those questions.

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In fact, I think it's quite likely Y is one of these odd questions. If you line up six freaks with IQs of 200, probably only 2 of them think it's true. 4 of them think it's false. When you survey 100 people with IQs of 150, around 25 think it's true and 75 think it's false.

I dont see what grounds you have for thinking it's probably true, since most people think it's false (including the super-geniuses). If you're going to go with false, you have to then explain why the high-IQ people are more likely to get it wrong. Y being in the hypothetical category I'm talking about is probably a good explanation, dont you think?

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See my edit as well for another reason I'm not convinced a higher IQ individual is more likely to solve a problem than a lower IQ individual. Test conditions necessarily impose artificial limitations.

I'll ponder on some examples - I dont have a catalog, I just expect the category exists, since it seems unlikely to me that we have been able to formulate the optimal approach for solving all problems.

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Well, this is more about groups than individuals. Of course one individual can have more common sense than another, but I'd like to hear how IQ can bias thinking strongly enough, across the group of smart individuals, that their important advantages in other areas would be wiped out.

The reason I challenged you to come up with examples is because it seems your comments are just coming from a gut feeling. If what you say is true, there should be examples in the world.

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It was definitely a gut feeling and I'll think on it further. However, I by no means meant to suggest that the class of problems I am referring to was either large, nor important in a real-world sense.

I think the situation DS is describing would be explained either by Y being in this class of anti-IQ problems or being so difficult that it is beyond human limits. I approach life from the arrogant position that I can solve anything if I think about it long enough, so I've probably discounted this second explanation without adequate justification. [img]/images/graemlins/smile.gif[/img]

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There were no constraints on Y in DS's scenario. I agree with you that a high IQ is a good indicator of problem solving ability in general. I dont think it's right to annoint it as the be-all and end-all though - I suspect a category of (perhaps odd) questions exists which will deceive people who approach problems in the way that scoring highly on an IQ test requires - perhaps Y is one of those questions.

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Okay, I'll grant that. But I would also say that there's no reliable way to evaluate such "odd" questions. If IQ is a liability, then I think reason is (almost always, you'd basically have to use set theory to find a counterexample) also a liability. But I don't think we can discover truths objectively and collectively without applying reason - subjectively and personally perhaps...

Re: Spin Off Logic Problem From Genius-Religion Debate
 

Stop with the off the subject IQ debate. Stipulate that the higher your IQ, the more likely you are to be right.

This is an interesting problem regarding our right to extrapolate. The Sklansky Extrapolation Question. I personally have not decided on an answer.

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There were no constraints on Y in DS's scenario. I agree with you that a high IQ is a good indicator of problem solving ability in general. I dont think it's right to annoint it as the be-all and end-all though - I suspect a category of (perhaps odd) questions exists which will deceive people who approach problems in the way that scoring highly on an IQ test requires - perhaps Y is one of those questions.

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Okay, I'll grant that. But I would also say that there's no reliable way to evaluate such "odd" questions. If IQ is a liability, then I think reason is (almost always, you'd basically have to use set theory to find a counterexample) also a liability. But I don't think we can discover truths objectively and collectively without applying reason - subjectively and personally perhaps...

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Sure we can - if a class of these questions was discovered a good method of answering one would be to give it to lots of dumb people and see what they thought. [img]/images/graemlins/smile.gif[/img]

Perhaps any real-world example of what I'm speculating exists would involve a "trick question" flavour. Where the mental habits of logical, deep thinking people led them to make unwarranted assumptions which led away from the correct answer. Do you think the "groupthink" phenomenon Phil153 mentioned exists? If it does, isnt it reasonable it exists at some level amongst the "group" of high IQ individuals - from adopting similar mental habits and approaches to problems and acquiring similar blind spots?

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Sure - my new answer is that you're not justified to think it is more likely. Most super geniuses think it's wrong, a larger proportion of geniuses and an even bigger majority of very, very clever people. Given our history I dont see how you can bet against all those smart people telling you Y is false. (Though the reasons the dissenting super geniuses give are worth investigating, just in case)

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In that small subset of questions, high IQ will be a liability.

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I can't imagine a high IQ being a liability in practical terms. Maybe an absurd hypothetical like "in order to get the question right, you must fail to understand it," but in the real world - high IQ a liability?

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It doesn't have to be that esoteric. How bout "Read the following IQ question. Now tell me if those who have IQs between 90-100 are more than 50% to get it right"

But even those questions are not slam dunks, I will admit. In fact I think I'd do better at them then a 95 IQ would.

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As long as Y is the kind of thing you score points for getting right in an IQ test.

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This is far from clear. Notice that if you only surveyed very smart people you would have no reason to bet Y was correct.

