Whomever versus whoever?

When do you use whomever and when do you use whoever?

Rule 1. To determine whether to use whoever or whomever, here is the rule:
him + he = whoever
him + him = whomever

Examples: Give it to whoever/whomever asks for it first.

Give it to him. He asks for it first.

Therefore, Give it to whoever asks for it first.

We will hire whoever/whomever you recommend.
We will hire him. You recommend him.
him + him = whomever
We will hire whoever/whomever is most qualified.
We will hire him. He is most qualified.
him + he = whoever

Rule 2. When the entire whoever/whomever clause is the subject of the verb that follows the clause, look inside the clause to determine whether to use whoever or whomever.
Examples: Whoever is elected will serve a four-year term.

Whoever is elected is the subject of will serve.

Whoever is the subject of is.

Whomever you elect will serve a four-year term.

Whomever you elect is the subject of will serve.

Whomever is the object of you elect.

Wow. . . . I just learned something new. . . Hope I can remember that. . . .