Is the Ransom Atonement and Whose Value Sets the Price

"If a ransom is laid upon him" (Exodus 21:30) - and let a man [who himself kills] be liable to ransom by an a fortiori argument: if an ox, which is not liable for four categories [of damages a person must pay an injured party], is nonetheless liable for ransom, then a man, who is liable for the four categories, is it not logical that he should be liable for ransom? [To refute this,] Scripture says, "if a ransom is laid upon him" - upon him [the ox's owner in this case], and not upon a man [who himself kills, who instead is executed]. Our Rabbis taught: "and he shall give the redemption of his life" (Exodus 21:30) - [this means] the monetary value of the victim. Rabbi Ishmael the son of Rabbi Yochanan ben Beroka says: the monetary value of the one who caused the damage. Shall we say they dispute this: that the Rabbis hold the ransom is monetary [compensation], while Rabbi Ishmael holds the ransom is atonement? Rav Pappa said: No, all agree the ransom is atonement, and here is what they dispute: the Rabbis hold we assess by the victim. What is the reason of the Rabbis? "Laying" is said above ["if a ransom is laid upon him"] and "laying" is said below; just as there it refers to the victim, so here it refers to the victim [gezeira shava, a verbal analogy linking the two verses]. And Rabbi Ishmael holds, "the redemption of his life" is written [meaning the life of the one who caused the harm]. And the Rabbis [reply]: yes, "the redemption of his life" is written, but when we assess, we assess by the victim.