Two Arkansas Supreme Court justices say they will remain on the bench to hear a challenge to a proposed constitutional amendment that would ban same-sex marriages. On Tuesday, the Arkansas Marriage Amendment Committee, which backs the proposal, alleged Justices Robert L. Brown and Anabelle Clinton Imber have potential conflicts of interests. The justices, without explanation, on Thursday said they would not step down from hearing arguments in a lawsuit that seeks to knock the proposal off the November second ballot. Martha Adcock, an attorney for the committee, said she is confident the justices would be impartial. Had the justices stepped down, Governor Mike Huckabee would have named replacements to hear the case. Huckabee backs the amendment.