Spin Off Logic Problem From Genius-Religion Debate

[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.