The sea beast of Revelation 13 entices everyone to worship him “whose name has not been written from the foundation of the world in the book of life of the Lamb” (v. 8). Interpreters commonly take the book of life as an image of election: It is a list of the names of all those chosen for eternal salvation before the world began.
Problem is, the Bible speaks of erasures in the book of life. Jesus promises not to erase the names of those in Sardis who overcome (Revelation 3:5). He doesn’t exactly say that some names will or can be erased, but it’s a natural inference. And Moses is willing to be blotted out of God’s book if it can save idolatrous Israel (Exodus 32:32). In neither case is anyone actually erased, but the implication is that the contents of the book vary. And that means it cannot be a roll of the eternally elect. (It might be said that there are distinct books, but that seems to me special pleading.)
What then? In a graduate seminar, Leta Sundet asked whether it might be a narrative rather than a list, and that suggestion quickly led to the suggestion that the book is a genealogy, a narratively-structured set of names. That makes a great deal of sense. Names can be deleted in biblical genealogies (there is no toledoth for Abraham in Genesis; Dan is missing from the tribal genealogies in Chronicles and Revelation); other names can be entered as they are grafted into the tree of Israel.