There is also the related problem of intelligence being negatively correlated with fertility, which leads to a dysgenic trend. Even if preventing people below a certain level of intelligence to have children was realistically possible, it would make another problem more severe: the fertility of smarter people is far below replacement, leading to quickly shrinking populations. Though fertility is likely partially heritable, and would go up again after some generations, once the descendants of the (currently rare) high-fertility people start to dominate.
There is also the related problem of intelligence being negatively correlated with fertility, which leads to a dysgenic trend. Even if preventing people below a certain level of intelligence to have children was realistically possible, it would make another problem more severe: the fertility of smarter people is far below replacement, leading to quickly shrinking populations. Though fertility is likely partially heritable, and would go up again after some generations, once the descendants of the (currently rare) high-fertility people start to dominate.