Ok, I’ll try to provide some clarification from what I know:
-
In modern terminology “Condorcet” is a criterion, not a method, and it can be asked of any kind of electoral system. As @hpy said, it means that if a candidate would win against every other candidate in a one-to-one election (this is called a Condorcet Winner), then he must win the overall election. Any electoral method that respect this criterion can be called a “Condorcet method”. I think everyone would agree this is an essential property for an election system. Therefore, modern methods that do not respect Condorcet are required to argue that the situations where they violate Condorcet are very unlikely to happen in practice.
-
When there is a candidate that would win a one-to-one election against all others, then all Condorcet methods agree on the result. It means it doesn’t matter what method you use in these situations. However, situations may arise where there is no candidate that would win a one-to-one election against all others. Each electoral method that wants to respect the Condorcet criterion must therefore provide a “tie-breaking” rule. That’s where you get the variety of “Condorcet methods”.
-
Ranked choice methods are methods where people rank candidates according to their preference, often with the possibility of saying placing candidates at the same rank. Among ranked choice methods, “instant run-off voting” does not respect the Condorcet criterion. This has always been known. People decided to use it anyway, because it’s simple. Turned out it was a bad idea.
-
Schulze, Minimax-PM and the other methods supported by CIVS all respect the Condorcet criterion. Therefore, they only differ when there is no Condorcet Winner. The way they differ will determine other properties of the election system, such as other criteria and how vulnerable they may be to different types of strategic voting.
-
Minmax-PM, the default method in CIVS, seems to do very well against strategic voting (from reading the paper CIVS refers to). Minmax simply means that in case there is no Condorcet Winner, then we pick the candidate who is closest to become a Condorcet Winner (i.e., whose biggest loss to another candidate is the smallest - in some precise mathematical sense). I think this is quite easy to grasp.
-
(here’s more opinion that knowledge) From what I’ve read, score systems may be more vulnerable to strategic voting than the best ranked systems. They also fail the Condorcet criterion, though their proponents argue this won’t happen in practice. I personally think score systems are needlessly complicated. Ranking is much easier: once we have considered the choices, we know what we prefer almost intuitively. Scores force you to put down to numbers something that has no actual numeric correspondence in your head (or in reality). They thus demand more investment from voters, may demotivate voters who have less time to vote, and may worsen the overall quality of votes.
-
In approval voting you can’t express preference of one choice over the other. So I feel its application is restricted to a few situations where this makes sense. And like for score voting, I feel these systems are less mature and not sufficiently understood.
-
I know it sounds great to say “oh, let’s leave it open and not fix on one method”, but I actually think picking a single method has very important advantages: People get used to it, they eventually come to familiarize themselves, understand it and trust it. This improves both their disposition to vote, the quality of their votes. It increases the proportion of people who actually understand and can check the results. And decreases the energy spent on discussions (see what is going on here) and mistrust from not understanding a method or not understanding why was it picked for a particular task. Picking one single method reduces the “black box” aspect of modern electoral methods. Honestly, they all do pretty much the same thing. I feel it is much wiser for an organization to choose one method and go with it. Again, see the case of Debian.
Well, hope this is useful =) cheers!
.~´