What you're leaving out, in Canada's case, is that the norm is a strict party-line vote. In rare cases, the PM will allow a "conscience vote", where individuals vote as they will; in every other case, you vote as your party directs or you're kicked out of the party. As party-line voting is the norm, sitting as an independent is basically worthless in terms of accomplishing anything--no access to party resources or assignments.
So in practice, the PM of a majority gov't (i.e., has a majority of seats) gets to pass whatever they want to pass; the saving grace of this is that, without having to haggle and herd cats and trade horses, the legislation is the legislation--there's no poison pills, no payoff amendments, no loopholes to capture one person's support, and no extreme bits to trade away. It's just "this is the law we want", which I think leads to higher quality legislation over all.
The PM of a minority gov't (i.e., only has a plurality of seats) may have to secure another party's vote to pass, but that's a negotiation with a second entity, not a hundred other voting entities.
Consensus doesn't play a significant part in it, I believe. Within the bounds of the law, the PM of a majority is nearly a polite dictator.
This all very true but I just wanted to add one more thing I think is a strength of parliaments.
In a parliament majority, the buck stops with the Prime Minister and win or lose his performance is on the line in the next election. There's no (effective) hand-waving about opposition or other excuses to deflect accountability. Elections are a black/white referendum of the incumbent's performance.
In the US it's a lot easier to muddy the waters and a lot harder for people to arrive at a clear conclusion and often nobody is happy.
"YES I don't like X BUT it wasn't Y's fault it was Z"
I agree with this, and I would further add that "confidence votes", where if the vote fails, the gov't falls, are another valuable safety hatch. Budgetary votes are always confidence votes, but anyone can move for a vote of no-confidence if they have the votes. With a majority gov't, this is hard to do unless the majority is slim and a couple people are sick (or "cross the aisle", switching parties), but with minority gov'ts it's a significant risk--the PM can't afford to alienate a large enough number of MPs to falll to a confidence vote, which is literally a ten-minute affair if it occurs. US politics has nothing of this effectiveness.
So in practice, the PM of a majority gov't (i.e., has a majority of seats) gets to pass whatever they want to pass; the saving grace of this is that, without having to haggle and herd cats and trade horses, the legislation is the legislation--there's no poison pills, no payoff amendments, no loopholes to capture one person's support, and no extreme bits to trade away. It's just "this is the law we want", which I think leads to higher quality legislation over all.
The PM of a minority gov't (i.e., only has a plurality of seats) may have to secure another party's vote to pass, but that's a negotiation with a second entity, not a hundred other voting entities.
Consensus doesn't play a significant part in it, I believe. Within the bounds of the law, the PM of a majority is nearly a polite dictator.