Just to confirm, the rounds continue until we’re down to 2 candidates, correct? Even if someone has already reached a majority of votes?

That’s right.  If there is no majority winner – 50%+1 in the first round – the elimination rounds continue until there are only 2 candidates left.  The winner is the candidate in the final two with the most votes. Depending on the unique circumstances of each election, it can take many rounds to reach a final 2 candidates. 

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