Public administration is an immense task, and it makes sense to divide areas into different administrative districts to simplify and delegate responsibility. They also allow different areas to set different administrative parameters, since different areas have different concerns. Polities in deserts must treat water rights and access much more cautiously than those in rainforests, and dense cities with developed transit systems are much better suited for high fuel taxes than remote rural areas.
However borders of administrative districts are often extremely arbitrary and inefficient, almost always decided by far-off officials with little understanding of the areas in question, or during a historical period with completely different social and economic realities.
We can once again use persistent documents to solve this problem. The highest level of administration would have one document specifying sub-district borders, and each of those resulting sub-districts would fractally have their own documents specifying sub-districts.
Most countries have some fixed set of district levels, for example the United States has Country > State > County > Municipality
. We don't really need to be concerned with that kind of control, and can allow each district to subdivide itself in whatever way seems optimal to them, including allowing no subdivision at all.
Importantly, districts can't have incompatible definitions of rights, justice, and legislative codes without actually becoming different countries. Districts should only allow administrative differences such as precise tax rates and descriptions of public agencies and their officials. All rights, justice, and legislative documents must be shared at the highest possible level. I'll discuss this topic more in the future.
Notably, the existing problem of gerrymandering is completely unrelated to this districting system. Persistent democracy makes almost all legislative representatives unnecessary, so the concept of districts to elect representatives is largely irrelevant. Even when district boundaries do effect what kinds of decisions are made, choosing districts democratically is arguably the best possible way to do so.
It might be possible to make district decisions in a more fluid and "bottom-up" way with a more complex system. One alternative I toyed with was using democratic weights to define "enclosing perimeters" around areas that some group wished to exercise some administrative control over, and using concepts like distance from centroid to change how the weights of different people affected their vote on such a perimeter. As technically interesting as such ideas are, they're likely too complex even if I could prove their efficiency. I might revisit such concepts in the future, but it seems more likely to be a fun exercise than to provide any real use.