Adding on to Zayphora's post, I have thought that each regional League (Indigo, Johto, Orange, Hoenn, etc.) was governed by its own "Board of Directors", similar to a public school district's Board of Education, city council, or a corporate board of directors.
From my imagination, a typical league board setup would consist of a President, Vice-President, Treasurer, and several Trustees. Such a governing body makes all the policies of the league, including policies regulating trainers, gyms and Gym Leaders, as well as league championship events (including the Elite Four), appoints certain other officials, appoints/confirms Gym Leaders and Elite Four Members, and other such activities.
