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The parliament can create two-person electorates for the House of Representatives and ensure equal gender representation in the Senate

There is no need for a referendum to ensure balanced gender representation in the federal Parliament. All that is required – without making a bigger Parliament – is to change the Commonwealth Electoral Act 1918 to firstly halve the number of electorates and then provide that each electorate elect a male and a female candidate.  McCulloch suggested this in 2009.

Creating larger electorates with a male and a female representative represents a truly democratic model to achieve equal gender representation. Equal representation of women in parliament can be legislated for in the life of one parliament. 

For a detailed account of repeated change to the Electoral law for the Senate, see this blog post by Antony Green who comments:

To borrow a metaphor from biology, the Senate's electoral system is a maladapted product of evolution rather than constructed by intelligent design. The system has come about by accretion, incorporating features added to make it consistent with voting systems in the House of Representatives, but also interacting with experience gained as the states have changed their electoral systems since the 1970s.   

WIDE POWER already exists

In 2001, then Chief Justice Gleeson referred to the wide power given to the Federal Parliament over electoral law in a speech in Melbourne:

A feature of the Australian Constitution is how little it has to say about the election of members of the Parliament; and how much choice it leaves to the Parliament itself in determining, from time to time, the form of representative democracy to be enjoyed by Australians. 
That is not surprising, bearing in mind the context in which the Constitution was framed.  Most Australian women were not entitled to vote.  No one was compelled to vote.  Aboriginal Australians were not counted.  The Upper Houses of State parliaments were not democratically constituted.  The framers of the Constitution did not approach their task with a rigid view of what constituted representative democracy; and that is just as well for us. 
Democracy is always in a state of evolution, and adaptation to changing ideas and circumstances.  The Constitution does not seek to entrench more than the bare minimum of conditions for democratic government; it is left to the Parliament to fill in the details, and to alter them from time to time in response to public opinion expressed through political pressure and conflict.

The wide power given to parliament was confirmed by the High Court in the case of Roach v Electoral Commissioner [2007] HCA 43, which was about whether prisoners could be excluded from the vote. The High Court made clear that the Constitution imposed few restrictions on Commonwealth power over Commonwealth elections, provided that members of parliament are "directly chosen by the people of the Commonwealth" and that this be read to include a qualified right to universal suffrage. This gives power to the parliament to solve the gender equity problem as easily as passing a law regulating lighthouses.

A wide restriction on prisoner voting disallowed by the High Court in Roach and the law was amended to restore the right to vote for most prisoners serving a term of less than three years imprisonment. The High Court decision was later summarised  by the Joint Standing Committee on Electoral Matters report into the 2010 Federal Election in chapter five (5.17-5.19):

In Roach, in a 4-2 judgement, the High Court ruled on 26 September 2007, that:
...the 2006 amendments were inconsistent with the system of representative democracy established by the Constitution. The Court held that voting in elections lies at the heart of that system of representative government and disenfranchisement of a group of adult citizens without a substantial reason would not be consistent with it.

Earlier in that report, the Joint Committee commented on changes to the Electoral Act over time to reflect changing values (5.1-5.2):

Australia has enjoyed electoral legislation that has become increasingly inclusive. There have been a number of changes to make it more so occurring in the past 50 years, including extending the franchise to Aboriginal Australians (1962), allowing British Subjects to retain the franchise when Australian citizenship became the new qualification (1984), and extending the franchise to include certain Norfolk Islanders (1992).
Similarly, other amendments allow itinerant electors to remain enrolled even thought they do not meet the one month residency qualification for enrolment. Australian citizens who depart for overseas, who have a fixed intention to return to Australia within a defined period (currently six years) may remain enrolled, or enrol from outside Australia under certain conditions, and provisional enrolment is now available to Australian citizens over 16 years of age and those who have applied for Australian citizenship.

CREATING TWO PERSON (MALE & FEMALE) ELECTORATES IS NOT A NEW IDEA

There have been numerous calls for equal gender representation in parliament in Australia.

Legislating for equal gender representation has failed to receive really serious attention. Perhaps it is thought to be too difficult to achieve as a matter of law or it is seen as simply unthinkable. For example, in 2007 there were two passing references in the 2020 Summit to the importance of setting a goal of equal gender representation (at pages 321 and 397).

However, halving the number of House of Representatives electorates so that each may have a male and a female representative is a truly democratic model to achieve equal gender representation. In Australia there is no constitutional impediment to doing this. Indeed this model was suggested by former Liberal Party Minister Jim Carlton in an article "How to break parliament’s male monopoly" in The Independent Monthly in February 1994. This avenue was also canvassed by McCulloch in 2009. 

The original proposal by Carlton (first made in 1993) was referred to in a paper by Marie Swain for the NSW Parliamentary Library Research Service in 1997 (at p 30). Swain says:

The ‘Carlton proposal’
In mid-1993 while still a member of the House of Representatives, the Liberal MP Jim Carlton put forward a radical proposal for achieving a greater representation of women.  He suggested that the Commonwealth Electoral Act be amended to allow voters to elect equal numbers of men and women to both the House of Representatives and the Senate.  To avoid simply doubling the number of politicians, he proposed that the number of electorates be halved.  At election time the voters would be given two lists of candidates - one for the male candidates and another for the female.  The voters would fill out a separate ballot paper for each group and the winning candidate in each list would jointly represent the electorate.
In this way the House of Representatives would be made up of equal numbers of men and women. A similar procedure would be used in the Senate. Generally this proposal was not well received.
Given that it would require many standing male parliamentarians to relinquish their seats, it is not difficult to understand why men did not embrace the idea.
In more recent times similar proposals have been put: the Australian Women’s Party has a policy which includes changing the Constitution so that voters would elect one male and one female candidate in each seat.  To avoid adding to the number of parliamentarians, seats would be clustered; and the Women Into Politics group has also asked the Federal Parliament’s Standing Committee on Electoral Matters to investigate two-member electorates, with a male and female MP apiece.

