By self selecting, I mean that the leadership is decided by the leadership. The Vatican is run by cardinals, who were appointed by the pope, who was appointed by the cardinals (and so on). The Académie française is run by a forty member board whose members are appointed by the board.
There is an adjective “self-perpetuating” (from the Merriam-Webster Unabridged: “capable of continuing or renewing oneself or itself indefinitely”); one of the example quotes given is “administered by its own self-perpetuating board of trustees”, which sounds like the sort of thing the OP is talking about.
oligarchy (ŏl`əgärkē) [Gr.,=rule by the few], rule by a few members of a community or group. When referring to governments, the classical definition of oligarchy, as given for example by Aristotle, is of government by a few, usually the rich, for their own advantage. It is compared with both aristocracy
, which is defined as government by a few chosen for their virtue and ruling for the general good, and various forms of democracy
, or rule by the people. In practice, however, almost all governments, whatever their form, are run by a small minority of members. From this perspective, the major distinction between oligarchy and democracy is that in the latter, the elites compete with each other, gaining power by winning public support. The extent and type of barriers impeding those who attempt to join this ruling group is also significant.
(thefreedictionary)
If the word isn’t here, it probably doesn’t exist.
It seems like a profession, where the professional organization is made up of members of the profession, and the profession has the authority to self-regulate.
The characteristics of a profession include: [ul][li]Professional association: Professions usually have professional bodies organized by their members, which are intended to enhance the status of their members and have carefully controlled entrance requirements.[/li][li]Self-regulation: Professional bodies tend to insist that they should be self-regulating and independent from government. Professions tend to be policed and regulated by senior, respected practitioners and the most highly qualified members of the profession. [/li][*]Exclusion, monopoly and legal recognition: Professions tend to exclude those who have not met their requirements and joined the appropriate professional body. This is often termed professional closure, and seeks to bar entry for the unqualified and to sanction or expel incompetent members. [/ul]
However, that assumption is not part of the definition of the word; so “oligarchy” doesn’t satisfy the OP.
No. Did you?
There aren’t necessarily single words to fit every possible concept.
Seems rather too broad for the kind of organization mentioned in the OP. Would you really consider the Papal Curia or the Academie Francaise to be a “profession”?
You’re nitpicking a distinction between US and British English. In Rightpondia, things like committees, councils, athletic teams[sup]1[/sup] and even companies are considered to be composed of multiple people and thus take a plural verb. In Leftpondia, such are thought to be single entities and take a singular verb. So what clairobscur said is perfectly good English for many parts of the English speaking world.
[sup]1[/sup] Actually in the US, the verb for athletic teams depends on how the team is refered to. If one uses the geographic part of the name, then one uses the singular verb. But the plural is used when using the nickname, since that is usually a plural noun. In those few instances where the nickname is not plural (e.g. Utah Jazz), some use the plural and some use the singular.