Shortly after Charlie Beck announced he will retire as chief of the Los Angeles Police Department, City Councilman Joe Buscaino declared on Twitter that it was time for a woman to take his place.

Others speculated Friday about whether the department should be led by an insider or an outsider, someone who will keep the department on the same path or radically change its course, or someone who reflects the diversity of Los Angeles — perhaps a Latino, or an Asian American.