STEP 1. Suppose least 67% of voters, in an effort to maximize the impact of their vote, vote the two major parties
In Australia, which uses IRV, this currently happens about 90-95% of the time. In the USA, which uses Plurality, Nader-favorite voters in 2000 chose to vote other-than-Nader over 90% of the time (say NES poll data; Burden's paper). This behavior by voters is logical because with IRV there is favorite-betrayal incentive (it often is beneficial to voters to betray third-party favorites, especially when they might have a chance to win) whereas with range voting no such incentive exists. Ever.
STEP 2. It then is a theorem, which even IRV advocates ought to be able to prove, that a third party can never win. (In IRV voting.)
STEP 3. But what if we had the exact same voter thinking and behavior, but now using Approval or Range voting?
STEP 4. It then is a theorem, which even IRV advocates ought to be able to prove, that a third party candidate could win without necessarily experiencing any difficulty.
STEP 5. This is not a hypothetical scenario. It has actually really happened. A lot. Indeed, in the 2007 Australian elections, there appear to have been at least 9 (probably more like 20) federal IRV seats in which the Green was preferred by a voter majority over every rival, and the voters said that in their IRV votes. Of course, with IRV voting, the Green candidate lost every one of those races by a huge margin, not even coming close to either major-party candidate, and resulting as usual in zero IRV federal seats won by all Australian third parties. With Condorcet voting the Greens would have won those seats. With range and approval voting, they probably also would have.
STEP 6. So third parties are suicidally stupid to support IRV when they could support Range voting.
of course, like the Australian Greens, they want to lose every single IRV election for a federal IRV seat, they ever participate in (except for the single election the Aussie Green managed to win in 2002 when one of the major parties did not run for the seat). But oddly enough, the Australian Greens do not enjoy that! They want to abolish IRV and remake Australia so that IRV is never used in any election there ever again. They say so right in their party platform!
Now we predict, that if the USA switches to IRV, there still will be 2-party domination, just like in Australia – only more severe. We predict that then, at long last, the US Greens (assuming there are any remaining at that point) will then, just like the Australians, try to get rid of IRV because it has dawned on them that it causes them to lose essentially all the time.
I'm suggesting skipping forward a step in this process. I'm suggesting that the US Greens – and every other US third party – support a single-winner voting system that allows them to win races. (This is not to say we are opposed to having multi-winner voting systems also. But for Senator, Governor, President, and House seats in small states, multi-winner systems are simply not useable.)
I realize that winning a race is a stunning, incredible, idea that US Greens may not be ready to adjust to and perhaps would never have thought of without the aid of RangeVoting.org. But nevertheless, what the heck. I suggest it to them. After all, they claim the fate of the world is at stake and their ideas for saving it (ecology, etc) are key and heavily ignored by the top 2 parties. So perhaps the US and world would be better off if some Greens won federal seats.
Or, we could adopt a more complicated voting system – IRV – almost guaranteed to make them always lose. Which course seems wiser for the US Greens?
You choose to live, or you choose to die. Is this that hard a choice?