The person who is president get 2x the vote in case a vote is tied (abstention is permitted). Also the high honer of being the first to shake hands with foreign presidents when they arrive.
The Federal Council is both head of state and head of government.
Seems to be a pretty good system, the idea is to actually share this between different parties at all times. It always seems strange to me when in countries like the US there is the constant massive power shift back and forth every couple years.
Does Canada not have a Governor General, like other countries where Elizabeth II is the absentee monarch? The Governor General performs most of the functions of the head of state and technically has the power to appoint or dismiss the Prime Minister, but much like the Queen the role is mostly ceremonial.
The Governor General is mostly ceremonial, but is mostly a case of Chesterton's Fence. The Crown is an important safety value for when things are abnormal. For example, the Governor General of Canada in 2008 essentially chose who would be prime minister (See https://en.wikipedia.org/wiki/2008%E2%80%932009_Canadian_par...). The issue that arose was that, during a hung parliament, the opposition announced that they would vote non-confidence in the government at the next opportunity and intended to form a coalition. The prime minister at the time instead went to the Governor General to request prorogation, ending the parliamentary session.
This was a crisis that required judgement by the governor general. The prime minister clearly no longer held the confidence of the House, but not officially. On the other hand, the governor general is constitutionally required to follow the advice of the prime minister. She chose to follow the prime minister and prorogue Parliament for better or for worse. I'm not a legal scholar and I think the Governor General got it right, but having an independent individual make these decisions is a feature, not a bug.
I don't have one in mind, I don't think there's a likely one - there's an argument that it brings a sort of long-term stability that makes an actual application of its powers unnecessary, like a nuclear deterrent - I just think if there was some sort of unrest or rising dictatorial power in a state with ER as monarch 'we' would pay (even) more attention than otherwise?
The Governor-General of Australia has forcibly dissolved Australia's parliament before back in 1975, causing a constitutional crisis: https://en.wikipedia.org/wiki/1975_Australian_constitutional...
But yes, the current monarch strongly adheres to conventions of not exercising her devolved(?) powers.
Though they would typically be hosted by the Queen's representative in Canada, the Governor General (as of yesterday, R.H. Mary Simon). The Queen would never directly exercise her head-of-state powers in Canada. However, the GG does have to make some controversial decisions about choosing governments from time to time.
In the US, head of state and head of gov are the same (the President).
In Russia, the head of state is Putin. He's not officially head of gov, but c'mon, we all know who controls the show there.
In Canada, the Head of State is Queen Elizabeth II. But for all practical purposes, Justin Trudeau holds both rows. It's not like the Queen is handling Canada's foreign policy. She technically has the power to dissolve Canada's parliament, but it would be hard to imagine her exercising this power. When foreign leaders visit Canada, they aren't going to see the Queen, whereas they might if they visit the UK.