Ms. Breed rose up from modest means and has vociferous support among the city’s thinning African-American population. But she also had the backing of a prominent Silicon Valley investor, Ron Conway. Mr. Conway, an adviser to former Mayor Edwin Lee, whose death from a heart attack in December prompted the political scramble to replace him, has been a behind-the-scenes promoter of Ms. Breed’s candidacy. Ms. Breed, who in the lingo of San Francisco liberal politics is described as a moderate, is president of the Board of Supervisors. Holding both that position and being interim mayor gave her unchecked authority and what her ousters said was an unfair power of incumbency. Ms. Breed — who supports legalizing marijuana and recently wrote an op-ed on the need for cities to divest from fossil fuel companies — is considered right of the San Francisco center for her corporate ties and perceived receptiveness to the tech industry.