I like both of those, especially the play on telephone! Is the initial mailer the vote counter or are they participating too?
With both games I'm thinking you include your address at the bottom with something like "once it gets to this point mail this back to me" type thing. I'm still playing with that idea, as that could end up giving your address to a lot of people, I need to work it out but it's going to be SOMETHING like that I think. That or you create a custom hashtag on Twitter that everyone who has participated can follow, once they get it they post the tally of the votes on Twitter or Instagram (even though I don't use Insta LOL)