Several years ago Elder Howard W. Hunter said:

“Does it seem reasonable that persons who have lived upon the earth and died without the opportunity of baptism should be deprived throughout eternity? Is there anything unreasonable about the living performing the baptisms for the dead? Perhaps the greatest example of vicarious work for the dead is the Master himself. He gave his life as a vicarious atonement, that all who die shall live again and have life everlasting. He did for us what we could not do for ourselves. In a similar way we can perform ordinances for those who did not have the opportunity to do them in lifetime.”

Quoted by Russell M. Nelson,
October 1994 General Conference