It would be better-dressed, for one thing. The Spanish and Catalan women in Zapatero's cabinet are glamorous and modern, unlike the men at G8 summits. This isn't a trivial point: conservative taste in clothes is often a sign of conservative social attitudes.
I'm reading Jonathan Powell's book about the Irish peace process and I've been struck by the photos; apart from Mo Mowlam (an unconventional politician and a stylish dresser), women were largely excluded from Ulster politics. Abortion is banned in Northern Ireland, a consequence of women not having as much access to power as patriarchal men.
How much things would change depends on the kind of women in politics. In states where the political class is dominated by alpha males, they look and act like men, which is why Labour's front-bench women are mostly uninspiring.
They have to be thick-skinned because they're given an even harder time than men, which is saying something; last week, when people questioned the credentials of Zapatero's Defence Minister, Carme Chacon, I couldn't help wondering if she was less qualified than Des Browne. It's shocking that the UK has never had a woman defence secretary, when macho countries like Colombia and Spain have.
The Spanish PSOE's electoral success and its modern appearance are connected. It's brilliant on domestic violence and the Education Minister, Mercedes Cabrera, is facing down the Vatican on RE in schools. Now, if women were in charge of religion around the world everything would look different ...
'Say hello to egg-freezing, and female orgasms' says Catherine Townsend
We'd finally be free to sow wild oats without fear of being labelled "sluts". Men who slept around would be the ones who had to worry about their reputation.
Female politicians would sweep risqué incidents discreetly under the carpet before an election, in the same way that Ken Livingstone did with his five kids, and Boris Johnson with his affairs.
I don't believe the world would turn into a feminist utopia where everyone relied on hugs and cups of tea – Margaret Thatcher proved that women can rule with an iron fist – but I do think we'd choose our wars a bit more carefully. And not be arrogant enough to insist that God is still on our side when it becomes clear that no one else is.
Women could look forward to screaming tabloid headlines about the merits of "stay-at-home fathers" versus "working dads" – and would be safe in the knowledge they could have children and a career, since affordable child care would be universally available.
Egg freezing would quickly become a reality. Women who chose to delay motherhood until their mid-40s and beyond would be snapped strolling along the beach with their Ashton Kutcher-lookalike husband number two or three – without fear of newspapers labelling them "4x4", as they did Ulrika Jonsson.
And after the billions spent developing Viagra, maybe scientists would finally get the green light to study female orgasms properly, so men realise that they have to bring more to the party than just an erection. Then Italian scientists in white coats wouldn't be the only ones locating the ever-elusive G-spot.
'There'd be half as many pointless meetings' says Janet Street-Porter
If women ran Britain, there would be half as many pointless meetings, no special advisers, and bureaucracy and the cost of administering government would halve. Parliament would sit during normal working hours, MP's expenses would be abolished and their wage would cover child care and standard class travel on public transport.
We aren't interested in meaningless time-wasting ceremonies and traditions, so the roles of Speaker, serjeants-at-arms, county sheriffs and their ilk would be phased out, replaced by ordinary men and women in normal clothes without lace jabots, doing real jobs instead of phoney ones for half the salary.
Women are much better at multi-tasking and conciliation rather than confrontation, so we would see the end of the three-party system and move to consensus politics.
All female prisoners (except those serving life for violent crimes) would be released to serve their sentences working in the community. Juvenile offenders would work in old people's homes and hospitals, helping to feed and clothe those less fortunate than themselves. Basic cookery would be taught from the age of seven. All public bodies, hospital boards and police authorities would be forced to appoint the correct proportion of women to their governing bodies. Any organisation receiving public funding, from museums to sports facilities, would have to do the same.
Broadcasters' boards would have to be 50 per cent female to retain franchises. We'd stop meddling in other people's affairs overseas, recall troops from Iraq and Afghanistan, and declare ourselves a nuclear-free peace zone. The minimum wage would be raised – it's mostly women that have to try to live on it.
'Safer, saner, kinder - but ever so slightly dull' says Terence Blacker
So Harriet Harman is in charge, with Hazel Blears, Margaret Hodge and Tessa Jowell in major ministerial posts. Ignoring objections of tokenism, the PM has included one of her male colleagues – "Harman's Yes-Men", as the press call them – in the Cabinet. David Miliband will head the newly-formed Ministry for Children and Men.
On TV, The Apprentice is chaired by Anne Robinson, with Clare Balding replacing Jonathan Ross as the BBC's top interviewer. Men are not ignored: on a lunchtime show ChapTalk, Will Self, Jeremy Clarkson, Alan Sugar and Bill Oddie provide what the Radio Times calls "a feisty male perspective on the issues of the day". Book publishing remains unchanged.
