Former congresswoman Debbie Halvorson (D-Ill.) is trying to do what few before her have accomplished: win a majority-black district as a non-black candidate.

The white one-term member of Congress faces Rep. Jesse L. Jackson Jr. (D-Ill.) in a primary to represent a newly redrawn district that stretches from the South Side of Chicago to rural parts of Will County, which Halvorson represented until last year.

In recent years, only two majority-black congressional districts have been represented by lawmakers who are not black. One is the Memphis-based district currently held by Rep. Stephen I. Cohen (D); the other was a New Orleans-based district briefly held by Rep. Anh “Joseph” Cao (R).

Cao’s district was helped by the legal and ethical problems of his African American opponent, then-Rep. William Jefferson (D-La.), who was under indictment on charges of bribery, money laundering and racketeering during their 2008 race.

Jackson has problems of his own, including allegations of an extramarital affair and an ethics investigation into whether he tried to buy an appointment to the Senate in 2009. The House Ethics Committee has said that it will decide by Friday how to proceed on the latter issue. Those matters appear to have dimmed the political prospects for Jackson, who was once regarded as a potential candidate for the Senate and mayor of Chicago.

Jackson has spent hundreds of thousands of dollars from his campaign fund on legal fees, and the once-outspoken congressman has been significantly less visible in recent months.

The question is whether those problems have done enough damage to push black voters away from him.

A recent independent poll showed Jackson leading early, 35 to 18 percent, but with plenty of his constituents not sold on reelecting him.

Conventional wisdom has it that black voters vote for black candidates almost uniformly. But some say that’s an over-simplification.

“Contrary to what a lot of people think, black voters do tend to be very pragmatic,” said David Bositis, an expert on race and politics and a friend of Jackson’s. “They look to elect somebody who is going to benefit them.”

Still, there have been few non-black elected officials in majority-black areas. Aside from the two mentioned above, Rep. Lindy Boggs (D-La.), who is white, represented New Orleans for 18 years, and Bositis pointed to Maryland Gov. Martin O’Malley’s (D) terms as mayor of majority-black Baltimore.

Illinois Democratic consultant Dan Johnson said that Halvorson is very much an underdog, even though Chicago politics aren’t as racially polarized as elsewhere in the country.

“It’s not unusual for white candidates to run in majority-black districts, but when it’s the top of the ticket, black voters have demonstrated solidarity when it’s a federal race,” Johnson said.

Jackson’s team has deduced that the primary electorate in his new district will be about 66 percent black, meaning Halvorson would need significant black support to win.

Halvorson’s team notes that, although the district is mostly Jackson’s territory, she has also represented most of it between her time in the state Senate and Congress.

“We’re basically back home, and people are thrilled to see us,” Halvorson said.