MaxElide and the Re-binding Problem

It is well-known that ellipsis constructions involving bound variables are sometimes ambiguous. For instance, the sentence uttered by Speaker B in ( 1 ) can be understood either as a statement about John (Speaker B 1, strict identity) or as a statement about Bill alone (Speaker B2, sloppy identity). (Angle brackets are used to mark the elided constituent (BC) and focused material is written in capital letters.)