Only there is a twist. All men now pay for all women and all children. They do this without receiving the benefit of having the women they support as mates nor the affection of the children. Considering the above, it is clear that single women, generally, vote Democratic because the Democratic Party seeks to replace the husband with the state. Just as strongly we can see why men vote Republican in higher numbers.
Men see the state as their enemy.
The state appropriates their income, outlaws their natural behavior, and imprisons them if they step out of line. Men are more frequently imprisoned for their crimes, sentenced to longer stays in prison, and executed more often than women. Thus, it is only natural that they would support the downsizing of the state. The source of these differences, of course, is embodiment. Women are more often than men left with the burden of caring for children.