Board Thread:Lore Discussion/@comment-71.182.239.123-20150701033008/@comment-24419876-20150706002622

The Archmage is the leader of the College of Winterhold. They are chosen by the Council of Mages via a vote. While an Archmage could be a master of all the schools, they don't have to be. So long as they win the vote, they are the Archmage.