If there is one thing that keeps Barack Obama awake at night between now and polling day, it could be the spectre of Tom Bradley. He was the African-American mayor of Los Angeles who suffered a shock defeat in the 1982 California governor’s race, after opinion polls gave him a commanding lead. Political scientists concluded that voters had told pollsters they would support Bradley (below), only to cast their ballots for his white opponent in the privacy of the polling booth. It became known as the “Bradley effect” and numerous other black politicians have experienced it since reports the Financial Times.

As Mr Obama sits atop an average 6 percentage point lead in national polls and a narrower margin in most key swing states, experts are pondering whether the Bradley effect could strike again this year. “There is going to be some difference between the polls and how people actually vote,” says David Epstein, political scientist at Columbia University. “We just don’t know how much.”

The Bradley effect is attributed to white voters feeling embarrassed to admit they plan to vote against a black candidate. Another factor could be the reluctance of low-income white people to take part in polls, making it hard for pollsters to reach the group that is seen as most susceptible to racial prejudice.

Most pollsters agree that the Bradley effect has diminished over time and argue that it will be offset this year by other factors. For example, young people, who are more likely to vote Democrat, are under-represented in some polls because many are not contactable through landline phones.

Perhaps the biggest uncertainty is whether polls are based on accurate assumptions about turnout. If Mr Obama’s push for participation by black and young voters exceeds expectations, the Bradley effect could be neutralised. But if his mobilisation efforts fall short, polls could be overstating his support. In the primaries, exit polls in 28 states overestimated Mr Obama’s share of the final vote – most notably in New Hampshire.