Spin Off Logic Problem From Genius-Religion Debate

[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.