Which do you prefer? Elmer loves golf more than I or Elmer loves golf more than me?
It used to be, not so long ago, that than was considered a preposition, and prepositions are followed by object pronouns (me, him, her, us, them). But than can also be considered a conjunction, which would need to be followed by subject pronouns (I, he she, we, they).
Times, they are a-changin’. Today, it’s generally acceptable to follow than by either a subject or an object pronoun, whichever one sounds better to you. This is progress! One problem with using the subject pronoun, however, is that your sentence is likely to be seen as stilted, pompous, or stuffy, somewhat la de dah. What you are saying in the first example in the first line is that Elmer loves golf more than I do. When you add those clarifying words, the stuffiness disappears. If you prefer using the object pronoun, you may have to also add clarifying words: Elmer loves golf more than he loves me.
A side note: Than and then may sound very similar, but they have very different meanings:
Than is used to compare things: more than, less than, taller than, stronger than, closer than….
Then shows relationships in which one thing follows another or results from it: Sam came home from school famished; he then emptied the refrigerator for his afternoon snack.