When will the Democratic or Republican party nominee for US president receive fewer votes than a candidate not representing one of those parties?

In every US presidential election from 1856 to 1908, the Republican and Democratic parties received the most or second-most popular votes. In 1912 former Republican president Theodore Roosevelt took second place, beating Republican nominee Taft. That feat has not since been repeated. See this image.

Yet about 56% of Americans say the US would be better represented by a third party, according to a September 2022 Gallup poll.