Assuming the autonomy and independence of churches from outside interference or external governance, I see four forms of polity:
- Elder-rule without consensus. Elders may build or assure consensus from congregation, but it is not principally and finally required. Pronouncements on major decisions made at the gathering may normally but not necessarily imply consensus between elders and congregation.
- Elder-rule with consensus. Neither the majority of members nor the majority of elders can overrule the other on accepting/expunging members or elders. General consensus of some (at least implicit) kind is required. Voting on elders is common. Major decisions like adding new members don’t always require a congregational vote. The elders do not derive their authority from the congregation, but directly from Christ.
- Elder-led congregationalism. Requires express vote for all major decisions (especially accepting/expunging members or elders). Sees the congregation as having final authority over the elders and delegating authority to the elders. Consensus between congregation and elders not principally required, but often practically secured if elders are normally the ones to bring matters to vote.
- Strict congregationalism. Members can unilaterally both bring matters forward for vote and overrule elders. The church and even its elders are ruled by plurality of members and committees.
Worth a mention: Single-elder rule, deacon board rule, or a combination thereof.