Each vote is an ordering of the N candidates from best to worst.
(Voters are not allowed to omit a candidate they know nothing about, and are
not allowed to regard two candidates as equal.)
The top ranked candidate gets a score of N-1, the bottom ranked 0, and more generally the
Kth-ranked gets a score of N-K. All scores are summed and the candidate with the
highest total score wins.
Range voting offers more expressivity to voters than Borda voting.
Range voting can be done on regular
plurality-style voting machines – Borda cannot.
Range voting is simpler than Borda voting.
Borda commonly exhibits horrible pathologies such as electing the candidate
unanimously agreed to be worst, if voters act "strategically."
But range voting reacts only mildly to strategic voting.
Similar pathologies happened immediately
in the only government (Kiribati) ever to employ Borda voting.
Therefore Kiribati abandoned Borda voting.
The withdrawal of a seemingly-irrelevant loser
candidate from the race, can cause the Borda election results to
such a withdrawal has no effect on a range voting election.