Political: Alma and Amulek are bound and take for judgment to the chief judge. This tells us that as part of the general Nephite political sphere, Ammonihah operated under the form of government established by Mosiah for the Nephite polities. Even though the Ammonihahites were is some ways dissenters, they were not completely separate from Zarahemla, and followed the Zarahemla form of government.
Ammonihah also appears to have followed the Mosiahn policy of having some separation between the religious and the political. When Alma is brought before the chief judge, he is brought on religious grounds. While we may be tempted to see politics behind the accusation that Alma and Amulek had spoken against the layers and judges, it is the specifics of what they said that more fully shows the issues. The real issues are the places where the preaching of Alma has contradicted that of the order of Nehor:
[and also testified that there was but one God, and that he should send his Son among the people] This is the trap Zeezrom laid. The people are contending that Alma is confused because he proclaims only one God, but also a Son of God. The Ammonihahites see this are two gods, not the one Alma proclaimed.
[but he should not save them] This is the classic Nehorite doctrine. God will save all, therefore there is no need for an Atoning Messiah. Repentance is not required because God will forgive all sin.
The mechanics of this particular complaint appear to be the accusation against the offenders, and the presentation before the judge for judgment. This follows a rather understandable procedure. What is not clearly present is the voice of the people. While there are many people involved in the accusation, the formal mechanism of the voice of the people is not applied in this case. The chief judge has power to judge, and will exercise his power unilaterally.