A country run by the learned has a higher chance at being effective than a country governed by all. If the intelligent run the country, then the chances of a democratic mistake go down, because they are intelligent.
This premise conflates intelligence with accuracy, success, and competence. Intelligence has some relationships with those things but is none of them in itself. Many highly intelligent people can also be totally incompetent in various contexts as well as highly unsuccessful and/or inaccurate. Intelligence alone does not replace experience, education, and, dare I say, wisdom.
You are displaying a clear overvaluation and positive bias for intellect and intelligence over all the things which must compliment it for it to manifest and work in the world.
The very idea that voting rights in general should be reserved to a specific class of person is inherently undemocratic and therefore any system that restricts voting to a specific class in general is no longer a democracy.
What you are talking about is an aristocracy, meritocracy, or other.
The social disturbance this would cause probably highly surpass the potential gain of people voting a little better : Voting is a way to compromise between people unable to agree, remove it and conflicts will become more violent.
Intelligence alone does not determine whether an individual knows what's best for a country. In fact, "what's best" is an at least somewhat subjective notion in itself and people of various sorts, including those of similar intellect will disagree about "what's best".