To call the sex abuse scandal in the Catholic Church the elephant in the room ahead of the conclave to choose the next pope is to not do justice to the enormity of the problem the institution still faces, and will likely face for years to come.

Addressing the problem directly, abuse victims and their advocates in four countries so far have begun naming various cardinals they believe should either be removed from papal consideration, or even from the very process to name the next pontiff, due to their actions around the scandal. Some of the names they have singled out are considered front-runners by Vatican observers.

"It is difficult. Who would be a good pope? I don't know," said Becky Ianni, Washington, D.C. and Virginia director for the advocacy group SNAP, Survivors Network of those Abuse by Priests. "It's really hard to say."

SNAP has singled out a "Dirty Dozen" cardinals who are contenders for pope that they consider "to be the worst choices in terms of protecting kids, healing victims, and exposing corruption."

The members of the "Dirty Dozen" cardinals, according to SNAP, are: Oscar Andres Rodriguez Maradiaga (Honduras), Norberto Rivera (Mexico), Marc Ouellet (Canada), Peter Turkson (Ghana), George Pell (Australia), Tarcisio Bertone (Italy), Angelo Scola (Italy), Leonardo Sandri (Argentina), Dominik Duka (Czech Republic), Sean O'Malley (United States), Timothy Dolan (United States), and Donald Wuerl (United States).

Of those, Vatican magazine senior editor and CBS News contributor Delia Gallagher identified Dolan, Maradiga, O'Malley, Ouellet, Sandri, Scola, Turkson, and Carrera as legitimate contenders to be the next pope.

Victims in Mexico also singled out Cardinal Rivera, who is among SNAP's "Dirty Dozen." In a change.org petition, they wrote directly to Rivera, saying "covering up and not acting to prevent sexual abuses of children by pedophile priests strips you of the moral stature required to participate in the election of the new leader of the Catholic Church." So far, they have received nearly 19,000 signatures.

Beyond those who are in contention for becoming pope, many say abuse-tainted cardinals shouldn't even vote in the conclave.

Italian Cardinal Domenico Calcagno is among the many who advocates say should not participate in choosing the next pope. He is singled out for "complete and utter failure to act against pedophile priests... in which he allowed (them) to act like wolves in a flock of sheep," according to a Google translation of the change.org petition calling for him to drop out of the conclave. So far the petition on Calcagno has received nearly 3,000 signatures.

Victims in Chile said recently said Cardinal Francisco Javier Errazuriz failed to act on accusations that they were abused by one of the country's most popular priests, even refusing to meet them in person, reports the Associated Press.

One cardinal long since singled out as someone who shouldn't vote for the next pope is the disgraced former Archbishop of Los Angeles Roger Mahony, who was stripped of all his public duties after thousands of pages of evidence were released as part of a lawsuit against the church showing he participated in a bold cover up of priest sex abuse in his diocese. Victims' groups are outraged that he has not publicly wavered over his determination to participate in the conclave.