Amish as a culture is broken down into many different sects. Old order, New order, reformed, etc. What they all have in common is a set of laws each community must follow called the "ordung". This is governed by the Bishop of the community, who becomes the defacto leader. They are installed via various methods, most common being either a vote Amoung the elder men of the church or a random straw pull lottery.
Amish beliefs in the Bible do make a cornerstone of their faith, but not in their governance. Their laws dictate everything about their lives. And the laws vary from community to community. If you choose not to follow said laws, punishment can range from community shunning for a period of time to outright expulsion. People may also choose to move to another community, but this is often seen as a nuclear option as doing so means severing all ties with their prior community and family. It's very cult like I'm that regard, harkening back to other groups like Mormons or JWs.
They also maintain a strict sense of autonomy from the world at large, seeing anyone not part of their community as "English" (similar to how some groups see nonbelivers as gentiles). This extends into their interactions with the local government and even local doctors. Anyone not in their circle is seen with suspicion. Interactions with the outside can lead to punishment by the Bishop and are done carefully for obvious reasons.
Let me know if you have any other questions
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