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@poppeacock a “Condorcet winner” is a candidate that beats every other candidate in a majoritarian head-to-head match up, also called a “beats all” winner. There can be at most one Condorcet winner in an election; however, there are pathological cases when a Condorcet winner does not exist at all, caused by what are known as Condorcet cycles.

The classic example is three voters using rank ballots over three candidates:

V1: A>B>C
V2: B>C>A
V3: C>A>B

You can see that A>B 2:1, B>C 2:1, but C>A 2:1. So A>B>C>A is a Condorcet cycle, which is a generalized “rock-paper-scissors” situation. Whichever candidate you choose as the winner, there is some majority of the voters who would have preferred a different candidate. That’s the unfortunate thing that happens when a Condorcet winner doesn’t exist…

Regardless, a Condorcet method is any method that guarantees electing the Condorcet winner when one exists. Condorcet methods differ in how they reconcile choosing a winner when the Condorcet winner does not exist, I.e. in effect how they determine which majority group(s) to jilt.

So for example, if Ranked Robin doesn’t specify how it resolves when there is no Condorcet winner, then it’s really a blanket term for Condorcet methods in general. Or maybe it’s a label for a particular curated subset of Condorcet methods.

@poppeacock I see, so the site is using “Ranked Robin” as the umbrella term for any Condorcet method?

@jack-waugh I agree, PR is probably preferable in many ways to alternatives. Still, I think we’re too entrenched in the way our current system works and it may be most effective to start by modifying single-winner systems, specifically transitioning from choose-one plurality to approval plurality.

@poppeacock yes it seems to be a rebranding of Ranked Robin; from your link:

“Carmen won the most match-ups against other candidates, so she is elected the winner.”

I do notice often that these pro- rank-based voting sites almost never address the issues with reconciling the possible nonexistence of a Condorcet winner.

Is the main advantage of Ranked Robin over other Condorcet methods that it is precinct summable?

@jack-waugh it definitely conforms to Frohnmeyer balance, what is Shentrup balance?

Unfortunately it fails participation as any Condorcet method must. I think Condorcet is also incompatible with favorite betrayal, that may need checking.

@sarawolk I can envision a natural progression as: (1) implement straight approval, (2) eventually indicate the shortcomings of approval in guaranteeing election of Smith set candidates, (3) reform to include a ranked primaries to restrict to the Smith set before the final approval vote.

I agree it is not feasible to implement the kind of change needed for the mentioned kind of system all at once.

If approval were established somehow, the (rational, IMO) debate relevant to (2) and (3) would probably be about majoritarianism versus participation and maybe some tactical considerations.

Your point about tie-breaking is fair. For example, why not use Bucklin voting restricted to the Smith set, adjusting ranks to include only those candidates, which is similar to your suggestion. One major reason in that specific case is because it fails independence of clones.

I’m not necessarily just after a simple tie breaker. My concern is with reconciling majority cycles, which can destabilize the system. Something like approval in a second round enables the competing majorities to compromise more directly with full information. Otherwise a true majority may feel jilted by an arbitrary tie breaking rule.

On the technical properties there are no issues here.

On the practical considerations there are a number.

1. It requires explaining the Smith Set
2. It requires explaining Condorcet winners
3. It requires explaining Approval voting.
4. It requires introducing two new voting methods , with two different ballot types, each with different instructions, at the same time.

I recommend having one voting method only. If you want to have a primary and general then use the same good method for both and don't narrow it down too much before the general. That's actually simpler and will get much broader support from stakeholder factions and minor parties who want real choices on the general election ballot.

Condorcet is accurate enough to just skip the primary all together unless there are too many candidates. If you want Condorcet with a simple tiebreaker why not just make the tiebreaker between the finalists (tied candidates) automatic in the event that it's even needed? In the tiebreaker, each voters ballot counts as a vote for their favorite(s) still in the running. If a voter ranked two candidates equally that would count as a vote for both. The finalist with the most votes wins.

The tiebreaker never even has to be explained. It's literally just a built in tiebreaker like a Plurality provision might call for a drawing of lots or a coin toss, but the ballots already have the tiebreaker info they need so it can be done instantly.

Two-stage voting systems seem like a hard sell in the USA. However, I think a two-stage system is an extremely natural way to satisfy principles of majority rule and self governance.

My opinion is that an ideal single-winner system consists of a first round (or primary) of rank-based voting. If there is a Condorcet winner, no second round is needed. This can be decided easily by a run of B2R and checking if the winner is Condorcet.

Otherwise, the Smith set can be computed and made public. Once known, a second round of approval voting can be run over the Smith set.

Does this have any objectionable properties other than requiring two rounds of voting?

@gregw I think Condorcet is great when a Condorcet winner exists, but when one doesn’t exist it’s really troublesome. Ideally, we would have a method to check whether one exists without unearthing the Condorcet cycle that reveals the jilted majority upon the choosing of any winner, but that is essentially impossible.

I think it makes sense to do Condorcet//Approval, in two separate rounds, the approval round restricted to the Smith set. But two round voting outright is a difficult sell in the USA (even though two-round voting is pretty common all over the rest of the world…).

People try to put the two together in a single round vote, but the strategic incentives of casting rank and approval/score indications on the same ballot cause issues.

My personal belief is that this system of two-round voting for single winner elections, I.e. approval conditional on already knowing the Smith set, would be most ideal. I think actually implementing the approval aspect first however is an easier sell than implementing the Condorcet aspect first. I can envision a natural progression as: (1) implement straight approval, (2) eventually indicate the shortcomings of approval in guaranteeing election of Smith set candidates, (3) reform to include a ranked primaries to restrict to the Smith set before the final approval vote.

I feel even having rank/Smith-based primaries makes way more sense than what we have if the subsequent system is approval. There’s no issue with vote splitting in that instance, and it fits at least partially into the political system we already have (although this would also require substantial changes).

@gregw hm I’m just not sure how well-studied this method in particular is, as in, why it needs to be “most wins, fewest losses.” It makes as much intuitive sense as anything else, and it’s Condorcet so that’s fine.

Also it’s obviously susceptible to potentially unfortunate results when the Condorcet winner does not exist (which the above has ignored in their last step of the “how it works” section as “the candidate who beats all the others wins.”)

I still think rank-based methods are going to be much more difficult to gain firm ground on than approval. IRV got some traction but now it’s facing backlash (some rightfully so). Approval on the other hand seems relatively hard to argue against. I think it would yield a more lasting forward step.