Judge and Livington looked at the relationship between what people think about men working and women taking care of the home - what they call "traditional gender orientation" - and how much they earn at their jobs. The big finding, which has been getting some play in the press, is that women who have traditional views of women in the home make less than more egalitarian women. Men with the traditional view make quite a bit more than egalitarian men do, with the traditional men averaging $34,000 per year, versus $23,000 annually for the egalitarian men.
The researchers believe that someone must be unfairly paying men with traditional views more:
This implies that traditional men are rewarded in the workplace for seeking to preserve the social order, whereas traditional women seeking to do the same are not necessarily penalized.
I think there is a major flaw in the question they asked, and a simpler explanation for the income gaps. The flaw is that they asked about the ideal division of labor between men and women, rather than between husbands and wives. The way the question is framed, however, implies that what they really mean is men and women in a married (or at least cohabiting) household. Neither do they make clear whether there is a difference between the single and married people in their responses - which there should be if the question is implicitly about married people's behavior.
The simpler explanation of their findings, I think, is that men who are husbands and fathers are more likely to think that it is their job to earn more for their families, so they seek industries, jobs, and assignments that maximize what they take home to their families. Men who are not husbands and fathers, or who do not think it is their job to earn more for their families, will not seek higher paying jobs if it means working harder, longer, or further from home. Likewise, women who are wives and mothers are more likely to forgo some earning opportunities in order to spend more time with their families, either breaking up their careers for small-child-related spells or investing less in their careers all along. Either way, married moms acting the way married moms usually do are likely, on average, to be making less than other women.