Well, if you go back far enough, there is a precedent for that.

The Athenians (Athens, incidentally, was the longest existing democracy in history, not the United States) chose their public officials not by vote, but by lottery. Athenian citizens were well educated, and were expected, as the civic duty of a citizen, to take an interest in public affairs and know what was going on, so if they were selected in the lottery, they would be prepared to take over the duties of the office.

At the end of their term, their performance in office was reviewed and evaluated by jury of 501 citizens (deemed too large a jury to bribe), and they were honored or censured according to their performance. Someone who really messed up could be banished. So it behooved them to keep well informed, and if chosen, keep their noses clean.

Not a bad system. . . .

Info from First Democracy : The Challenge of an Ancient Idea by Paul Woodruff.

Don Firth