Now, at first some of you might be thinking that it's obvious, we already have statistics showing the breakdown of votes by sex - we know how women and men vote, so we can imagine the results of a women-only vote. But no - this does not tell us what would happen.
It was not until 1920 in the US (it was 1918 in the UK for 30+ aged women, 1928 for equal voting rights to men) that women got the vote, a full half century after black men got the right in law (although not in practice in many areas in the US, even in those areas they were legally allowed and so could and did vote if they could find a way to fulfil upon the added requirements that were put in place in an attempt to thwart them). So, despite the history of full-fledged legal slave-ownership of black men - along with women, and children - black men were accepted by the people as capable and worthy of the right to vote. Women, of any colour, were not.
When women still could not vote, the argument many made was that a women does not need the right to vote because she would tend to just vote the same as her husband anyway. Extracting from the sexism, we can consider whether couples do tend to vote the same - and if so then why not let the women represent the household instead of the men? Of course, aside from the single and those whose relationships do not last long, you also have many married couples in which the partners disagree, but the idea that they tend to vote the same opens the question of whether having the woman (in a heterosexual couple) represent the couple/family in the voting booth would produce a different outcome than having the man do it. One can imagine some sexist - against either sex - replies to this query. And, one can see the power this position holds.
But the real power - and difference - comes through two avenues: (1) the attempt to win the votes and through it the selection of candidates, the issues addressed by them, the debates and campaigning--the public conversation and the private pandering & lobbying, and (2) the right to hold office and other rights which one cannot imagine without first the right to vote - and the consequences of the right to vote, i.e., who is voted into power.
So, now imagine that to make up for all those years when women had no right to vote it was decided that for (at least) one election, only women could vote. The parties would have to select candidates who would appeal to enough women and address issues in ways that would appeal to enough women -- the public conversation would change -- yes, even given Hillary Clinton. What about behind closed doors? What would we learn about lobbying and private pandering, from the 'old boys' clubs and networks (in the US and UK), that might have to be reinvented - and could be drastically different - if only women were voting, and therefore the old power structures were dismantled by virtue of suddenly not mattering?
Would the candidates actually be (significantly) different, if it were to happen today? How different would be the public conversation -- and would this take a couple of seasons to take real effect? Who would win--would it match up with polls of today or would enough change that the outcome would be truly different from the demographic breakouts? How would culture be affected, inside and outside the arena of politics? How different would the results, the policies, end up being? And, how long would it take to see the difference? And would we end up with a 'reverse sexism' problem...?
Please let me know your thoughts!