It's called sortition, people are chosen as a random sample from a larger pool of candidates.
Which means you can't buy an election, you can't use money to influence an outcome of an election. It would be like jury duty. You would be picked to serve for x number of years and then never serve again. That would mean the person would work on what they think is important and would be more willing to work with the other side. We use sortition today when we have trial by jury, you get picked to serve and you do the best job you can.
In ancient Athenian democracy, sortition was the primary method for appointing officials, and it was widely regarded as a principal characteristic of democracy.