For those who knew what happened in the future arc...
As far as we know, Byakuran took over the Mafia world (almost). However, after re-looking at everything that happened in the future arc, i noticed that Byakuran did not took over the normal world (the normal human society) . With his and Milliefore's strength, he could've done that easily. But he did not do that. Why? And I came up with a few possibilities:
1. The Vindice's rule does not allow that to happen
Or in other words, there is some kind of mafia law that prevents any mafia from taking over the world or involve themselves in politics. However, that is not possible because in the Kokuyo arc, Mukuro actually took over the bodies of prime ministers and politicians. He basically took over a (or more) country.
2. The mafia world is not yet completely took over by Millifiore
Chivalrone, Vongola (just part of it) and some random, miniature mafia families are not controlled by Byakuran. However, with the small strength of families. I doubt that they can stop Byakuran if he wanted to take over the world.
3. Byakuran's intention is not to take over the world
As from what we knew during the Choice arc and several chapters ago. Byakuran only wants to create a world of his. However, he decided to take over the mafia world before that. So, he could just take over the world later after taking over the mafia world and then gain the vongola rings and pacifiers.
The above are not completely the factors Byakuran did not take over the world. Now please take attention on the next possibility I am about to say
4. The government is actually STRONGER THAN MILLIFIORE
I know that this is completely impossible, however, do take a look at the strength of vongola now. In the first generation (vongola primo) , the vongola managed to make the police not to interfere with them. And form the 2nd to 9th generation, the vongola became stronger and stronger and dominated the mafia world, but they did not attempt to take over the world. What I think is that the government actually has stronger people that could defeat the mafia easily. And that is why Byakuran and the vongola did not attempt to take over the world.
Now, lets get straight to the point. How strong do you think is the government of the normal world is?