[JLS]

Is there any advantage to being Chief Justice, or is that just an honorary title?

I believe it is just an honorary title. Maybe it gets you a free sandwich at the commissary on Fridays?
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When in the majority the Chief Justice assigns which Justice writes the opinion of the court, I believe.

[Theodore R.]

The chief justice is also paid some $10,000 per year more than the associate justices on the grounds that he has more administrative duties. The chief justice, Speaker, and vice president are all paid approximatley $202,000. The Senate majority leader is also paid more than regular senators but well over $20,000 less than the chief justice, Speaker, and vice president.

[rollo tomasi]

Chief Justice the head of the Judiciary Branch of our government.

The Chief Justice is the chair of the Judicial Conference and the Federal Judicial Center and oversees the Administrative Office of the U. S. Courts.

The Chief Justice has a position on the board of the National Gallery of Art, is the Chancellor of the Smithsonian Institution, and the Hirshorn Museum.

The Chief Justice also presides over impeachment trials of the President. Not exactly a figure head has a lot of other duties.