This is how they do it on the Mars Trilogy after setting up a colony on Mars. Of course the trilogy is entirely fictional, but the idea sounds like it couldn't be worse than the current situation, where those with narcissistic/psycho/sociopath tendencies winning elections i.e. those who seek power and/or those who have proficient oration abilities, not necessarily those who are most capable.
Lenin once said that "Every cook should learn to govern the state."
And that's how we should do it. Random lottery, pretty much the same way we choose election assessors or jury members.