We crowdsource information on approximately 22,000 train rides undertaken by commuters on Rio de Janeiro's SuperVia to study sexual harassment in the public space and its effects on demand for a women-reserved space. 1) Women in the public space experience harassment approximately once a week, but being randomly tasked to ride in a women-reserved space halves harassment. 2) Demand for and benefits from the reserved space is not uniform across riders-top-tercile users make up 80 percent of the demand and experience half of the harassment. 3) Over half of commuters associate women in the public space with more sexual openness; women who perceive this attitude to be the prevailing norm are more likely to use the reserved space. 4) Perceptions of norms around the reserved space may limit women's agency; policies that directly address harassment and its perpetrators will be important improving women's mobility.