Arthur Bouvier is a deceased member of the Bouvier Family, the family of Marge Simpson.
Arthur's exact relationship within the Bouvier family is unknown, although it is implied he is Marge's brother or uncle. He has only been mentioned on one occasion, by Marge, who told Bart that he used to have a saying, "Shoot 'em all and let God sort 'em out," until one day he put his theory into practice, and it "took 75 federal marshals to bring him down."
Arthur seems to be a source of shame and embarrassment to the family. After Marge finished telling Arthur's story to Bart, she said, "Now let's never speak of him again."