I'm a Canadian struggling to understand what voting system would be the best for my country as an alternative to first-past-the-post. STV appears to be better than proportional representation because it produces proportional results similarly to proportional representation while simulating several rounds of votes where the voters who did not vote the first time for an elected representative get to vote again (they therefore don't need to consider what other people are voting when they are voting). Does open-list proportional representation have an advantage over single transferable vote (STV)?
Open list proportional representation is a type of party-list proportional representation. This means that the party gets to choose who appears on the list. And in general candidates must associate themselves with a party to get elected. Votes for a candidate help the party, even if the candidate does not get elected.
Single Transferable Vote (STV) does not require candidates to associate themselves with a party. As such, it allows fusion candidates, where multiple parties endorse the same candidate. And voting for a candidate won't help a party unless the candidate wins.
STV is a ranked form of voting. You vote for a list of candidates. In the basic form, your single vote counts for the first candidate on the list. If that candidate is eliminated your vote transfers to the next candidate (recursively). If the candidate is elected, then a portion of the single vote rolls to the next candidate. The portion is determined by how much over quota the winning candidate is. There are other versions with different ways of handling the rollover and elimination.
There are a variety of open list methods as well. They can range from a system where the party gets to determine which candidates who do not meet quota will fill out the party's proportion to a system where the most popular candidates with voters win. With panachage, each voter receives multiple votes and can vote for multiple lists.
Party-list systems can have simpler ballots than STV systems. They can be as simple as first-past-the-post ballots, where you vote for one candidate per post. Or they can offer more control and be more complicated. STV systems require generating an ordered list of candidates, so each voter makes more decisions and exerts more control over the final winners.
As a general rule, party list systems leave candidates more beholden to parties than STV systems do. This encourages party discipline, where the entire party votes the same way on most issues. Party discipline makes it easier to pass legislative initiatives, as once the party decides the whole party votes the same way. With STV systems, candidates get elected more on their own and have more room to represent their voters. So it really depends what you value more, passing legislation or individual action. Or simplicity versus ability to choose.
Actually, no one is proposing open-list proportional representation for Canada. You may be thinking of the Mixed Member Proportional system with regional open lists, as recommended by the Law Commission of Canada and supported by the New Democratic Party, the Green Party, many Liberals and some Conservatives. It was one of the options researched by the Electoral Reform Committee in 2016, but rejected by Justin Trudeau. One summary of such a model can be found here:
One disadvantage of STV is that all MPs are from multi-member districts, which is fine in the eight largest metropolitan areas, but any area smaller than Winnipeg will find very moderate proportionality (little chance of electing a Green Party MP), and for more than 40% of Canada's population who live in single-MP communities, they will find they have lost their local representation.