Adding a bit more info:
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Apparently, sometimes gamepads 3 and 4 are both assigned to player/character 2, so character 1 is only controlled by gamepad 1, but character 2 is controlled by the other 3 gamepads.
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After confirming the characters and proceeding to gameplay, the characters spawned in the character selection menu are destroyed, and new ones are created for the players to control during real gameplay. These characters, possessed by player controllers 1 and 2, can also be controlled by gamepads 3 and 4, so the issue persists outside the menu and with new character actors.
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I would say that the last point confirms that several gamepads are being assigned the same id for some reason.