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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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