I am not familiar with the lunar political system, but here in the UK you do not vote for the PM. You vote for your MP. The party with the most elected MPs choses the PM. It is usually the party leader. The current situation follows the protocol to the letter.

The 4 years part sounds a bit iffy but, believe it or not, it is also by the rules. There is no fixed schedule for general elections. The current ruling government decides when the next election is going to be.

This is what you get in a country without a written.constitution