The point is that those societies have had a ‘final authority’, though the people filling those positions have been chosen, usually by a council. The position is not inheritable and anyone who would attempt simply to assert such authority would not be accepted. Based on your definition of government, as having authority unto taking life in enforcing the rules that govern society (straight outta Hobbes), those societies have in fact had governments.

I define government as the functional core of the political process. The political process is the process of effecting choices for a community as a whole. Any formally organized group of human beings must effect choices for the group as a whole. It starts with formally organizing as a group. Government is the set of institutions through which those choices are effected once the community is formally organized — and through which the community sees to it that choices that have been effected are in fact realized, to include having the laws that have been enacted for the community obeyed.

A great area of discussion, to me, is what can be said to constitute the grounds for a ‘legitimate’ law. Can a concrete set of criteria be set forth?

That gets us to the distinction between government and governance. The question I have sought to answer is how governance can be justly governed.