Is it more effective to vote for a woman?
Consider the following cases when you are the marginal voter (i.e. you decide the election):


Two men $m_1$ and $m_2$ have $&gt;n$ votes, two other men $m_3$ and $m_4$ have $n$ votes, and one woman $w_1$ has $&lt;n$ votes. If you support $m_3$ and $w_1$ equally and support $m_4$ less, then you should vote for $m_3$, such that both $m_3$ and $w_1$ will be in the top four.
Three men have $&gt;n+1$ votes, one man $m_x$ has $n$ votes and two women $w_1$ and $w_2$ have $k&lt;n$ votes each. If you support $m_3$ and $w_1$ equally, you should vote for $w_1$ regardless of $x$ because $m_x$ will definitely lose, and $w_1$ will only win with certainty with your vote.
Men $m_3$ and $m_4$ have $n$ votes, two women $w_1$ and $w_2$ have $k&lt;n$ votes. What happens in the case of a tie is unclear, and (given one vote) it will end in a tie either way. 


Thus, it seems as though there is no advantage to voting for either a woman or a man over the other.