Quebec & Louisiana have very different systems of government. Quebec is a parliamentary monarchy modelled after the UK (sans upper house); Louisiana is a presidential republic modelled after the US federal government.
The person in the lead right now for Governor of Alaska ran as an Independent, Bill Walker. It is close and it will be weeks for all the mail in votes to be counted so it is nowhere near done.
Why would a party comprising a majority of the whole electorate field more than two candidates in such an open vote, though?
Why one? How can such a party be hurt by “anointing” two reliable candidates? Even if the entire other/non-party opposition unites behind one other candidate, the majority party still sees one of its guys in the final. And without unified opposition, they might knock out all rivals in the first round.
Maybe you are assuming that there are only democrats and republicans around.
There are people who don’t think they fit in, and even in groups large enough to form different parties.
And we have some crazy parties up here and it is starting to worry me. Some of the stuff they say is starting to make sense a little bit.
Getting back to the basic question asked by the OP, the short answer is that in the US, state laws govern the election of federal officials, including federal Senators. There is therefore no uniformity in the election processes from state to state, even for federal Senators.
That basic point is implied in several of the answers already, but I thought I might be helpful to make it explicit.
Isn’t the answer that in the US, the parties don’t field candidates? Any one who wants to run as a Dem or a Pub can do so, and re parties can’t stop a candidate from running?
Theoretically, yes, although party-boss backing for campaigns is usually pretty important. Anywhere there I’m addressing the “back room” scenario, which is not so obviously terrible to me as it is presented.
Here, we always have run-offs. Except we run the run-off at the same time as the first round: you write down your preference for who would win the run off at the same time you cast your primary vote.
It’s not as complicated as I made it sound: you just number the candidates on you ballot paper. But it does require you to be able to count, and it wouldn’t work with your voting machines.
In actual effect, it DOES NOT promote a two-party only system. It has the opposite direction. The guaranteed run-off means that it is safe to vote for a minority party, and if your crazy favorite doesn’t get into the run-off, you still get to vote for your default main-stream party.
We (AUS) have strong two-party system, where the crazy minorities only rarely get into power, but that is because of the way the country works at the Senate/House of Reps level.
I haven’t seen an analysis of the way a decent preferential voting system would work in the USA: you’ve got other disfunctional aspects to your system (districting, omnibus bills), so preferential voting is perhaps not top of the list of the things to fix.