I am not sure I understand your question. The way it works is that somebody authors the majority opinion, and the other members of the majority join in that opinion. But in order to get them to join, there often is a great deal of collaboration on the drafting of the opinion. Sometimes other judges will write separate concurring opinions if they don't believe the majority opinion explains all of the issues in the way they prefer. The members of the minority write a dissenting opinion which may be joined. It is not unusual for there to be several concurring or dissenting opinions, particularly if it is an important topic.
If Sotomayor wrote the majority opinion, then she voted with the majority. If she wrote the dissenting opinion, then she voted against the majority. Nothing is intentionally obscured.
If Sotomayor wrote the majority opinion, then she voted with the majority. If she wrote the dissenting opinion, then she voted against the majority. Nothing is intentionally obscured.
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