“There was no one cause of mass incarceration,” Ms. Chettiar said. “Many of these laws passed by the federal government and states were joint contributors.”

Leading on climate change

What Mr. Biden Said

“I said back in 1987, I said we have an existential threat.”

— Hampton, N.H., in May

True.

Mr. Biden was one of the first members of Congress to introduce climate change legislation. In 1986, Mr. Biden introduced the Global Climate Protection Act, which directed the president to create a task force on developing and enforcing a strategy to combat climate change.

While there is no record of him using the exact words “existential threat,” Mr. Biden spoke at length on the Senate floor in January 1987 about the risk of “global warming — a term, though seemingly esoteric, that could, as time passes, come to signify an environmental disaster second only to nuclear war.”

“Global warming, should it occur in accord with the direst predictions, would be a catastrophe of biblical proportions for the entire world,” Mr. Biden said then. “Even though decades away, the most serious consequences of global warming could prove unavoidable unless we act now to prevent them. Our failure to show foresight when the dangers are clearly discernible would be an unforgivable dereliction of duty to our children and all mankind not yet born.”

His bill eventually made its way into foreign relations funding legislation that was signed into law in 1987.

That ‘moderate’ label

What Mr. Biden Said

“I have the most progressive record of anybody running for the — anybody who would run”

— Delaware, in March “I was always labeled one of the most liberal members of the United States Congress.”

— ABC interview, in April

This is exaggerated.

The Biden campaign pointed to scoring from DW-Nominate, an ideological position tracker based on votes and maintained by the University of California at Los Angeles, that shows Mr. Biden as more liberal than 74 percent of members of Congress after being elected to the Senate in 1972.

Among members of his own party, though, Mr. Biden was consistently in the ideological center, according to DW-Nominate. In his last term in the Senate, which ended in 2008, Mr. Biden ranked to the right of fellow 2020 candidates Senator Bernie Sanders of Vermont and to the left of Senator Amy Klobuchar of Minnesota. (The other Democratic senators running for president did not take office until after Mr. Biden left the Senate.)