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Herman Cain is showing initial resilience in the face of allegations of sexual impropriety: More than half of potential Republican voters say the controversy is not serious, fewer than a quarter say it makes them less likely to support Cain, and he’s running essentially evenly with Mitt Romney for the Republican presidential nomination.

Yet the controversy does pose risks for Cain. Just under four in 10 Republicans and Republican-leaning independents in this ABC News/Washington Post poll do say the allegations are a serious matter. Half of them say it makes them less apt to support Cain, and Romney leads him for the nomination in this group by nearly 20 points. If views of the seriousness of the issue were to increase, Cain’s support could be at risk.

As things stand, 24 percent of leaned Republicans favor Romney for the nomination and 23 percent support Cain — essentially a dead heat between the two. Rick Perry trails with 13 percent support — less than half his peak in September — and Newt Gingrich has advanced to 12 percent, essentially even with Perry. This marks Gingrich’s first foray out of the single digits.

Cain’s support is up from 16 percent in an ABC/Post poll a month ago. Cain, however had a 7-point advantage over Romney, 30-23 percent, in a Quinnipiac University poll completed Monday night. This survey, done Monday through Thursday, finds a closer contest between them.

There’s plenty of room for movement, marking the potential risks during this crucial decision-making stage of the Republican contest. Among those who have a candidate preference, this poll, produced for ABC by Langer Research Associates, finds that a vast 69 percent of potential Republican voters say there’s at least some chance they could change their minds — and 45 percent say there’s a “good chance” of it. That’s not unheard of; comparable numbers were even higher in a late October 2003 ABC/Post poll on that year’s Democratic presidential contest.

While support for other candidates has moved, Romney’s has remained remarkably stable since summer, neither gaining nor losing substantial ground, with comparatively weak support among self-described “very conservative” Republicans, who’ve shifted among Michele Bachmann, Perry, and most recently Cain.

ALLEGATION – Fifty-five percent of Republicans and Republican-leaning independents say they do not regard the allegation of sexual misconduct as a serious matter. But while 22 percent of Cain’s own supporters call it serious, that jumps to 44 percent among those who aren’t backing Cain. Among Romney’s supporters it’s similar, at 49 percent.

As noted, it makes a difference. Among all leaned Republicans, 69 percent say the controversy surrounding Cain does not make a difference in their vote; 23 percent say it makes them less likely to support him. That “less likely” number, however, shrinks to 3 percent among those who see it as not serious — but swells to 52 percent of those who do see it as a serious matter.

Indeed, among Republicans and Republican-leaning independents who say the matter is not serious, Cain leads Romney by 12 points, 32 percent to 20 percent. Among those who say it is serious, by contrast, Romney leads Cain by an 18-point margin, 31-13 percent.

There was a slight difference in one result, in Cain’s favor, as the week progressed. Monday night, 49 percent saw the issue as not serious, compared with 59 percent in interviews from Tuesday through Thursday.

GROUPS – To some extent, perhaps unsurprisingly, views of the controversy reflect political predispositions. Strong supporters of the Tea Party political movement are among those most likely to support Cain over Romney, at 36 percent to 21 percent; they’re also among those least likely to see the misconduct issue as serious , with 20 percent saying so.

Among moderates, by contrast, the tables are turned — Romney leads Cain by 31-16 percent, and far more, 47 percent, see the allegations against Cain as serious.

Among other groups, about equal numbers of leaned Republican men and women say the matter is not a serious one, at 56 and 54 percent, respectively. Women are more apt to say it makes them less likely to support Cain, 28 percent vs. 18 percent; however his overall support from men and women is essentially identical, 25 and 21 percent, respectively.

HORSE RACE – The number of leaned Republicans who express a willingness to change their minds both explains shifts in the GOP horse race since summer and suggests that more could be in the offing. Bachmann premiered with 16 percent support in July; she’s declined steadily since, down to 4 percent support — a new low, in this survey. Perry stormed onstage with 29 percent support in September; as noted, he’s at 13 percent now. In the same period Cain’s gone from 4 percent to his current 23 percent support.

While his movement has been less dramatic, Gingrich has gone from 6 and 7 percent support to a numerical high, 12 percent, now. Ron Paul’s support has been more or less steady, now 8 percent. Jon Huntsman and Rick Santorum have 1 percent apiece.

Romney’s support ranges from 27 to 32 percent among “somewhat” conservative, moderate and the few liberal leaned Republicans, but drops markedly, to 15 percent, among those who identify themselves as very conservative, a group that accounts for nearly three in 10 potential GOP voters. Cain has double Romney’s support among very conservatives, but his best gain has been among somewhat conservatives, up from 11 percent in early October to 24 percent, rivaling Romney, now. Cain’s support is lower among moderates.

Even among the frontrunners, 71 percent of Romney’s supporters, and 66 percent of Cain’s, say there’s a chance they’ll change their minds and vote for someone else; in both cases a third or more say there’s a good chance of it, at 33 and 39 percent, respectively. That rises among leaned Republicans who currently support any of the other candidates; in this group more than half, 56 percent, say there’s a good chance they’ll change their minds.

METHODOLOGY – This ABC News/Washington Post poll was conducted by telephone Oct. 31-Nov. 3, 2011, among a random national sample of 1,004 adults, including landline and cell-phone-only respondents, and 438 leaned Republicans. Results have a margin of sampling error of 3.5 points for the full sample and 5.5 points for leaned Republicans. The survey was produced for ABC News by Langer Research Associates of New York, N.Y., with sampling, data collection and tabulation by Abt-SRBI of New York, N.Y.