[chaoxu]

You say hard rules can cause A beats B, B beats C, and C beats A. Is it because hard rules itself can have cycles, or because hard rule and scores together causing cycles? What does tie-breaker even mean here, how does it change the ordering?

Let's ignore tie-breaker. Is it the following abstract problem?

Given a partial order A (the hard rules) and a total order B (the scores). Find a total order C that is an linear extension of A and "agrees" with B the most.

I feel if phrase this way, then there is probably some faster greedy approximation of w/e "agrees" you are thinking about, because w/e you are doing here is also just an approximation of w/e true best you are thinking.