The gender gap debate has taken some surprising turns in recent days. Conservative critics have argued for years that the reason women make only 77 cents for every dollar earned by men is that they work fewer work hours and in lower paid occupations, not because of rampant sexism at the office or factory. Once it came to light that President Obama and several Democratic senators presided over sizable gaps in their own offices, this criticism of the 77 cent meme gained some new followers, including reliably left-leaning Ruth Marcus who went so far as to accuse the administration of “demagoguery.”

So does that mean we can all get along now? Hardly. There is still a fundamental philosophical divide between liberals and conservatives on the issue, one that leads to entirely different ideas about policy.

In a nutshell, the disagreement is this: Liberals believe that when it comes to the labor market, there are no natural, relevant differences between the sexes. Conservatives, obviously, don’t see it this way. They believe there are basic differences between men and women that are innate, not created by social or political forces.

According to liberals, if women are becoming pediatricians instead of neuro-surgeons, public interest rather than corporate lawyers, child care workers rather than coal miners, and are working 35 rather than 40 hours a week, as they are, it’s because of what Frank Bruni described as a culture that “places a different set of expectations and burdens on women and that still nudges or even shames them into certain roles.”

Get rid of gender stereotyping, inflexible workplaces, bastards on the couch, and mom-shaming, and we will have a society where, as Sheryl Sandberg has put it, “half our homes are run by men and half our institutions are run by women.”

In the conservative view, it’s the natural differences between men and women which lead them to make many of the life choices they do, differences that could probably not be resolved by anything less than mandatory universal hormone injections.

The two sides are not likely to reach agreement on this nature/nurture debate anytime soon. What they can do, though, is look at how far the world’s most egalitarian societies using precisely the policies that liberals say would loosen the grip of gender roles, have travelled towards Sandberg’s vision. The answer is not far at all.

Consider Sweden, a country where the goal of gender parity is close to a national religion. Swedes have extensive paid parental leave designed so that it has to be shared by mothers and fathers in order for couples to receive the full 13 months off. They have high quality child care, and political party quotas to equalize the number of men and women running for office. Children’s clothes, toy and book companies try to design products to discourage any thoughts of boy or girl stuff. In some preschools teachers say “good morning, buddies” to avoid the offensive “good morning, boys and girls.”

The results are not what anyone could call revolutionary. Yes, women make up 45% of the Swedish parliament compared to a paltry 18% in the U.S Congress. And, yes, Swedish women are more likely to be in the labor force than their American counterparts. (Most of the data that follows comes from the 2012 OECD report “Closing the Gender Gap”). But the difference in labor force participation is not dramatic, and in most respects, Swedish women behave much as sisters do in the U.S.

Like Americans, Swedish women work substantially fewer hours than men; they are 2 times as likely to be part timers. They are the vast majority of social workers, teachers, and child care workers and a small minority of scientists (PDF) and CEO’s (PDF). In fact, Sweden’s labor market is among the most sex segregated (PDF) in the world and their wage gap shows it. Mothers take in only about 20% as men, much the same as in the United States.

The results in other countries committed to gender role busting are much the same. Iceland has been crowned the most gender equal country in the world by the World Economic Forum (PDF) every year since 2009. They provide many of the same supports as Sweden. So does Norway, third on the WEF list and famous as the first country to institute a 40% female quota in corporate boardrooms. Women in both countries are well represented in parliament—about 40%. Yet the ladies still work fewer hours than their male counterparts and they are two times as likely to be part timers. They remain segregated in more traditionally “female” occupations. Their mommy wage gap? About the same as Sweden and the U.S.

What about workplace flexibility, the answer du jour to the wage gap? There are many reasons to love flexibility, not least that both women and men want more of it. In what is probably the most detailed recent analysis (PDF) of the gap, Harvard economist Claudia Goldin and Lawrence Katz found that professions which have restructured themselves to create more flexible workplaces are closest to closing the gender gap. But that’s only for hourly wages; when you consider annual income, the story changes markedly for the simple reason that women in almost every field work fewer hours than men and are more likely to have part time positions. Thus even pharmacists, lucky enough to be in what the writers call “the most egalitarian profession,” still have considerable hours (PDF) and, therefore, as those hours accumulate over the year, an income gender gap.

Now, it’s possible that a more clever society in the future will figure out the right policies and educational practices to eradicate the attitudes that keep women from working longer hours and in higher paying occupations. It’s also possible that the gender gap reflects a basic truth about human nature, and that on average mothers really are more invested in day to day childrearing than fathers. Note that everywhere in the world, single parents are just about always women, and that those women, if for logistical reasons alone, earn less than other women, not to mention men.

Perhaps the predominance of single mothers as opposed to single fathers is also a result of social expectations. But with over 40% of American children born to unmarried mothers, the vision of half of all homes run by men and half of all institutions by women will remain a Nordic fairy tale for a very long time to come.