I got into an interesting situation with loyalty in my current game where a city seems to be caught in a perpetual loop of flipping back and forth. It's the industrial age and Australia (AI) for some bizarre reason decides to settle a lone, isolated city up in the tundra on the edge of the north pole ice tiles. The city is closer to my empire than Australia so naturally it feels a lot of loyalty pressure from my empire. So of course, the city immediately rebels and becomes a free city. A few turns later, the free city flips to me. I don't want the city because of it's super crappy location. So I refuse the city. The city goes back to Australia but because of loyalty pressure, immediately rebels a few turns later and becomes a free city again. But since I refused, this time, it flips back to Australia. But because of my loyalty pressure, it declares independence again and becomes a free city. Basically, the city cannot stay Australian so it constantly flips back to being a free city. So this time, I capture the free city and liberate it back to Australia. The text says that the city won't feel any loyalty pressure from me anymore so I think the city will stay part of Australia for good this time. I don't care if Australia has the city since it is crappy, plus I get a diplo bonus with Australia for returning the city which can't hurt. But no, the city flips back to being a free city. And it will soon flip back to Australia but as soon as it does, it flips back to being a free city. A perpetual loop again. It seems the only way to break the loop is to either raze the city or keep the crappy city.