Iceland's reputation as a world leader on gender equality has been tarnished by alarming figures for sexual assaults including rape. Iceland's reputation as a world leader on gender equality has been tarnished by alarming figures for sexual assaults including rape. Ms Petursdottir said the "myth" that Iceland's record on gender equality makes it a safe haven for women is a distraction from the steps needed to fight systematic abuse. Her appointment is another point on the Global Gender Gap index for a country regarded as a champion of gender equality. Iceland may be far from perfect, but its politicians have taken gender equality seriously.