A few readers asked me to discuss range voting. Wikipedia defines it as following:
Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score system or point system) is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins. Range voting was used in all public elections in Ancient Sparta in the form of measuring how loud the crowd shouted for different candidates. Approval voting can be considered to be range voting with only 2 levels (approved (1) and disapproved (0)).
The main question to get out of your head is whether or not range voting satisfies Arrow's Impossibility Theorem. (In fact it doesn't, most forms of range voting violate the independence of irrelevant alternatives, but don't worry about that!). There's no major reason why a democratic system should follow all of Arrow's axioms as defined across universal domain, which means you have to rule out the very possibility of paradoxes. Can anyone do that? No, not even when you're deciding which book to read next. (But should you stop reading? No.) We do, however, care if the system can:
1. Deliver decent economic growth and an acceptable level of civil liberties.
2. Build consensus and legitimacy going forward, and
3. Toss out the truly bad politicians.
Ideally, we'd even like:
4. The democratic process itself educates people, raises the level of discourse, and makes for a better society.
On those counts, it is not clear what advantage range voting brings over either a two-party winner-take-all system or some form of proportional representation. Do we really need to count the preference intensity of voters? That could sooner be harmful in extreme situations. Do we really need to teach voters complicated aggregation systems? The relatively well-educated Germans used a "vote twice but ultimately only the party vote counts" form of PR and for decades most of them never understood it and now they are changing it, finally.
Most countries don't use range voting. Ireland and Tasmania have had some experience with the Single Transferable Vote (STV) system. What happens is that a bunch of candidates run for each post, party identification is weak, and reps emphasize constituency service. That's probably the major dominant effect, namely that most systems of range voting weaken political parties.
The bottom line: Range voting is a solution in search of a problem. The main problems with democracy include poorly informed, irrational, and short-term voters and politicians. Range voting doesn't cure any of those and arguably by weakening party affiliation it makes some of them worse.