Spin Off Logic Problem From Genius-Religion Debate

[Taraz]

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I would guess that 30% of the smartest people don't think that dressing nicely with matching clothes and grooming is important. Since smart people probably value ideas more than appearance, this is not a far stretch. In this case would you assume that being careless with your appearance is the correct way to go?

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Apples and oranges. You are talking about a lifestyle opinion, the importance of which changes drastically from person to person. I'm sure it's "correct" for many people to not care about their appearance.

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That was kind of my point though. We have to be more specific about what Y is in this case. Is it some fact about the physical world, a belief about society, or something else?

[MaxWeiss]

I would guess that Y is less than 50% likely true but more than 30%. Am I close?? What's the answer?????

[madnak]

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Yes, but it's not an interesting "no" answer. Assume there are 20 poker tournaments in a given town on a given day that finish at the same time. Exactly one of them has attendance in inverse proportion to IQ (lots of idiots, few geniuses). Somebody at this tournament flops back-to-back royal flushes. After the tournaments end, everybody is surveyed and asked "Do you believe somebody flopped back to back royals at tournament 1? Tournament 2? etc." Everybody not at the tournament will answer no to all with >95% confidence since it's a ridiculous longshot. Everybody at the tournament will answer yes (for their tournament) with 100% confidence since they saw it. Since this tournament is disproportionately dumb people, the number of people who say "no back-to-back royals" will increase with IQ, and they'll be wrong. Manipulate this tournament's IQ and attendance and you can come up with any survey results you want. This "counterexample" doesn't address the intent of the question.

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I don't think this is an example of IQ being a liability, but of IQ being irrelevant. IQ might be seen as a liability because those with low IQ are more likely to have the unjustified but coincidentally true belief that someone flopped two straight flushes but it's still circumstantial. The correct response happens to be inaccurate - that doesn't mean IQ is a liability. (Hopefully this clarifies my position wrt bunny's arguments.)

I agree this has little bearing on the OP.

[madnak]

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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%)

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Right, I didn't make my point well. When smart and dumb people will both tend to get the correct answer, but dumb people will get it more often than smart people, a coin flip may not do better than a dumb person. However, if we isolate the point where the smart people and the dumb people diverge, a coin flip will be more effective than the "smart approach." But that's getting convoluted. I think there's a statistical point to be made regarding coin-flips and correctness, but I'm having trouble specifying it.

The point I made in response to TomCowley and the clarification I'm going to make in response to Taraz are more relevant, I may put some thought into what I'm trying to say about coin-flips. I think I'm trying to say that any process according to which dumb people can be expected to be correct, all things being equal, must be no better than random. I'll make it clearer in a sec.

[madnak]

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I don't think that such a fact necessarily means that Y must be true. It would be a small piece of evidence in favor of Y being true, but it wouldn't be overwhelming.

It could easily be the case that being smart would put you in a special position which would blind you to the factors surrounding Y. Perhaps you surround yourself with people with similar intelligence so you are insulated from the larger community and therefore hold certain beliefs. Or maybe society treats you differently systematically and this results in your belief that Y is true when it is actually false.

It could even be the case that this increase in intelligence lets this group to notice certain trends around them that most people don't notice, but 30% of them misattribute the cause of these trends to Y. So in this case, the fact that they were smart let them notice something unusual and they misinterpreted its significance.

The fact that such a large percentage of the "smartest people alive" do not believe Y should actually decrease the chance that Y is true unless it is a very complex and nuanced concept.

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I'm assuming ceteris paribus here. This is valid if we know nothing about Y. So long as smart people are consistently and systematically more likely to be right, their opinions should be valued higher than those of dumb people in general. There are some situations in which smart people are less likely to be right, but there are (by definition) many more situations in which smart people are more likely to be right. Since Y is unknown in the OP, all this is irrelevant.

In terms of the IQ as liability argument, I didn't appropriately consider the impact of IQ on the personal history of the individual. I should have made my assumption that all other things are equal explicit. While environmental factors related to IQ may result in a situation in which high IQ individuals are less likely to be correct, I don't think IQ itself is likely to have a negative impact.

This is what I was saying about Tom's example, too - I think we have to assume everyone has the same information, etc.

The situation in which being partially right results in the wrong answer more often than being clueless is interesting, and it's exactly the type of situation that I think a good statistical argument can get at. I was trying to come up with such a statement with my coin-flip response to bunny, but there's something more complete... In these situations, I think the responses of dumb people can be considered random somehow. Maybe I'll be able to articulate it later, or someone else will help out.

I don't think it's possible to say anything interesting about the OP that Tom hasn't already said.

[madnak]

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I would guess that Y is less than 50% likely true but more than 30%. Am I close?? What's the answer?????

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I'm not sure it's possible to determine what the actual "price" of Y is, given Tom's model. I'm not sure of the statistical meaning of some of his terms, but it could be as low as 0% or as high as 100% (depending on the influence we allow variance - 0% is clearly less likely than 100% if the tendency to go >50% rises with IQ, but if variance is unknown then I don't think anything is certain). Someone who knows math will have to take it from there.

I stand by the position that there's not enough information presented in the OP to evaluate Y (even if we grant Tom's trivially necessary assumptions).

[MrMore]

First let me say that I'm more or less an atheist, and high IQ, and believe that anyone intelligent who has sincerely, open-mindedly, thought about the question of whether there is a God as the major religions paint it MUST conclude, in the least, that the major religions are nonsensical.

That said, if Y is not the pointless question "does God exist," but the more tangible question, "would the average person be happier if there were no religions,"

I wouldn't jump to the conclusion that high IQ people would be more apt to get the answer right.

I personally think the net level of happiness in the world would increase with the absence of religion. Probably so do most of you. But that doesn't mean we're right. Which is why I brought up the point of market function answers.

[madnak]

I don't think either question is actually consistent with the OP. In particular, we have enough specific information about claims regarding God that we don't need to rely on this sort of reasoning. Also, that new information may change the problem. And I don't think a specific claim should be evaluated based on its popularity - the "smart people" standard is at best a last-ditch when no other information is available IMO.