How were Native Americans politically organized before the arrival of the Europeans?If I'm not mistaken the chief was head of the tribe and the...

Keep in mind there were hundreds of tribes scattered
across the Americas, and that the exact form of government they practiced varied from
place to place and people to people.  But many tribes practiced a council form of
government.  The Council consisted of the tribal elders, the Chief, and the Shaman,
along with some warriors.  There were War Councils (like today's subcommittees in
Congress, but more efficient) that dealt with emergency
threats.

The Chief's word was law, and the Council served
as advisers, although their advice usually carried
weight.

The Judicial Branch of the tribes was the whole
tribe.  The Chief or the head of each household would mete out punishments, and the
tribe lived according to an old and clear code where everyone knew what was expected,
and what punishments would be for offenses.  These punishments were enforced by all
tribal members.

Since native peoples were scattered, they
were loosely organized into bands, tribes and nations that could cover tens of thousands
of square miles.  Some bands of the same tribe might never come into contact with one
another, or at least very rarely.  In situations where the threat was to the entire
nation as opposed to just one band, sometimes councils of the chiefs of the different
tribes would take place.