It's off your timeframe, but the 1995 made-for-tv adaptation of Harrison Bergeron fits part of the bill.
From Wikipedia:
Unfortunately, his first intelligent conversation ever (with "mind whore" Phillipa) is interrupted by a police bust. While the raid on the police station is underway Phillipa addresses a hidden camera saying, not to take him away, and that she likes him. While being held captive in the police station, he is approached by a special agent who offers him an alternative to the lobotomy - to join what turns out to be the secret elite that runs the government.
At 28'19, Harrison is told that:
AGENT: The problem is, to run such a society requires certain high administrative functions that the average person is simply incapable of performing.
HARRISON: You mean like Senator or President?
AGENT: Oh good lord, no! I mean, anyone with average intelligence or less could handle those.
At 34'00, he is given the task to pick the new governor of Connecticut, an agent having explained to him that formerly this was done with elections, but the average (read: stupid) person can do it, so the process saves time and money, and people don't really care or make a difference.
Harrison does die at the end, though.