I've got a setting in a low-fantasy world roughly at the technology level of late 15th century Earth. You have ocean-going sailboats and gunpowder, but no steam power or telescopes, and the world is rife with feudal and theocratic states.
A little additional info: to be clear, this is not set on Earth. This world is more interconnected, and it developed far more slowly. That means that the entire planet has long been mapped out by the historic nations in their peaceful or violent engagements, and technology and society is mildly more homogeneous. But only mildly so. Perhaps compare this planet as a whole, culturally and socially speaking, to the patchwork of civilisations from Rome to Bengal in the mentioned era: diverse as a Pollok painting, but generally aware of one other and they can all be called civilisations. Scale-wise though this planet is not much smaller than Earth.
Now, the story requires a world government. But, not a tyrannic emperor with a totalitarian regime with faceless goons dedicated to bring about universal suffering. To make this setting more plausible, and possibly more interesting, I am stretching the definition of "government" to refer to an organ with only the following powers:
- Cultural influence. The opinion of the guy on top is very important to even the lowest peasants.
- Arbitership. Not that there's world peace in the 1400's, but this institution regularly prevents wars and resolves disputes through some form of intervention, and as a whole the world is more peaceful and prosperous than before they came to be. Everyone can agree on that.
So, that means that they do not actually have to administer every continent, necessarily. It is more like a UN, except that its power is derived from something besides its allegiant nations, and people actually respect it :)
Furthermore, the following properties are required to still consider them a "world government":
- They "reign" over the whole world. Or at least enough of it to say that they rule the world. That includes people of vastly different cultures, beliefs and heritage than the government or the leader.
- They have lasted for at least 50 years, went through multiple generations of leaders (otherwise it wouldn't be considered an institution), and show no sign of weakening.
Other qualities which I would personally like to see:
- The institution is almost universally respected, and seen as benign. Few states are trying to leave its influence, and those that do are seen the way the EU sees Brexiteers.
- Though the setting is low fantasy, there's no hallucination or hypnosis magic to manipulate everyone into doing their bidding. In fact, I would prefer for the guy on top to be a muggle, and openly so.
So, what options do I have, for an authority that is respected by kings and countrymen alike? Religion is the obvious answer, and the powers I described were held by the Pope in this era, to various degrees in different parts of Europe. However, the Pope's reach was continental at best; I need it to be global. Furthermore, you can only have a Pope-like figure when everyone already shares a religion, and that would make this world too homogeneous. I would rather it be diverse, and the goal of this institution to be to homogenise it over time.
I was personally thinking of a huge bank; the Medici family on steroids. They would have started out as regular bankers who lent a large loan to a nation at war, with one of its provinces as contingency. The nation unexpectedly lost the war, went bankrupt, and the bankers got worldly possessions. From there they expanded their wealth and power, until they owned the majority of gold in the world and can coerce kings and emperors to make peace, lest they lose the funding they need to stay in power. In the middle of their reign, they invented the printing press (and kept it to themselves), and the guy on top has cultural influence because every book in the world was written by him.
But, I can see nations become envious of this bank's massive wealth, so this may not be stable for fifty years. That's why I'm asking for other ways to make this government, or one with similar powers, work. Even though this is not Earth at all; for inspiration I do like to play with a historic entity, and just make it as powerful as it logically can be. However, pure fantasy ideas are fine too.