It's obviously a very complex question. Cornixia values honour and loyalty. You keep the person next to you in the trench safe and they do the same. Dishonesty and selfishness are the worst qualities to her.
Lyra doesn't care how much you lie, steal or cheat, as long as you don't step on or take advantage of the little guy she likes you. And so they both can get along.
Silver values sharing knowledge and spreading wealth and giving cultures the respect they deserve. Hoarding is the worst trait a person can have to her.
Sophie values community and taking responsibility. A burden shared is a burden halved. As such they all share the same moral compass and goal, even if their methods and upbringings differ and sometimes contradict.