A lottery would have no selective pressure, so no Idiocracy tendancy. That was part of the reason I suggested that. But the only thing I think the system needs is to have some very basic requirements, and then choose mostly randomly among applicants that want to have children.
Anything more, like only allowing the smartest or the most wealthy is going to get dystopian pretty fast, I would think
The movie is based on the idea that intellegence has a large inherited (~.7) component. Whatever is causing the Flynn effect is acting on the smaller non-genetic component. Interestingly the Flynn effect is only acting on the bottom half of the bell curve suggesting it is the result of the removal of environmental factors that destroy intelligence - things like lead or poor nutrition.
It would be nice to reverse Idiocracy tendancies (Stupid people procreating more than intelligent leading to a general decline)