We contend that there is in fact no requirement to amend the Australian Constitution. As Swain indicates, the 'Carlton' proposal was considered by the Commonwealth Parliamentary Research Service in a report by Consie Larmour in 1994. This report was prepared for the Standing Committee on Electoral Matters as part of its investigation into the request by the Women into Politics Group (referred to by Swain above), at page 17, Larmour noted:

While the proposal has been rejected by non-Liberal women parliamentarians as unrealistic (and by liberal women on the grounds that women should succeed on merit, not by quota), it received a good deal of media attention. Commentator Paddy McGuinness supported the proposal as an idea quote almost of genius", and Robert Macklin labelled it as an idea whose time has come.

Lamour continued (somewhat cryptically):

The Carlton proposal is opposed strongly by both government and coalition women members of parliament. However, although to require half of the parliament to be constituted of women may not have any special merit at some time in a utopian future, certainly it is now recognised that women have a claim to positive action to provide a political system which will serve both sexes.
(it would seem that the words 'may not have any special merit' should read 'may have merit')

If, we are right to say that there is no constitutional impediment to 'the Carlton proposal', then debate about equal gender representation needs to be taken away from the political parties.

The Carlton proposal was seriously canvassed by Rosemary Whip in 2003. Whip also refers to a US proposal for separate gender constituencies, and discussion by George Bernard Shaw:

One proponent of such an approach was George Bernard Shaw, who believed that the enfranchisement of women in England had not resulted in representative government. In the Preface of his historical play, ‘In Good King Charles’ Golden Days’, he argued for a constitutional amendment requiring that all representative bodies should consist of equal numbers of women and men, to be ensured by the ‘Coupled Vote’ in which ‘The representative unit must be not a man or a woman but a man and a woman. Every vote, to be valid, must be for a human pair, with the result that the elected body must consist of men and women in equal numbers.’

Rosemary Whip 2003, The 1996 Australian federal election and its aftermath: A case for equal gender representation Australian Feminist Studies 18:40 73-97 (76). The passage from Shaw is:

THE FUTURE OF WOMEN IN POLITICS
The establishment of representative government in England is assumed to have been completed by the enfranchisement of women in 1928. The enormous hiatus left by their previous disenfranchisement is supposed to have been filled up and finished with. As a matter of fact it has only reduced Votes for Women to absurdity; for the women immediately used their vote to keep women out of Parliament. After seventeen years of it the nation, consisting of men and women in virtually equal numbers, is misrepresented at Westminster by 24 women and 616 men. During the Suffragette revolt of 1913 I gave great offence to the agitators by forecasting this result, and urging that what was needed was not the vote, but a constitutional amendment enacting that all representative bodies shall consist of women and men in equal numbers, whether elected or nominated or co-opted or registered or picked up in the street like a coroner's jury.

Whip concludes:

Perhaps it is time to revisit Jim Carlton’s proposal for equal representation. It appears that the most effective strategy for achieving equal gender representation would be one such as he has suggested. Carlton’s proposal provides for equal representation in a way which does not single women out for treatment different from that of men. It would ensure that women occupied seats ranging from marginal to safe just as their male counterparts do, and by providing for separate pre-selection for male and female candidates would allow them to be evaluated according to gender-specific characteristics and experiences. Women and men selected and elected under such a system could be chosen on the basis of what they, as individuals, could bring to the parliament and would have the numbers and the diversity to represent the multiple diversity of both genders.
Such a system, in which women compete for pre-selection against other women, has definite advantages according to some of the women selected from all-women shortlists prior to the 1997 British election. One remarked that, with such a shortlist, gender ceased to be an issue and the selection was based only on the abilities of the individual candidates, while another said that constituency parties, presented with shortlists of four or five women, rather than of one woman among a number of men, found that the choice they were offered was among ‘very different politicians who happened to be women’ which ‘broke through the notion that women are just one particular type of politician’.
An approach such as Carlton’s also has the advantage that equal representation would be achieved not by a gradual increase in the number of female representatives, such as we are seeing at present, but instantaneously, and would deliver a sharp shock to the institution of parliament. The resulting upheaval might well alter the entrenched male ethos in a way that a gradual increase is unlikely to do.
As a solution to the problem of equal gender representation, the Carlton proposal seems to warrant more serious consideration than it has received to date. Although its effectiveness rests on suggestions for change likely to be perceived as so radical as to have difficulty gaining widespread acceptance—and Carlton himself has described it as ‘entirely workable’ but ‘maybe not politically acceptable’152—one might question whether such an initiative, at the beginning of the twenty-first century, would really be any more ‘radical’ than giving women the vote was at the beginning of the twentieth century.

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In the UK, the idea of having a male and female elected in half the number of existing single-person electorates was floated by Ruth Fox in 2012 and repeated in 2015 by James Connelly in the Conversation.

Joint male and female representation for each electorate was a core principle in The Commonwealth of Britain Bill introduced in 1991 by Tony Benn in the UK, echoing the words of George Bernard Shaw. However, this was also part of a package from Benn that involved abolition of the monarchy. 

The role of the monarchy is a Constitutional matter in Australia and we are not advocating for the same package of reform.

See also the development of electoral parity laws in France.