Player gets booted- a message appears...
"A player has been removed from the game world.
Hold ◾️: re invite player
Hold ✖️: matchmaking"
The remaining players vote for the outcome.
Or, in the case of others, they wouldn't have to worry because they would have opted out of matchmaking completely, right from the beginning.
OPTIONAL matchmaking.
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It could be even simpler. Fire team leader set to public and it matchmakes. Set it to friends only or closed and it doesn't.