It’s a good question, and considering how much there are opinion polls released before every election in most democratic countries, there should be enough detailed data for someone interested. Even though we cannot know who the people actually voted for, a good study should be able to determine at least something.
It depends a lot on the election system. In a two-party race in majoritarian system gender means probably less than the party. In a list election in proportional system one votes for party, not person. In a typical proportional vote, though, people vote for a candidate, benefitting other candidates in same party’s list: this is the system used here in Finland, for example. As a voter has several alternatives within the same party, they will always have a choice whether to vote for man or woman, even when they always vote for the same party. Unfortunately our opinion polls usually only ask people what party they vote for and not their candidate preferences.
Presidential elections are different, though. In the three elections we have had since Finland took in use the French-style presidential elections (two rounds of popular vote; if someone gets over half of all votes in first round, they win; otherwise the two that had the most votes have a second round), the presidency has always been decided at the second round, with a male candidate against a female candidate. Women have been more likely to vote the female candidate. Here’s some early poll data before the first round of 2006 elections. According to it, 70 % of women backed the incumbent female president, while only 44 % of men supported her. Ultimately though the second round was needed, and she won, mostly by female vote. It should be noted though, that Halonen represents the socially liberal and progressive values that are usually (in Finland, at least) more embraced by women, for example increased gay rights, environmentalism etc. (Her popularity among the youngest voters is also partly explained by this). A right-wing socially conservative and traditionalist woman would probably have rather different support numbers between genders. There are also those who say that women would be more likely to support the incumbent president, whoever that is, but I doubt that’s a major factor in elections, even if it was true.
On the other hand, let’s look at Chile. Coincidentally, Chilean presidential elections of 1993, 1999 and 2005 have all been held only a few weeks before the Finnish ones, and in all these six elections in both countries the more left-wing candidate has won. Chileans elected their first female president, socialist Michelle Bachelet, in second round of 2005 elections (January 2006). In international media Bachelet’s victory was mainly seen as a victory of women in general. Chile is interesting, because men and women vote in different places so their votes are also counted separately and the results are public by gender. Looking at election data of Chile we find that in the 1st round of 2005 the Mujeres were more likely to vote Bachelet than the Varones. But in the second round, Bachelet’s percentage is slightly higher among Varones than Mujeres. So in fact, women were less likely to vote for woman than men were.
However, we must look at these Chilean statistics in context. I don’t know much about politics there, but to me the other results show that in Chile, women are more right-wing than men and thus are more likely to vote for right-wing candidates. When Chileans elected socialist Ricardo Lagos in 1999, the difference between genders was several percentage points, and women actually gave more votes to former Pinochet’s man Lavin than to leader of democratic movement Lagos. I don’t know why the Chilean women are so right-wing, especially as the country has often been called male-dominated conservative society, but so it seems. So when put in context, since Bachelet was almost equally favored by both genders, and therefore did better among women than Concertacion candidates usually do, there seems to have been some women-voting-women effect in play.
Can’t say what to make of all this. One thing is for sure, though. All national parliaments and almost all regional entities in the world have a clear majority of men, while women are in minority, sometimes in a very tiny one, too. So even if women are more likely to elect a woman than men are, it’s clear than both genders, when combined, still are more likely to elect a man. And it sure seems that in most elections, majority of women vote for a male candidate, even when there would be women available.