Groupthink never holds a vote. Everyone puts in what they want, then options get ruled out by a named person's stated limit. It is not finished until every person signs.
Separate several with commas. Duplicates merge. Who put in what is hidden while everyone votes, so people rule on the option and not on whose it was.
Then one device, passed around once. Nobody sees anyone else's answers, and the screen clears before it reaches the next pair of hands.
Rule on every option on the table. Nobody sees what you pick, and no option says whose it was. Answer honestly, not diplomatically. That is the entire point.
Great is a real yes. Fine means you would live with it. Can't is a hard limit and it kills the option outright, so you have to say why.