CNN

Willie Brown said Tuesday that race may cost Obama 4 or 5 percentage points in certain states.

(CNN) – Former San Francisco Mayor Willie Brown said the so-called Bradley effect could cost Barack Obama several battleground states— and possibly the presidency.

Watch: Willie Brown on the Bradley effect

The political phenomenon that has afflicted some African-American politicians is mostly closely associated with the failed gubernatorial hopes of Tom Bradley, who was mayor of Los Angeles in 1982 when he ran for California’s highest political office. In the 1980s and early 1990s, polls in statewide or other high-profile races in which a white candidate was running against a black candidate typically overestimated the share of the vote that the black candidate ultimately received.

Because this affected black candidates like Tom Bradley in California, Douglas Wilder in Virginia, and David Dinkins in New York City, this has variously been known as the "Bradley effect," the "Wilder effect," or the "Dinkins effect." In the past 15 years or so, there is no indication that this phenomenon has been a factor in statewide races — but no national test, since Obama is the first African-American candidate with a legitimate chance at the White House.

Race “is still a problem in this country,” Brown told American Morning’s John Roberts. “It goes away when there are other troubles that are more challenging and right now, whether or not we survive in the economy is more challenging. But race could rear its ugly head. I just hope it doesn’t before November 4.”

Brown also said there’s “absolutely” a possibility that support for Obama is being overestimated in polls - and that race may cost Obama 4 or 5 percentage points in key states like Ohio, Pennsylvania, North Carolina, and Virginia.