It's clear to me how quotation as a male form of communication would mean that women quote less, which you could check by comparing the usernames of quoters to the post-weighted sex distriubtion on LW. It's not as clear to me how it would mean women get quoted less- that would have to be either because of my first or second explanations. (I'm counting "men quote men more frequently than they quote women, and men dominate LW" as part of my second point.)