Just by glancing at the top result it should be quite obvious to anyone that the study is correct; nevertheless, there may be a few fleeting doubts, so let's take a look at the paper itself. As it turns out, of course, the paper is not primarily about the desirability of men in different countries - trust the daily media to focus on that aspect - but really about how gender equality affects the rate of cohabitation and marriage as opposed to single households. Why is that important? The degree of cohabitation affects the birthrate, something countries like Japan and Italy - that battle low birthrates and have low gender equality - should be concerned with.
There's a lot of details - and details matter for this kind of modeling - but Dr. Sevilla-Sanz' idea in brief is that both women and men prefer partners that shoulder their share of the housework, child rearing and other responsibilities in the partnership.
In economic terms (she is an economist), the cost - in time and effort as well as money - of sharing a household increases for a woman when the man is not willing or able to pitch in and help. And when shared households become more expensive, women will become more choosy, and fewer women will live with a partner. On the other hand, of course, in a hypothetical society where men did more than their fair share they would be hesitant to make a household together. The optimal point is when the work is shared equally.
Of course, social norms make men and women shoulder different amounts of responsibility, which decreases the number of shared households. She shows that it is the availability of egalitarian men that is the limiting factor. This has the effect that in a given society, for men that want a partner it's better to be egalitarian, whereas for women it's better not to be. But it's better for both if the society as a whole has a more egalitarian attitude.
To test this model, she looked at an international survey on division of labour and social norms, selecting 13 countries. She compared the survey results with the proportion of people who are married or cohabiting. he finds that indeed, people are more likely to live together in more egalitarian countries and it does seem consistent with the explanation her model gives us. She looks at various other factors (such as age distribution, attitudes towards cohabitation and divorce and the education level of men and women - higher education generally means you're less likely to live with somebody) but she finds they can't explain this effect.
So, men from more egalitarian societies (like *cough* Sweden) are more desirable long-term partners than those from more unequal countries; likewise for women. And whereas more egalitarian men from a given country are more desirable, more egalitarian women are somewhat less so - though that effect is much weaker than the countrywide differences.
As she points out, the proportion of people that live with a partner really affects the countrywide birthrate. I argued in a post a couple of years ago that part reason for the birthrate deline in these societies was that the conservative norms in these countries no longer matched the reality of modern life, making marriage and child rearing too expensive (in a broad sense) for more and more people. Of course, I was pretty much talking out of my hat, like bloggers are wont to do, without any hard data or models to back me up. Dr. Sevilla-Sanz does have a model and data for part of this. As she puts it in the conclusion:
The study of below replacement fertility characteristic of industrialized countries has traditionally overlooked household formation processes. However, cross-country differences in household formation rates are significant. Both, declines in marriage rates and increases in cohabitation rates have followed very different trends across the developed world. In particular, the so-called lowest-low fertility countries, like Italy, Japan or Spain, have experienced a decline in marriage rates that have not been accompanied by increases in cohabitation (and out-of wedlock fertility) rates characteristic of other developed countries. It becomes thus increasingly important to look at household formation processes for the study of fertility.