Interesting case! It does seem to depend on a the perhaps-unusual condition that the game itself punishes the majority of players for being a majority.
But “majority” is an incorrect description of the losing coalition Really “odd” is the right description, which happens to be a majority in some cases, and not others. In the 7-player game, the 4-player majority coalition “wins” and the 3-player minority “loses”.
In the larger game, coalitions which are an integral multiple of m can guarantee a “win”, others cannot.
Interesting case! It does seem to depend on a the perhaps-unusual condition that the game itself punishes the majority of players for being a majority.
But “majority” is an incorrect description of the losing coalition Really “odd” is the right description, which happens to be a majority in some cases, and not others. In the 7-player game, the 4-player majority coalition “wins” and the 3-player minority “loses”.
In the larger game, coalitions which are an integral multiple of m can guarantee a “win”, others cannot.