Approval voting is the special case of range voting where
each score must be the maximum or the minimum (intermediate scores forbidden).
So range voting offers more expressivity to voters than Approval voting.
"Honest" voters tend to want to take advantage of that extra expressivity, but "strategic" voters
don't.
So in situations with a lot of voter honesty, range voting will produce better results than
approval voting, whereas in situations dominated by strategic voters,
range and approval voting
will deliver the same election results.
That is the reason why range voting experimentally delivers much
better Bayesian Regret
than approval voting if the voters are honest.
Borda voting also is far superior to approval if the voters
are honest (more superior the more candidates there are),
but Borda is far worse with strategic voters.
With range voting we get the
best of both worlds – as good performance as approval with strategic voters
(indeed even a bit better),
and also even better performance than Borda with honest voters.
Experimentally (and surprisingly to many),
considerable honesty is common (about 75%) among range voters
in US presidential elections.
Therefore range voting should deliver results far superior to approval results in
important real-world elections.
Approval voting is simpler than range voting, but the better results we get from
range voting (e.g. better US presidents) are well worth the small
cost of that extra complexity.
Also, on many kinds of voting machines
(and this also is surprising to many people, but true) both range and approval appear very
easy to the voter. Try demo.
Both range and approval voting are usable on every voting machine in the USA, including
noncomputerized ones, right now,
without modification and without reprogramming (also surprising, but true).
Due to the (enormous) nursery effect,
range voting is much more likely than approval voting to
allow third parties to
survive and grow.
Range voting is
much less likely to lead to a tie than approval voting.
(The Brams-Hansen-Orrison paper
describes an approval-voting election that reached an exact tie, but with range voting there almost
certainly would not have been a tie.)
Range voting is much less likely than approval to lead to backsliding
to plurality voting (such as the IEEE's backslide). Why adopt
a voting system if that improvement will just get revoked later?
Approval voting is subject to a problem which
Nagel dubbed Burr's dilemma.
Range voting is less subject to that problem.
We recommend approval voting in situations where simplicity and speed are paramount
(manual votes in large meetings). We also recommend approval voting
as a temporary stopgap measure, ultimately
to be replaced with range voting, in situations where the voting machines are such that approval
is much easier for the voter than range. (The two can
be scaled to
coexist in
the same election.)
But we recommend range in situations where the quality of the election results
are more important than the minor cost of increased complexity of range voting –
i.e, most situations.