"Voting for a third party accomplishes one thing. It takes votes away from one of the other major-party candidates. Given that the status quo favors the Republican candidate – think the Electoral College – voting for a third party is probably going to take votes away from Joe Biden. Whatever you think of him, he’s better than the alternative. (The alternative, by the way, likes making jokes about being a dictator.)
Actually, it accomplishes another thing. It enriches presidential candidates for third parties that do not work in cooperation with one of the major parties. (It’s called “fusion voting.”) For instance, the Green Party — these people know they can’t win. They know the status quo prevents them from winning. They don’t say that, though. In the space between what they know and what their supporters don’t know is a scam. In the absence of systemic change, third parties that don’t cooperate with one of the major parties are inherently exploitative."
For the time being, it would effectively move fringe-party votes to the nearest major party - ensuring that e.g. Trump doesnt win if the majority of people had Harris or some third party candidate ranked above Trump.
Current “third” parties have a long way to go before they would end up in the winning slot - but, presuming the elimination rounds’ stats are published and not just the final winner, we could better gauge the support for them since voters could show preference for them on the ballot without “wasting their vote”.
After a while, evidence of sustained support may snowball, or a particularly compelling candidate may be ranked above a “major” party candidate on a majority of ballots - leading to a win.