Is Ranked-Pairs really the best Condorcet System?
If there is a Condorcet winner in respect of any given election, every Condorcet method will determine this same winner. They’re all as good as each other, at this point.
The different methods differ, however, in how they resolve cases where there is not a Condorcet winner, which is to say when there is no candidate who wins all the pairwise match-ups against the other candidates. In practice these cases are arguably infrequent, but, arguably, still occur, and it is easy to construct such scenarios.
I suggest that once we’re resolved to use a Condorcet method to evaluate our elections the distinction of which particular one to use is of far lesser importance. Though there are fine distinctions among them all, with slightly different mathematical properties, in practical terms it is essential to pick a method that is easily visualized and understood by non-theorists, and straightforward to implement, both in legislation and any attendant technology.
On this basis I discounted “hybrid” solutions such as Condorcet-Hare (Condorcet-IRV), and such, since they typically involve two distinct tallying systems: if a Condorcet winner is found, we’re good with the Condorcet tally, and if not we count and tally again, according to IRV (e.g.). Not a big deal if we’re counting by computer, but I don’t buy-in to the idea of a second, different tally when there are good systems that work well without.
In the end it came down, in my estimation, to Ranked Pairs vs Shultze, and on balance I find that Ranked Pairs is easier to follow, which is why I propose Ranked Pairs at this time. But Ranked Pairs and Shultze will give the same results “most of the time.”
I also engaged an email conversation with Dr. Nicolaus Tideman, Department of Economics, Virginia Polytechnic Institute and State University, the originator of the Ranked-Pairs method and a prominent contributor in the field of voting theory, and I thank him for his patience in conversing with me.
Dr. Tideman suggested that I should consider Minimax, as well. Minimax is mathematically very easy, but while mathematically simple, once we have the Condorcet tally, it is not to me as persuasive nor as clear as Ranked Pairs.
It also (in limited circumstances) fails the “Independence of Clones” criterion, which means that the outcome can be sensitive to the presence of “similar” candidates, though as Dr Tideman advises, based on his experience with patterns of voters rankings in ballots and surveys: “I would give you even money that if we examined half a million five-candidate comparisons based on real elections or surveys with more than 1,000 voters, we would not find a single example where Ranked Pairs produced a different result than Minimax, though I would agree that Ranked Pairs would handle such a case in a more satisfying way. And if you wanted me to take the other side of the bet, you would need to give me odds of at least 10 to 1.”
He advised further that: “If there is no problem with getting voters to accept the complexity of Ranked Pairs, it is the better choice. But if they balk at the complexity, then Minimax may be the best that is attainable.”
All in all, then, I propose Ranked Pairs is the way to go here, and I have worked through the details accordingly. But I would be nevertheless amply content with any other Condorcet method, if it were seen as more likely, and while some of the details would change, such changes would not be exorbitant.