[<PERSON> was listed in the Guinness Book of World Records under "Highest IQ" from 1986 to 1989[9] and entered the Guinness Book of World Records Hall of Fame in 1988.[9][10] Guinness retired the "Highest IQ" category in 1990 after concluding IQ tests were too unreliable to designate a single record holder.[9] The listing drew nationwide attention.[11]
Guinness cited <PERSON> performance on two intelligence tests, the Stanford-Binet and the Mega Test. She took the 1937 Stanford-Binet, Second Revision test at age ten.[5] She claims her first test was in September 1956 and measured her mental age at 22 years and 10 months, yielding a 228 score.[5] This figure was listed in the Guinness Book of World Records; it is also listed in her books' biographical sections and was given by her in interviews.
https://en.wikipedia.org/wiki/Marilyn_vos_Savant
IQ is "supposed" to be normally distributed with mean 100 and sd 15. That puts an IQ of 228 as being 8.5 standard deviations from the mean. I tried to use Excel to calculate what percentile that would be, but it was so close to one that Excel rounded to exactly 1. Excel has 15 digits of accuracy, which corresponds to one quadrillion. So one should expect MvS levels of IQ in one in one quadrillion people. So it's understandable that Guinness has decided this is not a meaningful measure. At 130, IQ being normal would predict that we're already at the top 2.28%. 840
That's about the limit at which IQ is valid.
For a somewhat quantitative measure, I took the estimate of 80% heritability, and assumed this is constant across IQ levels (it's probably not, but I'm not sure how to account for that).
I initialized a population with
genotypes = random.normal(loc=100,scale = 15,size=1000000)
phenotypes = [.8*genotype+.2* random.normal(loc=100,scale = 15) for genotype in genotypes]
indices = [index for index in range(len(phenotypes)) if phenotypes[index]>125]
genotypes = [genotypes[index] for index in indices]
phenotypes = [phenotypes[index] for index in indices]
(Note that I took a minimum of 125 so that the average would be around 130)
Next, I did:
for i in range(5):
cutoff = sorted(phenotypes)[len(phenotypes)//2]
genotypes = [genotypes[index] for index in range(len(genotypes)) if phenotypes[index]>cutoff ] *2
phenotypes = [.8*genotype+.2* random.normal(loc=100,scale = 15) for genotype in genotypes]
print(sum(phenotypes)/len(phenotypes))
This simulates the top half of each generation having four kids per couple. I didn't bother modeling cross-breeding, assuming that it wouldn't affect the general trend much. The results I got were:
130.78537880060884 133.84842056079236 136.4018939835269 138.75734310708546 140.9813744502485
What if you have eight kids per couple? For that, I got
133.40673479773932 138.<PHONE_NUMBER>.82479867356096 146.75034206831734 151.<PHONE_NUMBER>
However, keep in mind that my numbers start after one generation of breeding. So, 133.4067 is the first generation to be bred. If "generation one" is just people taken from the general population with high IQ, then "generation five" corresponds to 146.75.
Also, 15 years is rather short for a generation. You have some leeway in that the people running this are, as you say "unscrupulous", and thus not concerned with age of consent, but even so, the whole reason (or at least, one of the reasons) that we have age of consent is that 15-year-olds' judgment is not the same as 20-year-olds. Some analyses have put the age at which the brain stops developing as late as 25. While you can take the 15-year-olds that are smarter relative to other 15-year-olds, and this would give you some information about their final intelligence, it would be of questionable validity. Furthermore, for a breeding program to work, you would have to have a lot of children; the more children you have, the more selective you can be. 882