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Can you extrapolate this Trend into hypothetical super IQ's? If that's what you want to do I think it's up to you to make the case. Extrapolating trends can be a tricky business. You are using the phrase "probably true" so your arguement needs to make some kind of sense of the term "probably" in this context. I don't think it makes sense to talk about believing Y to be "probably true" as a pig in a poke, where you don't even know what Y is. If you have more statistics or even guesses about statistics for how such trends extrapolate you might believe the Trend for Y falls into the statistics of extrapolated Trends for other Y's. Even then I think you need to see what Y is to judge whether it is similiar in nature to the Y's with extrapolated Trends that work in other statistics.

PairTheBoard

Re: Spin Off Logic Problem From Genius-Religion Debate
 

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Stop with the off the subject IQ debate. Stipulate that the higher your IQ, the more likely you are to be right.

This is an interesting problem regarding our right to extrapolate. The Sklansky Extrapolation Question. I personally have not decided on an answer.

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It wasn't really an IQ debate. It was a debate about whether measured intelligence does indeed match with correctness on every problem.

Part of the problem with your question is defining smarter, since the definition will throw it one way one or the other. Does smarter mean more likely to be correct on any given problem? If so, you should stipulate, because you're almost assuming the premise in that case.

If you want to start from that point, then the answer is yes, by definition. The true nature of any given problem, where opinion forms a part, is unknown, as is the IQ required to solve it correctly. Therefore the only data we have is that Y belief increases with smartness and correctness increases with smartness.

You can't abstract away the hard questions, Mr. Sklansky. If you're going to use a term like "smarter" then this question cannot be answered without determining what we mean by "smarter".

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Therefore the only data we have is that Y belief increases with smartness and correctness increases with smartness.

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No, we have the latter but not the former. We have a statistical indication that Y belief increases with smartness, but we don't know how reliable that indication is (most importantly, we don't know whether we can extrapolate). We also know that people tend to disbelieve Y even at the highest levels of intellect. So even given a definition of smart as "more likely to be correct," it's not simple to say that Y is likely to be true.

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Armed with this information, but with no information as to what Y is about, are you justified in believing that Y is probably true?

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No, but only for institutional reasons.

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Perhaps any real-world example of what I'm speculating exists would involve a "trick question" flavour. Where the mental habits of logical, deep thinking people led them to make unwarranted assumptions which led away from the correct answer. Do you think the "groupthink" phenomenon Phil153 mentioned exists? If it does, isnt it reasonable it exists at some level amongst the "group" of high IQ individuals - from adopting similar mental habits and approaches to problems and acquiring similar blind spots?

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But high IQs are better at checking their assumptions and at avoiding groupthink. In a specific case it's true that a genius could be more likely to be incorrect because of increased exposure to some erroneous assumption (while a total bumpkin, unaware of the assumption, wouldn't be limited by it). But that seems pretty thin to me. It would be a very contingent situation, and a random approach would have to be superior to the genius approach (in other words, a low IQ person might do better than a high IQ person, but only if a coin-flip would also do better than the high IQ person).

Even in these cases, a person with very high IQ but without a conventional upbringing/education (someone raised in the bush for instance) should be a massive favorite over anyone with a low IQ.

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Supposed evidence for Y: The smarter you are the more likely you are to believe Y.

I don't think that alone is enough to justify belief that Y IS true. However, at least in general it does make it more likely that Y is true, so assuming we have no other evidence then we are justified in believing Y is probably true. We started with 50% confidence Y was true, now we have some evidence that Y is true so our confidence should increase.

One potential problem would be certain beliefs which say 3% of brilliant physicists believe to be true and the rest believe to be false. For such a belief the smarter you are the more likely you are to believe it's true, and the more likely to believe it's false. This is because the only people that believe either way are brilliant physicists.

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Perhaps any real-world example of what I'm speculating exists would involve a "trick question" flavour. Where the mental habits of logical, deep thinking people led them to make unwarranted assumptions which led away from the correct answer. Do you think the "groupthink" phenomenon Phil153 mentioned exists? If it does, isnt it reasonable it exists at some level amongst the "group" of high IQ individuals - from adopting similar mental habits and approaches to problems and acquiring similar blind spots?

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But high IQs are better at checking their assumptions and at avoiding groupthink. In a specific case it's true that a genius could be more likely to be incorrect because of increased exposure to some erroneous assumption (while a total bumpkin, unaware of the assumption, wouldn't be limited by it). But that seems pretty thin to me. It would be a very contingent situation, and a random approach would have to be superior to the genius approach (in other words, a low IQ person might do better than a high IQ person, but only if a coin-flip would also do better than the high IQ person).

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Then are you claiming that Y must be true. (Since if Y is false, low IQ people do better which implies coin-flip is better than high IQ people who do better than 50%)

Re: Spin Off Logic Problem From Genius-Religion Debate
 

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Stop with the off the subject IQ debate. Stipulate that the higher your IQ, the more likely you are to be right.

This is an interesting problem regarding our right to extrapolate. The Sklansky Extrapolation Question. I personally have not decided on an answer.

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If you make that stipulation there is no problem. Y must be false for this Trend to be consistent with the stipulation. With the stipulation the Trend should not happen for a Y that is True. If Y is True this Trend says that for this Y, the higher your IQ the more likely you are to be wrong. That's why bunny's point is so relevant. The stipulation may not be realistic, especially for this particular Y.



