Sortition. If no one can vote, then there can't be any of the chicanery that comes from that. Political parties couldn't exist, because a party can't help someone get elected. We no longer have the problem of the only people in office being those who wanted to be in office enough to go to the trouble. No need for term limits (people are unlikely to win office twice, let alone more often).

And yet it preserves everything you like about democracy.