Interesting piece of US history: The Western states (such as Wyoming and Utah) were among the first to grant women’s suffrage, nearly 60 years before it became federal law. Among the reasons at the time were that the female vote was the only way to tame the rampant immoral behavior going on in the wild west, the assumption being that the women, who were the paragons of home and family values, were needed to vote for politicians who would be tough on bad behavior. It turned out to be true- in states where women were given the vote, tough laws against vices were passed and strictly enforced while lawlessness and chaos continued in those that did not.
I don’t know where halacha fits into all this, nor can I say that the logic of the 1860’s would apply today (if anything, it seems that today’s women would be more likely to vote for abortion rights than for morality), but it is certainly an interesting point to ponder.