A new Bloomberg report finds that out of the top executives at each of the companies in the S&P 500 index, only 8 percent were women, and that these women at the top ranks of Corporate America earned 18 percent less than men. It sounds like another story about businesses’ struggle to promote and pay women fairly.

But here’s the original headline Bloomberg came up with: “Best-Paid Women in S&P 500 Settle for Less with 18 percent pay gap.” (emphasis added) The first voice introduced in the story is Dawn Lepore, former chief executive at Drugstore.com, saying, “I was always focused on negotiating for my team but never as good at negotiating for myself.”

It’s true that women often don’t bargain hard enough for higher pay, as shown by a number of studies and a terrific book called “Women Don’t Ask” by Linda Babcock and Sara Laschever. The word is out, and solutions (hatched mostly by women) are already in the works, like coaching young women on how to get negotiate better before they enter the workforce.

But consider that women at the very top of the S&P 500 are probably among the best negotiators in the world, given their day jobs. And even if some of them might feel shy sometimes about asking for more money, the idea that their unwillingness to negotiate can account for an 18 percent pay gap flies in the face of study after study showing that gender inequality isn’t the result of women being scared to stand up for themselves. It’s subtle biases that inform how we all -- men and women -- evaluate one another.

Take one famous study about letters of recommendation for medical faculty at a large U.S. medical school in the mid-1990s. The authors of the study found that women candidates were more likely to be complimented for what they call “grindstone adjectives”: words like “hardworking,” “conscientious,” “dependable,” “meticulous,” “diligent,” “dedicated,” “careful.” They were also often praised for being “team players” and “collaborative.” The men, by contrast, were more likely to be described with “standout adjectives,” like “outstanding,” “superb,” or “exceptional.”

It doesn’t take long to see this play out in everyday media coverage and commentary.

Just cast your eyes to the debate over President Obama’s pick for the next Fed chair. Fed vice chairwoman Janet Yellen has been described as someone who “does her homework.” She writes “carefully crafted statements.” And Larry Summers? We haven’t heard much about his work ethic. It’s his “brilliance” that we’re always reminded of.

In the Bloomberg story about the pay gap, even Lepore, the female executive, wonders aloud: “Maybe women are more collaborative.”

There are other examples of how we unconsciously view men and women differently. Other research has shown that when employers evaluate workers for promotions, women tend to be considered on the basis of their performance, while men are often promoted for their potential.

“No one’s intending to be unfair. No one’s intending to be biased at all,” says Virginia Valian, professor of psychology at Hunter College and author of “Why So Slow? The Advancement of Women.” “But in many small ways, it’s as if men have little plus signs next to their names and women have little minus signs.”

And that’s the problem with pinning a sizable pay gap on women not asking for enough. Even if they negotiated perfectly every time, the success of any negotiation depends on a set of parameters. If a woman is subtly docked because the first word that comes to mind to describe her is “collaborative,” rather than “brilliant,” all the negotiation in the world isn’t going to get her paid fairly.

The real solution is targeting what Valian likes to call “cognitive errors”: mistakes that lead us to attach certain traits to men and women without seeing what we’re doing. People tend to do this even more in workplaces where everyone considers themselves more egalitarian.

“Once you sort of learn about how [these biases] work, you tend to be more thoughtful about how you make your own decisions,” says Shelley Corell, a professor of sociology at Stanford. “We’re not being biased because we’re bad people. We’re often biased because we’re in a rush.”

So it’s all well and good to tell women to always negotiate. But a problem this pervasive isn’t going to be solved by women just driving a harder bargain. It’s going to take people at the opposite side of the negotiating table demanding more of themselves, too, examining and testing their own assumptions. Employers who want to promote the best people in their workplaces should not be settling for anything less.