Companies work fairly hard to place one woman—but only one—in a top management position, according to research by Cristian Desz?, an associate professor at the Robert H. Smith School of Business, and two co-authors. The article found evidence of a "quota" effect: Once a company had appointed one woman to a top-tier job, the chances of a second woman landing an elite position at the same firm drop substantially—by about 50 percent, in fact.

The study's design did not allow a conclusion about whether the quota was the result of conscious discrimination or subconscious thinking. Desz? and his co-authors, David Gaddis Ross and Jose Uribe, of Columbia Business School, looked at the top officers at 1,500 firms from 1991 to 2011. Drawing on data from a Standard and Poor's database, supplemented with other sources, they looked at the top five most highly compensated managers at those companies.

Diversifying top management has become a significant priority for businesses—or, at least, it gets talked about a lot. While women make up nearly half of the workforce, 8.7 percent of top managers were women in 2011, according to the Bureau of Labor Statistics, up a bit from 5.8 percent who held such positions in 2000.

One possibility that the authors explored was that the hiring of one woman would lead to a snowball effect at a given company. "In fact, what we find is exactly the opposite," Desz? says. "Once they had appointed one woman, the men seem to have said, 'We have done our job.'" This may be because the men feel that such an appointment already puts them ahead of most companies (which is true).

Or they may feel that there are diminishing returns to hiring more women: One is enough to attract media attention, represent the company at "diversity" events, and satisfy activists pressuring the company. Or the men may perceive the first, pathbreaking women as off-the-charts exceptional, and subsequent female employees do not measure up, somehow.

In any case, one implication of the study is that such activists interested in promoting the presence of women in executive suites—whether those activists are board members, investors, or non-profit watchdogs—can't move on from a given company after one woman is hired, Dezs? says: "They need to keep up the pressure or even apply more pressure."

The quota effect was especially strong when a woman was hired into a high-paid professional position—say, head of human resources. Those positions hold less power than "line positions," like division heads. In other words, companies that promote a woman into a top professional job were especially unlikely to appoint another female executive.

Desz? and his colleagues used mathematical simulations to study the distribution of top female executives across the companies in their sample. If hiring one women eased the path for others, women should cluster together; if hiring a woman had no effect on future hires, you'd see a random distribution of female executives. But the authors found that the data best reflected a third possibility: Top female executives were isolated, repelling one another.

The authors considered and rejected the possibility of a "queen bee" effect—the idea that the first executive-level women hired would perceive other women as rivals, and work against hiring more. But if that were true, the authors said, the strongest evidence would be seen at those few companies with a female CEO (since a female CEO would have more say over executive appointments than other female executives would). But in fact, companies with female CEO's did slightly better at hiring a second woman than companies with a woman in a different senior position.

The 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.

Explore further New research proves gender bias extraordinarily prevalent in STEM careers

More information: "Is There an Implicit Quota on Women in Top Management? A Large-Sample Statistical Analysis," by Cristian L. Dezső, David Gaddis Ross, and Jose Uribe, is forthcoming in Strategic Management Journal.