I don't remember seeing "whomever" before, so I hope you don't mind me trying to understand where it is used.

I see that it is used for the object of a verb, and whoever for the subject of a verb, but I am a bit confused here, because here it is the object of "downvote", but the subject of "doubts", so I am confused.

In the sentence "I will look at whomever Bob greets.", I think I understand why it is "whomever", and in the sentence "Whoever enters the room next, they will encounter a surprise.", I think I understand why it is "whoever" and not "whomever", but in the case of your sentence, I don't know what the rule is.

Could you (or anyone else) please explain it to me?