Two-party system
Third parties, meaning a party other than one of the two dominant parties, are possible in two-party systems, but they are often unlikely to exert much influence by gaining control of legislatures or by winning elections. While there are occasional opinions in the media expressed about the possibility of third parties emerging in the United States, for example, political insiders such as the 1980 presidential candidate John Anderson think the chances of one appearing in the early twenty-first century is remote. A report in "The Guardian" suggested that American politics has been "stuck in a two-way fight between Republicans and Democrats" since the Civil War, and that third-party runs had little meaningful success.
Green Party of the United States
Gayle McLaughlin was twice elected mayor of Richmond, California, defeating two Democrats in 2006 and then reelected in 2010; and elected to City Council in 2014 after completing her second term as mayor. With a population of over 100,000 people, it was the largest American city with a Green mayor. Fairfax, California; Arcata, California; Sebastopol, California; and New Paltz, New York are the only towns in the United States to have had a Green Party majority in their town councils. Twin Ridges Elementary in Nevada County, California held the first Green Party majority school board in the United States.