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If Socialist Alternative or Green Party for eg was your first choice and Democrats were your second (the lesser of two evils option), your preferred choice (Socialist Alternative/Green) would be transferred over to your second choice (Democrats) in the second round if the Democrats had more votes than your preferred choice in the first round.
HOWEVER if your preferred choice had more votes than the Democrats in the first-round, it would be the Democrats who would get eliminated in the first-round. Leading to a run-off between your preferred candidate vs. the Republicans. In a head-to-head battle, the Democrats have a much better chance versus the Republicans than Green/Socialist Alternative would. Because the Democrats have more mass appeal than Green/Socialist Alternative. There are a lot of "moderate" voters who can swing either way (swing voters). Those kind of voters vote Democrat occasionally. But they would absolutely never vote for Socialist Alternative or Green.
So either way, as a third party voter, you lose. It doesn't make sense to me. In the first scenario where your preferred party got eliminated in the first round, the votes would transfer to the Democrat and so the Democrat might get elected.
In the second scenario, the Democrats get knocked out in the early rounds. And then the Republicans end up getting elected after crushing Socialist Alternative/Green in the final round.
Either way, you end up with no third party representative in Congress. The best way to ensure third party representation is Proportional Representation. If Socialist Alternative gets 3% of the vote, they'll get roughly 3% of the seats.
If you're not satisfied with that explanation, once again visit http://rangevoting.org/rangeVirv.html I don't know how I can be any more clear. Third-party voters think that IRV is a great for third-parties. But if it doesn't lead to third-party candidates getting elected, then what's the point? Proportional Representation has been proven time and time again to lead to third-party representation. Just look at continental Europe where PR is the dominant system. Look at the French regional elections which uses a 75% PR seats/25% winner-take-all bonus seats system.