^ i think erik's referring to the gerrymander that means trump got elected with the minority of the vote.
It's not really related to the Westminster system you refer to, because the countries you mention don't have a president, but i imagine all of those places have done all they can to iron out the sort of electoral discrepencies that lead to trump getting elected despite having more than 2 million less votes than his opponent.
I know what he's referring too, and my point stands. This is why I said head of government and not head of state.
The Westminster systems equivalent of head of state has no relevance to the US system, so I'm using the head of government office in the prime minister for the comparison. And in such systems, the party elects the leader, you elect the party (and even that is not by simple popular majority vote either) The leader of the winning party becomes head of government. The US president is head of government. He's also head of state but since it's a single office in then American system that's irrelivent.
But as was my point, that means in practice the people have even less direct involvement in who's head of government than in the American congressional system with the electoral college. At the very least, it's not a popular majority vote as erik said.
Some parliamentary republics have a majority publicly elected head of state in the office of president, but it's a largely symbolic office with little real power. And in all the countries I mentioned they are constitutional parliamentary monarchies where the head of state is arguably either the queen or the Governor General. And in neither case are they elected at all. But even in a republic where they are, it's not an equivalent office and has no say in matters of policy. So comparing how the head of states are elected in those cases is apples and oranges. We're talking about voting for the leader of the country in charge of policy (the head of government). The US president, or the prime minister in parliamentary systems.
And in ALL cases, republic or not, the head of government isn't elected by majority vote in a westminster parliamentary system. And in the constitutional monarchies, neither is the head of state, not that it matters since it's not a job of much functional power generally speaking. Given how many democracies that rules out, I doubt very very much that most countries elect their head of government by popular vote.
I actually largely support the electoral college system, but my point wasn't about the electoral college being a good thing, which is way too frustrating an argument for me to want to be involved with. It was that most other countries are NOT doing a majority public vote as Erik suggested. Which is a matter of fact easily proven or disproven and much less frustrating to debate.
As a dual American-Australian citizen brought up in the US but having spent all my adult life in Australia, I'm quite familiar with both systems.