This past New Year’s Eve, hordes of men from North Africa and the Middle East, many of them Muslim refugees and migrants, set off like predators on the streets of European cities. In Cologne, Salzburg, Zurich and Helsinki untold numbers of women were sexually assaulted, robbed and even raped. “They felt like they were in power and that they could do anything with the women who were out in the street,” one victim in Cologne told the BBC.

Germany’s Federal Criminal Police Office, which is investigating the Cologne attack, said,...