Why are we asking this question now?
David Cameron is determined to increase the number of women Tory MPs, and has introduced various measures to make it more likely that constituency associations in winnable Tory seats will select women candidates.
But there are signs that the activists who dominate these associations do not want to be told to change their ways by their young leader.
This has made some people ask whether, if Cameron does not get his way by exhortation, he will go for compulsion - and tell local associations that they will have to choose from all-women shortlists.
Do they work?
Yes. There is real evidence that the introduction of all-women shortlists in the Labour Party in the 1990s broke down age-old prejudices that prevented women from being selected or even putting their names forward. It became apparent that women had a better chance of being selected, even in those seats where they were competing for the nomination.
Patricia Hewitt, for instance, became Leicester's first woman MP in an open contest. But after Labour stopped using all-women shortlists, before the 2001 election, the number of women MPs fell slightly. When all-women shortlists were reintroduced the number went up again, peaking at 128 women MPs in May 2005. Since then deaths have, sadly, reduced their numbers by two.
Are more women needed in Parliament?
Some would say this is just like men asking, 100 years ago, whether women "needed" the vote. The House of Commons is expected to represent the whole nation, a strong argument for its composition to mirror that nation's population.
There were complaints that when the Commons was very heavily male-dominated, issues like women's health and childcare were not treated sufficiently seriously. But the increase in the number of women MPs has not noticeably "feminised" the party system. There is just as much barracking and exchanging of insults as ever, and women have been as likely as men to follow the orders they get from the Whip's office.
Has there been a male backlash?
Yes - and not only from men. The Labour Party was helped in the 1990s by the fact that most of its best-known women politicians - such as Harriet Harman, Clare Short, Tessa Jowell, and Mo Mowlam - backed all-women shortlists. So did several big unions. Even so, Labour in the 1990s was, in a sense, saved by the bell. They had shrewdly begun introducing all-women shortlists in those parts of the country where they anticipated the least resistance, but they still encountered lively opposition in some towns, including Slough. An employment tribunal ruling brought the whole process to an unexpectedly early finish - and spared Labour's harassed staff from having to go into Jarrow to tell the local Geordies that they had to select a woman.
There was also a suspicion that officials were using the all-women shortlists as a device to keep out certain men who were likely to make trouble for Tony Blair. This may have contributed to the spectacular disaster in Blaenau Gwent, a normally solid Labour seat in Wales with a tradition of selecting members of the awkward squad, including Aneurin Bevan. The locals were told three years ago they had to have an all-woman shortlist, and those who accepted this ruling selected a devout Blairite, Maggie Jones. The opposition to the proposal was led by a local councillor, Peter Law, who ran as an independent, and won, bringing down Labour's share of the vote from 72 per cent to 32 per cent, the biggest swing against Labour in its entire history. Mr Law died in April. Labour did not impose an all-women list for the resulting by-election in June, but it still lost to Dai Davis, one of Mr Law's supporters.
Will David Cameron bring them in?
He hasn't ruled them out, but it is very, very unlikely that he will risk it. He has said he will do "everything short of all-women shortlists" to persuade local parties to select more women in winnable seats, including an inducement for those associations that voluntarily select from an all-women list. If he tries to impose all-women lists on constituency associations that don't want them, he could provoke a reaction far more ferocious than the one in the Labour Party, because so many Tories, including many leading women Tories, oppose all-women shortlists as a matter of principle. Ann Widdecombe, for example, calls them an insult to women.
What about the Liberal Democrats?
The Liberal Democrat leader, Sir Menzies Campbell, is also very keen to increase the number of women MPs, but when his party has discussed all-women shortlists in the past, there has been lively opposition from the women MPs. It is noticeable that all Liberal Democrat women MPs are either childless, or have grown-up children. Their problem seems to be that women with young children do not feel able to give up the time needed to contest and hold a seat for the Lib Dems, rather than an unwillingness by local parties to select women.
Would another system work?
Prior to the 1999 elections to the European Parliament, the Liberal Democrats using a system called "zipping". They had lists of candidates for each of the 10 regions of the UK. The first name on five lists was a woman, with a man in second place; the other five lists were headed by a man, with a woman second. As a result, they had five women and five men elected as MEPs.
Sweden's ruling Social Democratic party pioneered this system in 1994, which is why Sweden now has the highest proportion of women legislators in the developed world. But this works only under a system of proportional representation in which there is a small number of constituencies each with several elected representatives. It cannot be applied to the British House of Commons.
David Cameron is trying out a bundle of measures including having constituency parties make their final selection from shortlists of two men and two women. Doubtless, Mr Cameron's campaign will make some difference, but whether it will enough of a difference to convince floating voters that the Tory party has genuinely changed has yet to be seen.
Should political parties operate all-women shortlists?
* Women are more than half the population, but less than 20 per cent of the House of Commons
* A heavily male legislature undervalues important issues such as childcare, education, family health and equality at work
* Pleading with local party organisers to select women has been shown by experience not to work
* All-women shortlists are undemocratic and patronising, and lead men to question the merits of MPs chosen without open competition
* The best women politicians have reached Parliament by showing they can stand up to men
* The Commons needs independent-minded MPs, not ones put there by party bosses