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I think all these proposals (and there have been a lot of these) relate back to a central problem in human relationships: Dunbar's Number. Principally, once you are beyond that threshold in terms of politics (and it need not be exclusively people, you could sacrifice some empathy and have families count as units, or even local neighborhoods) your influence on representation dramatically wanes.

Not necessarily because of ill intent, but because you become just another number to whoever "represents" you.

My personal philosophy is that one day we will conclude that the best way to govern is to treat it like we treat most things. Find someone in our community who we think best represents our collective interests, elect them to some council of several neighborhoods, who elect someone from their body to represent the community at the county level, who elects someone to the state level, so on. In practice, I would imagine that each level up you go, the less time you would spend at that level - ie, a national body would behave a lot like how infrequently the UN convenes, and even then it should be mostly to adopt laws from more local governments into the collective one when they have overwhelmingly popular support.

You end up with each layer representing more and more localized interests, and since your base unit of elected official will always be someone elected with social relationships to most / all of their constituents, corruption is much harder to see take root. Have each constituency able to impeach at will, and you can have fairly long or even no term limits, and they will replace bad actors with good ones until they find the best person to represent the majority.

I imagine a system like that would also factor social mobility, it lets you move where the local politics are in your favor and you would see the gradual accumulation of optimal policy where people prosper the most, which would naturally over generations grow in size. At the national level, you can probably use split partitioning of districts and a re-balancing every census to account for these migrations and growths. That means gradually the best communities gain influence over time.

It also has the added benefit of letting everyone cut off higher-tier governance wherever they disagree. You can organize countries based on regional commonality and the borders would be organic with which districts want to participate in which city, or which county, or which state, or which nation. You would almost certainly see similar borders - in the US for example - that these maps demonstrate in the OP because common cultures would align. The only thing missing after that is open borders for migration, so people can freely travel to places whose ideologies align with their own.

I don't know that I'd go as far as you, but I've often thought that, as our population has increased by two orders of magnitude since the founding of the Republic, we ought to add another level of indirection in our government to keep things manageable. Right now we have municipal, state, and federal. Perhaps something like the proposal in the article could be used to introduce a new intermediate level of organization between state and federal.

In other words, have something like the electoral college at every level? Ewww.

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