I don't really think it's a correlation. It's tough for any given entity to truly represent 10 people, let alone 10 million. And by the time you start speaking of the hundreds of millions, any meaningful notion of representation is just out the window. And now imagine this on a scale of billions, with countless groups that all have largely mutually exclusive views?
And this will become even more true in the future. Imagine what will happen as we start to be able to reach out and colonize other planets. The cultures, ideals, interests, and even language on those places will tend to constantly diverge from that on Earth. To have somebody try to represent somebody without even sharing the same fundamental values is a system doomed to trend towards authoritarianism at first, and ultimately to complete collapse and failure.
When it's you and a village, it's still relatively easy to enforce things because you have families and relationships. There's some inefficiency and some corruption from individuals but you can still try and monitor everything.
When it's you and a hundred million people, you could never even meet everyone let alone know them. So you need a thousand steps between. And every step and every system can have corruption and inefficiency. Unless you have some sort of central mandate like religion, it's very hard to motivate people because everyone is so separated. Even if you do, you still get corruption like in china.
CCP approval rate: 89%
https://www.statista.com/statistics/1116013/china-trust-in-g...
But maybe we can agree on some basics around fairly sharing food and toys and not trying to steal the other kids toys (or even half their yard).
One way to picture it is, imagine if there's a planet somewhere in the universe with life. Given enough time, do you expect it to have a unified government that fractally subdivides (like states, regions, city governments), or do you expect it to have multiple heads? I think it's way more likely that a dominant culture at some point appears, itself being a mesh of different cultures from the different regions, but at some point unifies. I just don't see another way.
Even if we look at history, while there's periods of fragmentation after periods of consolidation, in general things trend towards consolidation. We're more consolidated than ever before and I think it only goes in one direction. I'm talking here on the scale of thousands of years by the way. So like, in the year 5000, is there one world government or not? That would be the bet.
I'm not even saying it's desirable or not, just that it's likely to happen. For example if one country suddenly discovers a major technological advance, it's likely to exploit it by starting wars to consolidate, as it has happened all through history. And that only has to happen a few times over the course of thousands of years to get us to a world government. There aren't even 200 countries in the world!
Thus, I don't see a world government happening until we're so well into colonizing other worlds that it's more practical to deal in terms of planets than with individual countries. Even at that point though, I'd expect something similar to countries to continue to exist.
Put differently, I think a single entity with governance over the entirety of humanity is never going to happen (assuming we don't suffer some sort of near extinction level collapse).