There are no artists running for mayor of New York City this year, which makes next week’s election no different from most others. The one held in 1933 was an exception, however, because, as a new biography details, one of the postwar era’s most famous artists took his shot at becoming the city’s leader.

In Barnett Newman: Here, releasing today, art historian Amy Newman—no relation to the artist—briefly charts Barnett Newman’s failed run for mayor on a platform that was confusing at best.

What, exactly, did Newman stand for? You’d be forgiven at the time for not knowing. The man had yet to produce a painting; he was just 28 years old, with few bona fides to speak of. Amy Newman, his biographer, seems equally confused by Newman’s “pie-in-the-sky platform,” as she puts it.

What is clear is that Barnett Newman was running as a candidate opposed to a certain ascendant ideology among the left-wing crowd. He told the New York World-Telegram that he was running “specifically to oppose the possibility that a lot of intellectuals were being roped into Communism.”

Instead, he and his friend Alexander Borodulin, who was running fo...