Final answer:
A written Supreme Court opinion that represents the reasoning of most of the justices who side with the winning party in the absence of a majority opinion is called a plurality opinion.
Step-by-step explanation:
A written Supreme Court opinion that, in the absence of a majority opinion, represents the reasoning of most of the justices who side with the winning party is a plurality opinion. In the Supreme Court, a majority opinion expresses the Court's reasoning for their decision, and a majority of the justices must agree on the decision. However, if there is no majority opinion, a plurality opinion can represent the reasoning of most of the justices who side with the winning party.