That's not the gerund. That's its identical cousin, the participle. If it were a gerund, then you would use the genitive form "my":
- The likelihood of my doing this is small
In this example, "doing this" is a gerund phrase. "My" modifies the gerund phrase. The modified gerund phrase is the object of the preposition "of".
- The likelihood of me doing this is small
In this example, "doing this" is a participial phrase. Participial phrases can modify nouns. This participial phrase modifies "me". The modified objective personal pronoun is the object of the preposition "of".
Because there's no visible difference between the gerund and the so-called present participle, it almost looks like "me" and "my" are doing the same job. They aren't. The "me" acts as a modified object; the "my" acts as an object modifier. Of course, in both cases you end up with some modified object for the preposition "for". The overall meaning of each is much the same, and the choice between them is often no more than a question of stylistic convention.
If it helps, my personal preference is for the gerund construction. I prefer the action, rather than the person, to be the literal object.