@fathermackenzie since our group has an uneven distribution of game ownership, we bring things to the table and the first person to nominate a diverse set of N games (where N is the quantity of players) as a cohort of games starts the process. Then everyone gets to remove one game (the original selecting person doesn't because they defined the cohort) until you have just one title remaining.

That's effectively the "least bad" choice at the time, because people remove the title they least want to play and the remaining game is not the bottom choice. It also means you have to sort of read the audience for what they might go for (e.g. don't pick 5 train games for a mixed group where a disproportionate number don't like train games). Given enough time, everyone will get to define the cohort once.