The advantages of the ability of Range Voters
to express the intensities of their preferences

#voters

Their Vote

7

C>B>A

5

B>A>C

4

A>C>B

3

B>C>A

In this 19-voter 3-candidate election example,
C is preferred to every rival by majority ("Condorcet winner"),
i.e. beats A 10:9 and beats B 11:8. (C also wins under Instant Runoff Voting.)
On the other hand, B
wins under Plurality voting, AntiPlurality,
Borda or indeed any
Weighted Positional system.
Finally, if the red candidates are "approved" then
A is the winner under
Approval voting (9 approvals, beating B's 8 and C's 7).

Who really should win? Good question.
Range Voting, since it permits voters to express
quantitative intensities of preference, can make a sensible decision in a
situation like this. In fact, with range voting, any of
the three candidates can win here, depending on what range scores the voters
award. The other voting systems we've mentioned, since they ignore and never collect
any strength-of-preference information, really have no idea what to do. They just
do not have the information they need in order to make a sensible decision.