[mwl1]

It means that the chief justice gets to assign the lead writer to the majority opinion after the justices caucus over one case or another. The person who gets that appointment will often influence others one way or another based on their respective logic, their writing, legal precedent, and stream of consciousness.

There is an old saying that is applicable across government: people are policy.

[maryz]

Oh, sorry! It never occurred to me that assignment of the case meant that. I knew the chief justice could choose the majority opinion writers.