Presidential vs. Parliamentary systems

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Someone care to explain what a semi-presidential system is?

The President, who is the head of state, appoints the Prime Minister (and can't dismiss him), who is the Head of Government. So the two roles are distributed between the two offices.

[Vega]

What ended up happening is that the Prime Minister was dismissed by the Governor-General (the Australian representative for the Queen) who then appointed the Opposition Leader and Liberal Party Leader Malcolm Fraser as the new Prime Minister. Fraser got the bills passed to fund the government and then there was a double-dissolution where both houses of Parliament were completely dissolved and a new election was held.

It's always nice to see a Governor General or Queen actually break out of the figurehead mode and enact some real power. I guess that obviously made people upset, though.