I should frequently repost the comments that I make on interesting OKCupid questions. Today's question: "Would the world be a better place if people with low IQs were not allowed to reproduce?" No.
Taking the value of reproductive liberty as a given, there are also more complex and surprising reasons to reject this measure.
Suppose one's reason for supporting this measure is to get a smarter population of offspring. Those who know anything about genetics know that is not how it works. All you get is a population that is evolved to be good at rigging the eugenic system. They'll still be dumb in all other respects.
The best reason for dumb people not to reproduce is that children are their greatest source of misery (though they're too hopped-up on parent-infatuation hormones to recognize it). But I will defend to the death everyone's right to screw themselves up.
Most parents are not dumb, but nearly 100% of dumb people are parents-- depending on whether we define dumbness to include incompetence at family planning. But this illustrates how difficult it is to measurably define intelligence. Often, as in this case, measuring intelligence merely penalizes is people who are different from me, because I'm the one doing the measuring.