The Marching Morons is a
short story by
C.M. Kornbluth. Written in
1951 and published in
Galaxy, it can be found in Volume IIA of the
Science Fiction Hall of Fame.
The premise of the story is that because intelligent and responsible people tend to limit the number of their children, while the unwashed masses breed like rabbits, after some time the world average IQ will inevitably drop to moron level, with unpleasant consequences for the clever. The solution is far too devilish to give away here.
Those so inclined can find many instances of similarity to the book in today's lowest-common-denominator culture, without needing to invoke the Illuminati. Kornbluth nailed it, right down to game shows, inane catchphrases, and cars that make whooshing noises so you think you're going faster than you are.
Larry Niven and Isaac Asimov wrote an essay about the phenomenon and Zero Population Growth in the 19 January 1981 issue of Asimov's Science Fiction Magazine, titled "On the Marching Morons."
The phrase itself apparently came from the old conundrum of being unable to count the Chinese, because by the time one generation was counted another would have been born.