I think the relevant figure isn't how much more likely women are to file such suits but how much more likely they are to file them when no harassment has really occurred.
The problem is that "whether sexual harassment has occurred" isn't all that well-defined. You can of course define "sexual harassment" however you want but then you have to establish you it's a bad thing. For example, from a briefing at the company I work at the examples of "sexual harassment" was:
1) a woman goes to work in somewhat provocative/revealing clothing and a male coworker complements her on her appearance.
2) a manager used the phrase "guys and gals".
Frankly if these examples are typical of "sexual harassment", I'd say sexual harassment isn't a problem.
Did either of these examples result in lawsuits?
I remember seeing a talk of the concept of privilege show up in the discussion thread on contrarian views.
Some discussion got started from "Feminism is a good thing. Privilege is real."
This is an article that presents some of those ideas in a way that might be approachable for LW.
http://curt-rice.com/quotas-microaggression-and-meritocracy/
One of the ideas I take out of this is that these issues can be examined as the result of unconscious cognitive bias. IE sexism isn't the result of any conscious thought, but can be the result as a failure mode where we don't rationality correctly in these social situations.
Of course a broad view of these issues exist, and many people have different ways of looking at these issues, but I think it would be good to focus on the case presented in this article rather than your other associations.