The Collaborative International Dictionary of English v.0.48:
Litigiousness \Li*ti"gious*ness\, n. The state of being litigious; disposition to engage in or carry on lawsuits. [1913 Webster]WordNet (r) 3.0 (2006):
litigiousness n 1: a quarrelsome disposition to engage in or carry on lawsuits; "charges of litigiousness and widespread perjury"