Context: Quadrants are the four different types of romance recognized by trolls, in Homestuck.
Here’s a quote on how moirallegiance works:
“Trolls are a very angry and violent race. Some are more hot-tempered and dangerous than others, to the extent that if left to their own devices, they would present a serious threat to society, or even to themselves. Such trolls will have an instinctive pale attraction to a more even-tempered troll, who may become their moirail. The moirail is obliged to pacify the other, to function as the better half. The two partners in a strong pale relationship will serve to balance and complement each other’s emotional profiles, and thus allow their other relationships to be more successful (Homestuck, p. 2401HS).”