The statement does not make sense.
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The statement does not make sense. The plurality-with-elimination method eliminates the candidate with the lowest number of first-place votes in each round. If a candidate has a majority of the vote, that means that the candidate has the majority of the first-place votes. Every other candidate must have a smaller number of first-place votes in every round. That is, in every round, a candidate with the majority of the votes would always have the highest number of first-place votes and thus would never be eliminated. Therefore, a candidate with the majority of the vote would always win an election using the plurality-with-elimination method.