A new poll by The Hill shows that likely voters are about evenly split between those who believe presidential candidate Herman Cain versus those who believe the four women who have accused Cain of sexual harassment. Women, Democrats and blacks were the most likely to believe Cain's accusers.

Two weeks ago, Politico first reported that two women had accused Cain of sexual harassment while he was head of the National Restaurant Association (NRA) in the 1990s.

Later that week, another woman reported anonymously through a spokesperson that she had also been sexually harassed by Cain while she worked for the NRA. Then last Monday, Sharon Bialek held a press conference accusing Cain of inappropriate sexual conduct after she was fired from the NRA and went to Cain for help finding a new job.

Cain has fiercely denied all the charges, saying, at a press conference last Tuesday, “I have never acted inappropriately with anyone … period. The charges and the accusations, I absolutely reject. They simply did not happen.”

The Hill poll, conducted last Thursday, showed likely voters split on whether they believe Cain or his accusers. Forty percent believe Cain, 39 percent believe Bialek and Cain's other accusers, and 21 percent say they are not sure. A plurality, 47 percent, said that Cain should take a lie detector test, something Cain has said he would be willing to do.

While women, Democrats and blacks were more likely to believe Cain's accusers, men and Republicans were more likely to believe Cain. Forty-six percent of females believed Cain's accusers while forty-eight percent of males believed Cain. Fifty-six percent of Democrats believed Cain's accusers and 54 percent of Republicans believed Cain.

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Blacks were more likely (55 percent) to believe Cain's accusers. Whites were evenly split between those who believed Cain (38 percent) and those who believed Cain's accusers (40 percent). Blacks were, by far (77 percent), the strongest supporters of Cain taking a lie detector test.

When asked, “how serious a problem is sexual harassment in the workplace?” 74 percent of females, and 53 percent of males, answered “very serious” or “somewhat serious.”

The accusations appear to have had an impact on Cain's position in the presidential race. An NBC News/Wall Street Journal poll conducted the week the accusations started showed Cain at 27 percent, tied for the lead with former Massachusetts Governor Mitt Romney. The most recent poll, conducted Tuesday through Thursday by McClatchy/Marist shows Cain at 17 percent.

The Hill poll surveyed 1,000 likely voters and was conducted by Pulse Opinion Research. It has a three percentage points margin of error.