PairTheBoard

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One potential problem would be certain beliefs which say 3% of brilliant physicists believe to be true and the rest believe to be false. For such a belief the smarter you are the more likely you are to believe it's true, and the more likely to believe it's false. This is because the only people that believe either way are brilliant physicists.

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This is an excellent point -- I was going to say something very similar to this. I certainly agree with the above post, but I would actually take it farther than this -- let's say that the 3% of physicists believe in a theory which would (if correct) invalidate something that everyone else believes is obviously true -- not something they merely don't have an opinion about (for example, that time moves at the same rate for everyone/everything, or that all meter sticks measure the same length for everyone).

Such a theory could say some very great things and solve other problems (which cause 3% of physicists to find the theory to be absolutely compelling), but simply turn out to be wrong.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

It's a trivially necessary stipulation that all surveyed have been exposed to roughly the same information (otherwise critical obscure knowledge, like if some extreme longshot actually happened, could be disproportionately possessed either by idiots or by geniuses, depending on who witnessed it, which could skew the survey either way). Given that, then anything resembling objective probability precludes (statistically significant) groups of highly intelligent people splitting 70-30 into opposing positions, each with 95% confidence, and believing anything with >95% confidence that can't be analyzed to that level by objective probability is completely irrational.

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Opinion about Y must be decided by something correlated with IQ but not dependent on IQ. Introspection for example.

Y: "Less than one percent of the population would commit suicide to save their mother."

Or something like that...something about human nature under extreme and unreproducible duress.

Re: Spin Off Logic Problem From Genius-Religion Debate
 

The problem can be restated with only the trivially necessary stipluations, namely that there is a statistically meaningful correlation between IQ and belief in Y, and that the sampling method is robust enough to ensure confidence (90%, 95%, 99%, whatever) that the correlation is to IQ and not to a confounding factor also correlated to IQ. Is such a correlation enough to believe (with roughly the same confidence you have in the data) Y is true, even if the highest IQ group surveyed is only 30% to believe Y?

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Let's use a practical definition. A group of higher IQ will set the price with at least as much accuracy and at least as much precision (lower standard deviation) as a group with lower IQ. A group with infinitely high IQ will all give the same exact correct price. The name of the game is setting the price for Y- "believing Y" means setting the price over 50%.

Now, the question can be rephrased to "If the percentage of people who set the price at over 50% increases over a range of IQ, is the price guaranteed to be over 50%?", and the answer is no.

For a question where low intelligence will systematically bias the evaluation of the evidence to a lower answer, as IQ increases, the mean will increase. As long as the exact price is "near" 50%, but below it, and the mean increases proportionally faster than the standard deviation decreases, over the measured range of IQs, it's quite possible for an increasing amount ("the tail") of people to set the price over 50% as IQ rises. Eventually the mean will stop increasing fast enough relative to standard deviation decreasing, and the percentage will start dropping (eventually to 0) as IQ gets even higher and the SD decreases, but it's quite possible for this to happen outside the measured IQ range.

There's the abstract/nerd answer.

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How about a question of the value of a widget to the average IQ person? Might not high IQ people be less accurate in estimating the value than average IQ people? Especially if we sat the value accuracy's test is market dependent, in which case the aggregate average person's answer is pretty much the definition of the answer anyway.

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Armed with this information, but with no information as to what Y is about, are you justified in believing that Y is probably true?

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Well you have a position for claiming Y is more likely then 30% to be true. You seem to be considering extrapolating and assuming a linier relationship between IQ and believers just cause its pretty, where it could easily be a curve with an initial linear part with an asymptote at say 40%. So the claim that Y is probably true is much more debatable than Y is more than 30% true.

You could just use your judgement and assert that Y is probably true. Which is subjective but nether the less a reasonable position.

Of course once we know what Y is everything changes, the specifics of exactly what Y is will carry more weight to most people than the above argument.

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How about a question of the value of a widget to the average IQ person? Might not high IQ people be less accurate in estimating the value than average IQ people? Especially if we sat the value accuracy's test is market dependent, in which case the aggregate average person's answer is pretty much the definition of the answer anyway.

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Sure, if you take a "weak" definition of IQ and say that *on average*, higher IQ = more accurate and more precise, then you just cherry-pick the exceptional case (which could exist) to conclude that IQ and accuracy aren't necessary correlated, which isn't an interesting answer.

I showed a case where increased IQ was correlated to increased accuracy and increased precision and extrapolating still wouldn't be valid, which is a stronger result.

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Sure, if you take a "weak" definition of IQ and say that *on average*, higher IQ = more accurate and more precise, then you just cherry-pick the exceptional case (which could exist) to conclude that IQ and accuracy aren't necessary correlated, which begs the question of providing real-world examples, which is a mess.

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Can you rephrase this sentence? I don't understand what you mean by "weak" definition of IQ.