Of course, things run more smoothly. Women are better at not making fools of themselves. There is less mad egotism. The randy-little-chap school of European politician – Berlusconi, Sarkozy, that Finnish minister who texted a lap-dancer – has been replaced by different national versions of Angela Merkel.
Already my shoulders are drooping. I'm shrivelling in the chill wind of female efficiency. The world may be safer, saner and even kinder but without that wild, brave stupidity we men have, it has become ever so slightly dull.
And that is just public life. Within millions of homes, the sexual dynamic between men and women – a finely-tuned, hair-trigger mechanism built around power and powerlessness, control and lack of it – has gone hopelessly awry. Those glorious moments of private inappropriateness that shatter the proprieties of the outside world will be lost forever.
And what will happen to humour? Last year Martin Amis revealed that not only was he a feminist, he was "a gynocrat – that is to say, I believe in rule by chicks". Once chicks rule the world, there will be no place for that kind of joke.
'Their track record isn't exactly pretty' says Dan Snow
People talk about "women in charge" as if it was a revolutionary idea dreamt up by daring ideologues over a frappuccino – like Fairtrade or carbon trading. Yet for millennia, women have fought, ruled and directed the affairs of state.
The Iron Lady was far from Britain's first female supremo. The Falklands, a counter-insurgency in Northern Ireland, and calling Saddam's bluff look tame in comparison to her Amazonian forebears.
Boudicca leads women rampaging into recorded British history, with her genocide of Romans. Matilda fought a vicious civil war for England's throne. Isabella, wife of Edward II, invaded her husband's kingdom, jailed him and probably had him killed. Mary's campaign to return England to Catholicism is an oft-lamented epic of English lore.
Then there were queens. Elizabeth plunged England into a long war, settled plantations in Ireland and profited gleefully from slaves and piracy. Anne sided with William of Orange's invasion of her father's lands and spent all but a few weeks of her reign locked in a bloody conflict with Louis XIV. The "peaceful" reign of Victoria witnessed the largest imperial project in history.
Not to be outdone, two European empresses, Maria Theresa and Elisabeth, brought Frederick the Great's Prussia to the point of extinction, aided by Louis XV, egged on by his mistress, De Pompadour. Catherine the Great was the embodiment of autocratic rule when she succeeded her deposed husband. Bismarck's daughter made her children learn to eat with their left hands, preparing them for the wounds they would sustain in the service of the Prussian state.
Spartan women told their men to return from war victorious or dead, soldiers' wives of the 18th century slit the throats and robbed the wounded on the battlefield.
So a world run by women would hardly be one of milk and honey. History shows that any form of leadership in the face of scarcity, natural disaster and plague demands brutality – and men and women have shown equal determination to do whatever is necessary to survive in our indifferent world.
'If women ruled the world? They already do' says Adrian Hamilton
I don't know where the "if" comes in: women already run the world. Why else are presidents Sarkozy, Putin and the rest stripping off for the public gaze and arming themselves with young consorts, if it is not because they realise that in this day and age, the physiognomy is the message and that men have to become like women to get anywhere? If Berlusconi has any more operations, he'll become one.
And where does the word "rule" come from? The days when anybody "ruled" anything are long since past. Even the top industrialists such as Lord Browne can be felled at the first whiff of sexual tittle tattle. Nobody believes now that positions – judges, MPs, journalists or even doctors – are worthy of respect or bastions in need of storming.
Ten years ago my club achieved notoriety for refusing entry to women. The air was rent by feminists saying it should be forced to open its doors of influence and power. Now, if the club changed its rules, I doubt whether it would get a single female applicant. It is a place where men can laugh away their own irrelevance. Why disturb them?
Government could be seen as the final remnant of rule, the last point at which men (or women) can strut about as if they could influence things. But even here its power is basically to do harm, to wage war or tax the poor, rather than much good.
Judging from the way female MPs trooped through the lobbies to approve the Iraq invasion and Angela Smith withdrew her resignation the moment the Prime Minister rang her, we should not expect any difference if all the posts were held by women. They seek power and abuse it as much as men, as anyone who has had a female boss knows . The stratagems may be different but the intentions are the same.
The tone of discourse might change if all the top posts were held by women. But would that be a bad thing? For any man who doesn't like sport, these last years have been hell. You can't go to a hairdresser, let alone a pub, without being asked about Arsenal's latest match and every MP must declare which team he supports. Botox, babies or bras – anything is better than balls.
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