My game has many rooms of around 10 people where they compete. It's basically one big guy against the other small 9 people.
However, sometimes the one guy will intentionally 'troll' and make for an unfun game for the other 9 people. These people would like to kick the one guy to replace him with one of the other 9.
If the vote was required to be unanimous (other than the guy being kicked), then him just having one friend in the game would prevent the vote from passing. Likewise, if you did unanimous minus one, then two friends could stop the vote, etc.
There there is the issue with small rooms. If a room has only two or three people, then one guy can trivially kick other people.
Has any research been done for optimal votes required to kick someone from a room depending on how many people are in the room?