New Zealand Prime Minister Jacinda Ardern said on Tuesday that she will refuse to use the name of the shooter who killed 50 people at two mosques in the city of Christchurch last week.

“He sought many things from his act of terror, but one was notoriety,” Ardern said. “And that is why you will never hear me mention his name.” She added, “He is a terrorist, he is a criminal, he is an extremist. But he will, when I speak, be nameless.”

In the past few years, there’s been a growing push for not just leaders like Ardern but the media and the general public as well to do what she’s doing here. The concern: Mass shooters are carrying out these horrific tragedies in part for fame and notoriety. Naming them widely in public discussions and media coverage gives them what they want — and signals to future would-be perpetrators what they can expect in the wake of an attack.

Jaclyn Schildkraut, author of Mass Shootings: Media, Myths, and Realities, summarized the evidence for Vox:

The copycat effect is real. A 2015 study suggests that a mass shooting increases the likelihood of an additional mass shooting in the two-week period following the incident. A more recent study was less supportive of the thesis of short-term contagion but still cautioned that the media coverage of these attacks might well lead to copycat events over a longer period. An ABC News investigation in 2014 found that in the 14 years after Columbine, at least 17 school shooters — and 36 other students who threatened rampages that were averted —directly cited the Columbine shooting or its perpetrators as partial motivation for the attack. In short, making perpetrators famous has consequences.

In New Zealand’s case, the shooter seemed to be especially interested in getting attention, live-streaming parts of the shooting and posting a manifesto espousing white supremacist and Islamophobic views. So if the public, political leaders, and media deny him a platform, he doesn’t get what he wants.

But to do this, more people will need to get on board. Media around the world has widely reported the New Zealand shooter’s name and details from his manifesto, including, in some cases, linking directly to the manifesto itself. Until that changes, there will still be a strong incentive for potential copycats.