> Just like in the UK where the PM is elected by each democratically elected MP
That's not the case. The PM is appointed by the Monarch, who will almost always choose the leader of the party able to command a majority in the House of Commons. That leader will be chosen according to the rules of their party. Boris Johnson won an election where all eligible members of the Conservative Party had a vote; it is the case that the shortlist of two was decided by MPs.
The PM is also a regular MP and has to be elected by their local constituency voters.
Technically of course, however the monarch is "advised" by the previous prime minster, who by convention tells her the person who can command confidence the house, which is the person who will get 50%+1 of the votes.
If we're being technical the PM does not have to be an elected MP, and can be from the house of lords.
That's not the case. The PM is appointed by the Monarch, who will almost always choose the leader of the party able to command a majority in the House of Commons. That leader will be chosen according to the rules of their party. Boris Johnson won an election where all eligible members of the Conservative Party had a vote; it is the case that the shortlist of two was decided by MPs.
The PM is also a regular MP and has to be elected by their local constituency voters.