Liberal Democracy likely can not work in very ethnically divided countries without some common cultural denominators creating an overarching loyalty. You need to get past the tribal/clan based loyalties and that is next to impossible in some societies. But democracy can be established in other forms than the Western liberal version. A federation of clans or tribes could also be a democracy.
Well, I assume a democratic China would have strong ethnic separatist parties in regions like Xinjiang and Tibet.
I wonder what a Chinese election map would look like?
Poll
