Sexual harassment flourishes in workplaces where men dominate in management and in fields where few women hold the “core” jobs (think law enforcement and tech). Research shows that bringing more women into these roles can solve the problem at its roots. But companies know they can get away with cosmetic fixes instead. They stay out of legal trouble by requiring anti-harassment training and setting up grievance systems. Though training does increase the number of women in management at the organizational level, it can also antagonize likely harassers, making the problem worse at the individual level. And grievance systems often backfire, because harassers retaliate against people who complain. Until more women are in power and can shape workplace culture, it’s up to the men at the top to do that, by taking a strong public stand against harassment, being the first in line for training, and chairing the committees tasked with solving the problem.

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We already know how to reduce sexual harassment at work, and the answer is actually pretty simple: Hire and promote more women. Research suggests that this solution addresses two root causes of harassment.

First, as a raft of studies has shown, harassment flourishes in workplaces where men dominate in management and women have little power. We’ve recently seen this imbalance wreak havoc in the entertainment and media industries, where it’s long been understood that major players like movie producer Harvey Weinstein and former Fox News chief Roger Ailes could easily make or break women’s careers. But this is also happening across the economy, with women in tech and law, saleswomen (particularly in retail), waitresses, hotel maids, and many others. Male-dominated management teams have been found to tolerate, sanction, or even expect sexualized treatment of workers, which can lead to a culture of complicity. People may chuckle over misbehavior rather than calling it out, for example, or they may ostracize harassed women, privately ashamed of not having spoken up. Reducing power differentials can help, not only because women are less likely than men to harass but also because their presence in management can change workplace culture.

Second, harassment flourishes in organizations where few women hold the “core” jobs. Fixing this is about finding power in numbers, not just in authority and hierarchy. Female firefighters, police officers, construction workers, and miners are frequently harassed because they’re outnumbered. So are women in the tech industry, advertising, journalism, and our own field — academia. Again, the answer is to bring more of them into the ranks. In industries and workplaces where women are well represented in the core jobs, harassment is significantly less likely to occur.

If it’s that simple, why aren’t companies putting more women into management roles and core jobs? One reason, ironically, is that women tend to leave workplaces where sexual harassment is common and goes unaddressed; the fight can feel hopeless in an environment where gender bias runs rampant. Another reason is that companies don’t take the steps proven to be effective for hiring and retaining women, such as setting up special college recruitment programs to telegraph that they actually want women in management, or creating formal mentoring programs to make sure everyone who wants a mentor gets one.

Companies have also found that they can stay out of legal trouble by adopting cosmetic fixes, which is much easier than solving the problem of harassment at its roots. Beginning in the 1970s, when U.S. federal courts found on-the-job harassment to constitute sex discrimination, companies created anti-harassment training programs and set up systems to handle internal complaints. Many executives were skeptical that these measures would reduce harassment, but they thought they ought to do something to ward off lawsuits. And in that sense the measures worked. In 1998, to the surprise of many legal experts and social scientists, the Supreme Court found in dual judgments that providing anti-harassment training and grievance systems could shield companies against some types of harassment charges — even though such programs had never been proven effective.

Most companies had anti-harassment training (70%) and grievance procedures (90%) before the Supreme Court spoke in 1998. So, of course, the rulings didn’t solve the problem; the harassment numbers haven’t budged since the first surveys were conducted in the early 1980s. In studies over several decades, using random samples of workers, about 25% of women report having experienced harassment at work. Harassment charges filed with the Equal Employment Opportunity Commission doubled from 1990 to 2000, and they have gradually crept up since. By either measure — survey findings or charges filed — harassment isn’t going away.

The courts are partly to blame for this situation, because they often give employers with these programs a pass. But executives are responsible too. Most have installed training and grievance procedures and called it a day. They’re satisfied as long as the courts are. They don’t bother to ask themselves whether the programs work.

If they did ask, what would they learn? At the organizational level, our latest (unpublished) research shows that anti-harassment training for managers does lead to increases in women in both management and nonmanagement roles. It teaches managers what counts as harassment and what they can do when they see it, which in turn reduces harassment and the high quit rates of women who experience it. But at the individual level, findings are mixed. Though most people who undergo training are better able to define and recognize harassment and to intervene, that’s not true of everyone. Men who score high on a psychological scale for likelihood to harass women come out of training with significantly worse attitudes toward harassment, thinking it is no big deal. The received wisdom is that you have to get the worst offenders in the room for training. But it turns out that can aggravate the problem.

Executives might be excused for not realizing that training can backfire when people with negative attitudes are forced to attend — that’s counterintuitive. But company leaders should know that grievance systems are flawed, because they see firsthand what happens to employees who complain. Among people who file harassment complaints with the EEOC, at least one-third say that after complaining to the company they were demoted, moved to lousy jobs or shifts, fired, raped, or further harassed. Indeed, as several large-scale surveys show, people who file harassment complaints are much more likely to lose their jobs than those who experience similar levels of harassment and say nothing.

Our own analysis backs all this up: We’ve found that companies see significant declines in African American, Latina, and Asian American women in both management and nonmanagement roles after establishing grievance procedures for harassment. Percentages of white women in management go up slightly — perhaps they are better protected from retaliation because, on average, they are in more senior roles. But overall, women who file harassment complaints end up more likely to leave their jobs either involuntarily or of their own accord — and others may follow them when they see complaints badly handled, with the harassers still in their jobs.

So, that brings us back to moving more women into management and core jobs being the best way to reduce harassment. Since this takes considerable time and effort, what can companies do in the meantime, aside from waiting for the indirect positive effects of training (fewer women quitting) to kick in and offset the direct negative effects of training (likely offenders becoming likelier offenders) and grievance procedures (the accused retaliating)?

We need to fix how companies handle complaints so that the people being harassed aren’t the ones who get punished. An EEOC task force (on which one of us, Frank, served) recently recommended providing multiple avenues of redress for those who experience harassment, since grievance systems often fail to resolve complaints. One option is to establish a formal open-door policy that encourages employees to bring concerns to anyone in management. Sometimes the right person can put an end to harassment quietly, without eliciting retribution. It’s hard to imagine this approach reining in the superstar harassers of this world, though, when multiple multimillion-dollar settlements don’t seem to stop them. Confidential electronic systems that allow employees to report harassment, but embargo the report until someone else has complained about the same person — or until they can’t stand it any longer — might expose the misbehavior of serial harassers. But such systems, like open-door policies, put the onus on harassed employees to solve the problem. So it’s critical that leaders start accepting some of the responsibility that the courts have allowed them to brush off for such a long time.

CEOs must take a strong public stand against workplace harassment — and keep repeating that message. They should be first in line for training, and they should chair the committees tasked with solving the problem. The U.S. Armed Forces provide an instructive example. They had long experienced high rates of harassment: Surveys in the 1990s found that 65% to 79% of women were harassed each year. But leaders made a concerted effort to reduce harassment through consistent anti-harassment messages, regular training, formal and informal reporting mechanisms, and systematic investigation and remediation. Where women reported that their commanders supported these measures and modeled respectful behavior, they also reported that they had been harassed less in the last year, that they observed less harassment over several years, and that they were more satisfied with responses to their complaints.

That makes sense. After all, culture is shaped by behavior at the top. As long as men dominate in management, it’ll be up to them to make those changes.