Spin Off Logic Problem From Genius-Religion Debate

[PairTheBoard]

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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

[Metric]

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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.

[TomCowley]

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.

[Subfallen]

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.

[TomCowley]

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?

[TomCowley]

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.

[MrMore]

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.

[Piers]

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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.

[TomCowley]

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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.

[Subfallen]

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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.