First, I think we should use approval voting in the tournament polls. In approval voting, you can like whichever ideas you want, and we play whichever idea receives the most likes. This has several advantages:
If you like multiple ideas and can't choose a favorite, you can vote for all of them.
If you dislike a few ideas, you can vote for all the other ones.
You can still vote for only one idea if you want.
Approval voting tends to elect ideas that most people like, instead of ideas that a large minority is very obsessed with.
In "single-choice" or "plurality" voting, voting for your favorite idea requires taking a vote away from your second-favorite. In approval voting, you can just vote for both of them.
Second, I think tournament hosts should generate only the current round and nothing after that. I don't want players scouting and preparing for a specific sequence of opponents.