So now, in the waning days of the campaign, here is the alleged storyline: Those polls that show Barack Obama leading in the race against John McCain for president? Even widening his lead?

Those polls are warped. Among the millions of Americans who are telling pollsters that they could vote for Obama, there are (thousands of? millions of?) closeted racists who will not vote -- who never would vote -- for a black candidate under any circumstances. Their votes could tip the election to McCain.

In politically obsessed circles, this supposed phenomenon is known as the Bradley Effect:

Going into the election for California governor in 1982, polls gave Democratic Los Angeles Mayor Tom Bradley a lead of anywhere from 9 to 22 points over his Republican opponent, state Attorney General George Deukmejian. After the votes were cast and counted on Nov. 2, Bradley had lost by 1.2 percentage points. Bradley, who died in 1998 and was regarded as an honorable public servant and builder of bridges among cultures, was African-American.

The Bradley Effect is also known as the Wilder Effect:

Just days before the Nov. 7, 1989, general election, three polls put Douglas Wilder -- Democrat, African-American -- ahead of Republican Marshall Coleman by 11 points, 9 points and 4 points in the race for governor of Virginia. On Election Day, Wilder won -- by only four-tenths of 1 percent.

The discrepancy between how well Bradley and Wilder seemed to be doing before Election Day and how things actually turned out generally has been attributed to racism: When protected by the secret ballot, voters with hidden or repressed racist attitudes vote for the white guys -- no matter what they might tell pollsters.

The problem with trying to apply the Bradley/Wilder Effect to Obama's candidacy is that it's not 1982 or 1989 or even 1992, when black

Illinois Democrat Carol Moseley Braun won a U.S. Senate seat by a margin of 10 points after three polls close to Election Day showed her up by 20, 17 and 18 points.

It is, rather, 2008, and America has changed. For one thing, there's been a turnover of generations, and racial differences don't seem to carry as much significance -- at least, not as much negative significance -- for younger Americans as they have for some of us of older generations.

Maybe that's because younger generations have grown up in more racially blended schools; have lived and mixed socially with people of other races in the military and at community and four-year colleges; have worked alongside people of many races at their jobs; and have shared public spaces at stores, parks, movies, restaurants, sporting events and much more all over the country with whites, blacks, Asians, Latinos and others.

And in the political realm, although African-Americans still fall short of proportional representation to their numbers in the overall population, there's no longer anything odd or strange or even novel about black elected officials. In 2007, the number of black state legislators in the United States stood at 622, according to updated data from the Joint Center for Political and Economic Studies cited in a recent article on race in the New York Times. Nearly 189 of those officials represented districts that are predominantly white.

That has impact. When whites who might harbor racial prejudices personally experience the governance of black officials, it gives them hard information about performance in office that can displace race-based fears. In his 2007 book "Changing White Attitudes Toward Black Political Leadership," University of California professor Zoltan Hajnal wrote that a certain amount of common sense may be at work.

"As more blacks are elected to leadership positions over the years, " he said, "uncertainty regarding black leadership should decline in American society as a whole, and whites should become increasingly inclined to consider supporting black challengers."

Daniel Hopkins, a post-doctoral research fellow at Harvard, wonders whether there even is such a thing as a Bradley/Wilder Effect. In a research paper published in August, Hopkins looked at data from 139 different races for governor and senator from 1989 to 2006. He found some evidence of a Bradley-like effect in races involving black candidates prior to 1996, nothing after.

But even in the earlier contests, Hopkins found two other persuasive explanations for the discrepancies between pre-election polls and election results: The polls typically overestimated the support for front-runners, and some of the contests emphasized what he calls "racialized issues" such as welfare and crime. That's very different from voters rejecting African-American candidates purely because of their race.

A key Pew Research Center report published in February 2007 came to similar conclusions. Researchers Scott Keeter and Nilanthi Samaranayake tracked pre-election polls and results not only for the Bradley and Wilder contests but also for the April 1983 Chicago election in which Harold Washington just barely became the city's first black mayor; the November 1989 election in which David Dinkins beat Rudy Giuliani, just barely, to become New York's first black mayor; and, more significantly, five U.S. Senate and gubernatorial races in 2006 involving black candidates.

Four of the five black candidates lost their races: Lynn Swann in Pennsylvania; Ken Blackwell in Ohio; Harold Ford Jr., in Tennessee; and Michael Steele in Maryland. Only Deval Patrick, an African-American running for governor of Massachusetts, won his race.

But the point was that the election results turned out pretty much as the pre-election polls indicated. There was no "hidden" anti-black vote.

The Pew report emphasized that this doesn't indicate any particular improvement in polling methods. Rather, it said, "racism may be less of a factor in public judgments about African-American candidates than it was 10 or 20 years ago. . . . No one would deny that race still matters in U.S. politics," the report said. But its findings suggest that "fewer people are making judgments about candidates based solely or even mostly on race itself and that relatively few people are now unwilling to tell pollsters how they honestly feel about particular candidates."

I don't know if Barack Obama or John McCain will be elected the next president of the United States on Tuesday. Nor do I know if the Bradley/Wilder Effect was real.

But to the extent that Americans' feelings about race will affect their votes in 2008, it already is reflected in the polls we've seen. Of the many surprises that Election Day may hold, a hidden racist shift isn't one of them.

Mink is a columnist and the Commentary Page editor for the St. Louis Post-Dispatch.