This system promotes acceptability over popularity.
Each voter may express approval or disapproval for each candidate. This is equivalent to voting +1 or -1 in a range voting system.
Counting the Votes
The approvals for each candidate are summed. The candidates with the highest approval rating are elected.
Potential for Tactical Voting
Every voter must decide for each candidate between their favorite and disfavorite whether it's more important to them that their favorite candidate get elected over the current candidate or that the current candidate get elected over their disfavorite candidate. This does not promote inaccurate voting, but it does promote the use of strategy and outside information in the voting process.