According to some on-line sources (including Wikipedia) Vanguard is owned by its member funds. Furthermore, it is run by its Board of Directors. However, I could not find anything on Vanguard's web site that explains how the directors are chosen. Does anyone have a reference or perhaps a document that explains how Vanguard directors are chosen?
There are 11 members of Vanguard's Board of Directors. Nearly all are also members of the board of trustees of each Vanguard fund. The CEO of Vanguard is the Chairman of the Board of Directors. He is the only one of the 11 directors who is also actively involved in the management of Vanguard. As for the other board members,
These are some examples of the backgrounds of three of the ten (independent) Vanguard board members: corporate vice president of Xerox Corporation; former president of Rohm and Haas Co.; president of the University of Pennsylvania.
How are the Vanguard Board of Directors chosen?
The answer is in the description of their duties:
Emphasis mine. So it seems that existing directors select their replacements.
As for the reference to mutual funds as owners, see the company timeline, on the overview information page about Vanguard. Look at the entry for 1975. With John C. Bogle as CEO: