Our current voting system gives us a single vote for each government position, which encourages the election of divisive candidates...and gridlock. A system where we ranked each candidate in order by preference would encourage the LEAST divisive candidates.
So for five candidates running for the same position, your first choice would receive five points while your last choice would receive one point. All points would be tallied, and the candidate with the highest point total would be elected.
This system would discourage the election of highly divisive candidates (who would receive the most top AND bottom rankings), and instead encourage the election of the least divisive candidates (who might be everyone's second choice but who normally would have no chance of being elected).