Party discipline is much stronger in parliamentary systems than it is in the US system. If you stand for election for the Blue Party, and get elected, it’s pretty much guaranteed that you will support the Blue leader in the Commons.
So if on election night the Blues win a majority in the Commons, then the leader of the Blues will be the PM. There’s no need for a vote in the Commons. The leaders of the Red Party and the Chess Party will concede on election night, and the leader of the Blues will start forming a government : i.e., will decide which Blue Party MPs will be in Cabinet.
I don’t get that either. That doesn’t happen in Canada. It may be something unique to Australia.
On election night, if the Blues win a majority in the Commons, defeating the Reds, then the leader of the Reds will concede, because he knows he doesn’t have a majority and can’t form a government. The leader of the Blues will put together his cabinet list and the Crown will approve it, formally creating the new government.
If the Blues win a majority in the election, the leaders of the Reds and the Chess Party will concede on election night and the leader of the Blues will form a government, composed solely of Blue MPs.
If no party wins a majority, then it’s deal-making time. Suppose the Blues and the Reds have roughly the same number of seats in the Commons, and the Chess Party came in third.
The Chess Party holds the balance of power and probably right away on election night, the Blue leader and the Red leader will start making overtures to the leader of the Chess Party to see if they can reach a deal.
There are no specific constitutional or legal rules that govern that political deal-making. Both the big parties are trying to get Chess to support them on confidence and budget matters, while Chess is trying to get either of the big parties to implement some of the policies that are most important to the Chess Party.
Sooner or later, one of the two big parties will be able to reach a deal with Chess and will announce it. They may need to win a confidence vote in the House to be able to form the government, or it may be that the other big party will just concede.