The oligarchy of the Puritan church wasn't based upon elections or appointments, at least not in a traditional sense. Puritan elders were known as "visible saints" and recieved this coveted status through a lengthy observation process.
Visible saints were members of the church community who demonstrated to the rest of the congregation's satisfaction that they were one of the ones chosen by God as his own. Only the chosen would assend to heaven, so being recognized as one of these few by the community was like an appointment to leadership within the church. You were then a living example for the rest of the congregation to follow.
The number of elders in the congregtion varied, but it almost never exceeded ten at any given moment. The strength of these people made them obvious choices for appointment to leadership positions.