A recent study out of the University of Maryland revealed that companies that hire one high-level, female executive are about 50 percent less likely to hire another woman for a top-tier position.

The study’s authors, Cristian L. Dezső, David Gaddis Ross, and Jose Uribe, found what they described as a “quota effect” in their analysis of the hiring practices of 1,500 firms from 1991 to 2011. The authors had considered whether hiring one top-level, female executive might create a “snowball effect” where more women are hired to top jobs, but this proved not to be the case.

According to the release announcing the study's findings, “[t]he data suggest that hiring dynamics are different at the very elite ranks of firms than they are lower down. Other studies, for instance, have found that the presence of female middle managers leads to more hiring of women. But at the most rarified, highly paid levels of corporations, male managers may perceive more of a zero-sum environment. And so they protect their turf.”

Women make up roughly half of the work force, yet only 26 Fortune 500 companies have female CEOs, and in 2011, the last year included in the study’s evaluation, only 8.7 percent of top managerial positions were filled by women. Last month, a study found that men named John held more positions running large companies than women did.

Increasing the amount of female executives to more accurately reflect participation rates in the workforce would seem to be the fair thing to do. For those motivated less by a sense of fairness, and more by the bottom line, various studies have proven that women-run companies outperform S&P 500 companies and that having at least three female board members helps improve company performance.

Five-time CEO Margaret Heffernan wrote an article for Fortune in which she explored why only 26 Fortune 500 companies had female CEOs. Heffernan attributes this disparity to the tendency of women and other minority groups to “cover” or try to downplay their differences, as well as a female proclivity for “calculating,” or in other words, avoiding risks and attempting to fit in.

Heffernan writes, “Inclusion must be the goal now: creating workplaces where discussions of anything – family, kids, opera, novels – is comfortable and acceptable, where using flexible working policies doesn’t label you uncommitted and where applying for a job you don’t get at first is seen as a respectable, normal way to articulate ambition.”

Facebook COO and Lean In author Sheryl Sandberg has become in recent years an outspoken advocate for women in the workplace. Through her book, other writing, and appearances, Sandberg has identified a variety tendencies in both women and men that can inhibit female ambition and performance in the workplace. In a February editorial for The New York Times, Sheryl Sandberg and Adam Grant wrote about the trap of “office housework” that ensnares many women.

“This is the sad reality in workplaces around the world: Women help more but benefit less from it,” Sandberg and Grant wrote. “In keeping with deeply held gender stereotypes, we expect men to be ambitious and results-oriented, and women to be nurturing and communal. When a man offers to help, we shower him with praise and rewards. But when a woman helps, we feel less indebted.”

The idea that many women get stuck doing office housework rather than raising their hands for a promotion, whether true or not on an individual level, is emblematic of the ingrained gender stereotypes that Heffernan and Sandberg/Grant address. Confronting these stereotypes is the first step towards eschewing the “quota" mentality uncovered in the University of Maryland study. If companies make more of an effort to hire multiple top level female executives, whether in an active attempt to fight gender inequality or with a savvy eye towards the bottom line, women at the top can focus less on “protecting their turf” and more on helping other deserving women reach the same rung of the ladder.