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Here’s how to select a boardgame using scoring, then instant runoff.
Give everyone a paper list of the games on offer.
Everyone anonymously scores each game from zero to five stars, zero means don’t wanna play today and five means really wanna play today.
It’s OK to mark a bunch of zeroes and just one five, it’s OK to give all kinds of scores, it’s OK to have several fives or several threes or whatever. It works anyway.
Then gather up these ballots. For each game, count up the stars. For the two games with most total stars, look at all the ballots again but now instead of looking at the number of stars, count the amount of ballots where one of the two games has strictly more stars than the other.
For example let’s say Ticket to Ride has 30 stars, Carcassonne has 25, Uno has 24, Caylus has 18, and Dixit has 5. The two finalists are Ticket to Ride and Carcassonne. And then let’s say there are three ballots where Carcassone has more stars than TtR, one ballot where TtR has more stars than Carcassonne, and four where they are tied. Carcassonne won.