Almost all of our exposure to Gemkind takes the form of three (or four, depending on how you count) rebels who have been away from their brethren for thousands of years. We’ve been given enough hints to make some guesses about who rules in Gem society; it’s probably been stable (the titles in place, if not the Gems who hold those titles) for a while, but at the very least this should explain the current system.
Strength equals authority
Way back in Arcade Mania Amethyst said Garnet was the boss, standing by the statement even after Pearl said that Garnet merely had a special perceptive power they relied on. It wouldn’t have been worthy of much note at the time, and even less now that we know that Amethyst only knows of Gem culture that she’s been taught on Earth, except for an interesting observation: Rose Quartz was probably even more powerful than Garnet and had been the leader before passing her gem on to Steven. Of course we’ve learned more since then which allows us to call forth even more things the series has shown us, and even something from our own, real-world history.
On Earth, medieval rulers held their land by virtue of military strength—not just of the soldiers they commanded but themselves as individuals. A medieval lord was a powerful combatant, heavily armed and armored and very well-trained. Of course in the medieval era medieval rulers usually simply directed their troops and fought with the cavalry: only in stories would they engage the enemy commander directly in single combat.
In Steven Universe things seem to be a bit more… Storied. The mural in Serious Steven depicts Rose Quartz facing someone who appears to be White, or possibly Blue, Diamond in single combat, presumably during the rebellion.
The Diamonds, if Ronaldo is to be believed and as Jasper seems to imply, are the rulers of the Gem homeworld. If one fought Rose Quartz, who was almost certainly known to be a powerful Gem back during the rebellion (considering her personal symbol, a pink triangle, and her strength she may very well have been Pink Diamond), then it would only have been with expectation of success. That would then leave us with a rebellion against an authority where both sides are led by the strongest among them, just as Amethyst seemed to assume was the natural order of things. This meshes well with the next observation.
Fusion is just a cheap tactic to make weak Gems stronger
Taken by itself Jasper’s attitude towards Garnet could be interpreted as simple bigotry: she’s strong by herself (and despite having pupils probably isn’t a fusion—since she could identify Garnet just by looking at her she’s probably not secretly a fusion), so looks down on those who need to work together to reach the same level of strength.
It becomes far more interesting when considered alongside the apparent strength of the Gem leadership, because then assumptions about society start to come into play. If the strongest Gems rule, and strong Gems populate the top echelons of society, then those in power have a vested interest in setting the rules of the “game” so that only their strength is considered legitimate. Since they don’t need to fuse to be strong, they look down on fusion Gems.
They might still use fusion in war, since it’s too useful to deny, but that fusion could never expect to be treated by the Diamonds as an equal, even if she was stronger than any one of them. If she tried to claim authority she would find numerous Gems she had never crossed arrayed against her because her attempt at political power would be a threat to the source of their own: individual strength.