When the interrogative pronoun is the object of the preposition, the correct word choice is "whom." To self-correct, pretend that you're instead using a personal pronoun--would you use "she," which designates the subject of the sentence, or "her," which designates the object?
To make it even simpler, replace the interrogative pronoun with a personal pronoun and pick the version that sounds correct:
- Vote for she? OR
- Vote for her?
If you can remember that "who" is the same as "she" and "whom" is the same as "her," then you'll know that the correct wording is--
Vote for whom?
And yes, there ARE some other grammatical issues with that particular sentence, sigh.