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I'm sure the 130 IQ value is primarily for illustrative purposes, but there's no way in hell that when "popular"/modern democracy was established, the IQ of the average voter was in the 130s. I doubt you'd get there even if only considering land-owning freemen, let alone universal franchise for all "Anglos". It might be doable with a tight oligarchy, but that's not particularly democratic, is it?
To elaborate, 130 IQ is around 98th percentile. Early American democracy would probably have an average of 105-110, accounting for property requirements (implying some education and capabilities). The more universal it got, the closer it approached the population mean.
Since so many reactionaries and conservatives think that was America's heyday, by all right you only need 105 IQ "Anglos" to pull it off. That's not nearly as high a bar. Depending on which stats site you trust, that's only China, SK, Iran, Japan and Singapore. Well, minus being Anglos, but the Ancient Greeks weren't either and they did alright.
I can't speak for US and what bars one had to meet in order to be granted franchise there, but in 1900-01 Lower House elections in the Austrian part of Austria Hungary, 6% of adults had the right to vote. Assuming the population average IQ was 100 and enfranchisement being totally correlated with IQ, this correspends to the cut-off being 123.
But another way to think about it, is taking the meme to mean the average voter should have 130 IQ. Thus one has to find L, such that integrate(x*exp(-((x-mu)/15)^2/2)/sqrt(2pi)/15,x,L,infinity)/integrate(exp(-((x-mu)/15)^2/2)/sqrt(2pi)/15,x,L,infinity)=130. mu being population average IQ, and L the IQ bound for franchise, such that the average voter has 130 IQ. I don't have a CAS at hand to calculate L myself.
Apart from @EvanTh remark that the 6% of the voting class were not top 6% of the IQ, people 125 years ago had significantly lower IQ. This phenomenon is known as Flynn Effect and it has only recently started to plateau or even reverse.
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What makes you think their voting requirements were closely associated with IQ?
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Genuinely kind of surprised that our site doesn’t support native latex.
I mean, he could have used unicode and abbreviated the error function 𝒩 or φ, and the cumulant Φ which is perfectly usable notation. Would have saved like 80% of the chars and 90% of the parens. Not that I would object to having better math support here.
A cutoff of 123 does correspond to a (rounded) average value of 130 by my calculation (for a population mean 100). I didn't understand the need for a CAS though. Seems like something that any modern programing language can numerically solve for. Or just Newton's method if you're too lazy to open up the documentation for your favorite solver and can only remember one root finding algorithm like me.
Edit to add the calculation in case anyone doesn't trust my math (nullius in verba, etc):
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Yes of course, it’s a laughably high threshold. That said there are some (dubious) estimates that the average Anglo IQ in the Victorian era may have been as high as 108, so gentry landowners having a say 116 average really wouldn’t be out of the question.
Wild. Where can I find out more?
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Basic argument: Victorians had faster reaction times than moderns. Reaction time (which is known to be about 20% correlated with IQ at an individual level) may be a better measure of true population-level g if the Flynn effect (rising population-average IQ test scores over time) is driven by education and not g. If you convert the average Victorian reaction time into an IQ based on the modern reaction time-IQ curve, you get 108. And a 8 IQ-point drop in genetic g is consistent with what you would predict based on dysgenic fertility over the intervening 150 years.
Counterpoint - why do we think that "ability to function in modern society" is better measured by reaction time than performance on IQ tests? All the work which validates the IQ-functionality correlation uses test scores and not reaction time.
How does that work? Under what population parameters?
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There's an obvious potential confounder, and it seems to be present. I checked the first American study showing 208ms (Thompson, H. B. (1903). The mental traits of sex. An experimental investigation of the normal mind in men and women. Chicago, IL: The University of Chicago Press.) and the subjects it used were University of Chicago students.
I checked a later American study (Anger, W. K., Cassitto, M. G., Liang, Y. -X., Amador, R., Hooisma, J., Chrislip, D.W., et al. (1993). Comparison of performance from three continents on the WHO-recommended Neurobehavioral) showing 275.9ms. It used subjects living in working class and entry-level white collar housing. The University of Chicago is an elite university and in 1903, universities in general were considerably more elite than today (or 1993). These are different populations.
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