Women should not vote.
The reason that women shouldn't vote has nothing to do with intelligence. The reason is that men's instincts are designed for tribe formation and women's instincts aren't. The natural structure of tribes of both humans and chimpanzees is for the tribe to be run by males. Men have a sense of fairness that comes with this role. Women have no such sense of fairness. Men naturally develop a loyalty to the tribe and will act in the tribe's best interest. The loyalty of women is always primarily based on family, particularly her children. When women are given the vote, they will always support these things; a strong central government to support them, the right to sexually provoke men without consequences, and the right to cheat on their husbands. These are women's primary political concerns. In a democracy that includes women, immoral men and almost all women will vote for these things and ruin society.
For equality, one can have separate governments for men and women. Under this system, men would elect a men's government to govern men and women would elect a women's government to govern women. This would prevent women from using the government to oppress men. What would be the result of such a system? The answer is that women wouldn't bother voting in such a system. If you look at all the political actions of women, they are all about controlling men. Women have no interest in controlling or regulating women. Women want a strong government to force men to hire women, to protect women from men, and to tax men to support women. Women want divorce laws to force men to pay alimony and child support to women. And women want to be free to sexually provoke men while having the government prevent any response from men which women call "sexual harassment". There isn't one single thing that women want from government that involves restricting women in any way.