Here is the world's only actual data (as of 2005) about range & approval voting vis-a-vis David Cobb and Ralph Nader – given in my paper (#82 here) coauthored with Doug Greene & Jacqueline Quintal.
This is based on a pseudo-election we conducted with real US voters (122 range voters and 656 approval voters) simultaneously with the 2004 presidential election (as an exit poll).
| Candidate | Plur | RV | AV |
|---|---|---|---|
| Bush(Rep) | 50.7 | 40 | 39 |
| Kerry(Dem) | 48.3 | 55 | 61 |
| Nader | 0.38 | 25 | 21 |
| Badnarik | 0.32 | 9 | 0.6 |
| Cobb(Green) | 0.10 | 5 | 2 |
| Peroutka | 0.12 | 6 | 1 |
| Total3rd | 0.92 | 45 | 25 |
[Warning: last 2 columns are NY-state and Philadelphia suburbs only, hence different sample than the "plur" column which is nationwide; e.g. nationwide election was won by Bush, but Kerry won NY and PA state. The "Total3rd" row is just the sum of Nader, Badnarik, Cobb, and Peroutka results – which is admittedly somewhat meaningless – but anyhow as you can see it actually would have exceeded Bush's total under range voting. Please see the full paper if you want, e.g, statistical error bars, which are omitted here for simplicity.]
As you can see, under range voting (RV) Green candidate David Cobb would have gotten 2.5 times more votes than under approval voting (AV), and 50 times more votes that he actually got under plurality (plur).
Warning: It is not very valid to equate RV scores with "votes." One really should normalize the RV scores before comparing them to Plurality votes, because since RV vote totals can add up to greater than 100% the two are not directly comparable. But for the present election such normalization makes little difference because Bush and Kerry (the two top placers) were the same under either election system and got about the same scores under all elections systems. But since you insist:
Cobb got 1/507th as many Plurality votes as Bush; under Approval Voting, he got 1/20th; while under Range Voting, he got 1/8 times as many votes as Bush. That's a total improvement in the Cobb/Bush ratio of a factor of 63.
Cobb got 1/483th as many Plurality votes as Kerry; under Approval Voting, he got 1/30th; under Range Voting, he got 1/11 times as many votes as Kerry. That's a total improvement in the Cobb/Kerry ratio of a factor of 44 (or a factor of 3 if we start from that ratio under Approval Voting).
Both Cobb and Badnarik had supported IRV during the Badnarik-Cobb debates, a huge mistake by them both because IRV would simply continue to lead to self-reinforcing 2-party domination. (Democratic & Republican strategists must have been rolling in the aisles laughing when they heard the geniuses at the Libertarian and and Green parties had fallen hook, line, and sinker for IRV. See this, this, and especially this for more understanding of hooks and sinkers.)
Later Badnarik moved away from supporting IRV=Instant Runoff Voting after it dawned on Badnarik that approval voting was better.
Excellent move, we agree. But the table shows Badnarik still has a factor 15 further to go in his own favor by endorsing range voting, and Cobb also should endorse range voting (plus range voting is a better system objectively anyhow than approval voting).
(We now are happy to report some progress: Badnarik's running-mate Campagna endorsed our organization and range voting in September 2005, and Badnarik himself later provided an endorsement, but the Libertarian party as a party as yet has not provided an endorsement of Range Voting.)
Incidentally, suppose you are now thinking: "oh dear, it looks like some Greens made an idiotic mistake by advocating IRV voting, because we foolishly did not understand it still would just lead to 2-party domination shutting us out of power. But now that IRV has momentum, we have to keep pushing it, and we suspect it will lead to some benefit. If we switch away from IRV that would just divide reform efforts and prevent progress." We reply that a deeper analysis indicates that the line of thought in those last two sentences is just wrong. (Besides, there is not exactly a lot of "momentum" built up. Far more US cities have stopped using IRV over the last 60 years, than have started.) So don't stay with IRV like a suicidal idiot.
If this data doesn't get your and Cobb's attention, I don't know what will! (Worried about the nonlinearity bogeyman? Confused about IRV?) And in fact, this is not just about Greens. Every third party is helped by range voting (as is seen from the above data) and not helped by IRV and especially not by the present plurality system. By huge factors. Hence we can reasonably expect to get unified third party support, and that would hopefully be enough driving force to actually change something – for example the Iowa 2008 caucuses in which the major parties will also find it to their clear advantage to adopt Range Voting. So we hope this data will end the comedy of errors and we urge the Greens to join the Range Voting bandwagon.
The USA's immense and permanent 2-party domination is a consequence of the plurality voting system and Duverger's law. In any voting system in which Duverger's law holds (i.e. plurality, IRV, and all Condorcet systems with strict rank-orderings as votes), third parties are going to be permanent doormats, and the corporate-corrupted and moneyed top-2 parties are always going to crush everything before them. And the rest of us consequently are going to suffer from massively reduced voter choice, massive idea-deficit, and massive quality deficit in our government. Forever. IRV has led to massive 2-party domination in every IRV country in all the IRV seats. So don't fall for the myth that instant runoff voting (IRV) is going to be useful. You need range voting.
So in summary, the question for Greens when they consider "should we support range voting?" really is "do you like survival?" If you think survival is pretty important, then range voting should be your top priority. And I mean top. More important than every non-survival issue.
So join CRV now because it is the group pushing for range voting.