STV Magic

Australia's democratic system is superior for two important reasons: Single Transferable Vote; and compulsory voting. The latter is more important: voting is a duty not a right; and if voting is not compulsory then somehow the people in power manage to make it easier for some to vote and harder for others. However this little idea is about STV.
[For those that don't know: In STV people number the candidates. The candidate with the lowest total of votes is eliminated in each round and all of the people who voted for the eliminated candidate have their votes transferred to their next choice. Repeat. Finally there are 2 candidates and the one with more votes wins and it is a nice feature that he has, at that point, got more than 50% of the votes. There are subtleties, but one thing is sure: it's better than first past the post. I was shocked, disappointed and annoyed (not to mention disgusted) when the British people rejected STV in a recent referendum.]
Well here's an idea. First we run our STV election to get the first winner (we just go till someone has >50% of the votes). Then we eliminate all the candidates of the same sex as that winner, and we recount the election until all the votes have been distributed to the last two candidates (except that we never eliminate our initial winner in any round [if that could happen?]). So we end up with two candidates and all the votes allocated to one or the other. Then we send them both off to parliament: except that when they vote in parliament they vote that total number of votes they got: it is no longer just one person one vote in the House of parliament.
This has a couple of nice effects. Naturally we get an equal number of the sexes in parliament. Another thing is that it makes gerrymanders useless.
Assume there are two big parties. Each will have two candidates, one of each sex. At the end of counting you get one candidate from each party elected after the minor parties and independents are eliminated. But the total number of votes each party gets will represent their total votes across the whole country, irrespective of where the boundaries are drawn. Indeed one of the advantages is that it reduces the need for the electoral commissioner to draw artificial boundaries to equalize the electorates.

Update 2014-07-26: I know what I mean, but it needs an example. Suppose there are two main parties in Byzantium: Red and Green. In an election in a seat with 19,999 voters we distribute preferences. The Red lady wins with 10,000 votes. At this point we eliminate all other ladies in the election and we start again with the Red lady and all the guys. We just keep distributing in the normal STV way. Any votes for the eliminated ladies go automatically to their next preference up. We don't stop when one has 10,000 votes, we keep going till all the votes are allocated to the final 2 candidates. Typically we'll get something like: The Red lady has 11,000 votes and the Green guy has 8,999 votes. Then they go off to Byzantium parliament and when they vote there the Red lady votes her 11,000 votes, and the Green guy votes his 8,999 votes.

Update to the update: The key to this is determining the second winner. After that the votes get allocated to each according to their relative position on everyone's vote. People who know STV will not be surprised that the winner's excess should be counted in determining the second winner. Maybe after a quota of 1/3 rather than 1/2. Mostly it won't make any difference in who comes second, but if you don't do it after 1/3, then strategic voting becomes an issue. Don't ask.