To improve upon traditional democracy, various alternatives to the normal up down voting have been put forth such as range voting. (Range voting is a voting method for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.) For example RangeVoting.org describes how range voting could work.
I believe that San Francisco has experimented with something akin to this for their mayoral races.
What are the largest elections that have had some variant of range voting applied and how successful were the results? Were the constituents happy with the outcomes and did range voting remain in place or was it repealed?