On the Supreme Court, there is a hierarchy for listing opinions. The majority opinion always comes first. When the Court is fractured, and there is no clear majority, the opinion with the most support is usually listed first. When the case is an absolute cluster, sometimes the opinion by the Justice with the most seniority is listed first, but there is some play in the joints. After the majority/controlling opinion, the concurrences are listed by seniority. Next come the concurrences in judgment only, which are also listed by seniority. Finally, the dissents are listed, which again are sorted by seniority.
When there are multiple dissents, the majority opinion will refer to a particular dissent as the "principal dissent." But the term "principal concurrence" is far more rare. A quick search of Westlaw reveals only one such usage before 2021. In Morrison v. National Australia Bank Ltd.(2010), Justice Scalia wrote the majority opinion, Justice Breyer wrote an opinion concurring in part, and concurring in judgment, and Justice Stevens wrote an opinion concurring only in judgment. Justice Scalia referred to Justice Stevens's opinion as the "principal concurrence."
More recently, the phrase "principal concurrence" has popped up twice. In Lange v. California (2021), Justice Kagan wrote the majority opinion, Justice Kavanaugh wrote a concurrence, Justice Thomas wrote an opinion concurring in part and concurring in judgment, and Chief Justice Roberts wrote an opinion concurring in judgment. Justice Kagan's majority opinion referred to Justice Kavanaugh's opinion as the "principal concurrence."
