Coming back to the beginning of the threat, I would like to share this website from OECD:
http://www.oecd.org/site/0,3407,en_2..._1_1_1,00.html

What I found interesting in that particular site is the endorsement of the various governance frames and legitimacy sources in non western countries.
I believe that a good identification of what is the local understanding of local governance (basically what people expect from government, how they can get it and what government provides) is the starting point to be able to file Bob’s matrix.
Once you have this, you may have a starting point.
Naturally, it is set in the context of fragile state therefore; it is assumed that you have some sort of administration running somewhere. But still, the frame they propose is very interest in to understand what is at work in a non state context.
My primary assumption being that as mankind is a political animal, there is a form of governance what so ever at grass root level.

The various reports linked on that site may respond many of the questions raised here. (Not saying they are the bible and cannot be challenged, far from it).
Also, it’s a donor/development agencies oriented work. But still some good stuff in it.