Litigiousness is the habit, mood, or reputation of being very willing to take disagreements to court. It is the noun that sits behind litigious, and like that adjective it is often used with disapproval. Writers apply it to a person (‘his litigiousness’) or to a whole society (‘the litigiousness of the culture’). It is a formal, slightly scolding word, almost never spoken in everyday chat. Though actually, the person using it is already making a judgement: they think court is being used too fast, or too often. The word names that perceived habit. It does not, by itself, tell you whether any one case was fair.