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@isocratia yes it is sufficient to serve that function, my question is about whether the second phase is necessary to induce the same functionality. It seems like one could impose an approval threshold to remove undesirable candidates, and then proceed from there with a proportional approval method over the remaining candidates, requiring only a single approval indication. Is there something wrong with this?

I just manually checked mine (the first one) and it's correct. I suspect the second one counts equal preferences as half points for each candidate in the pairwise comparison. I haven't seen that before, but there is a metric that a voting method could use that would be screwed up by doing it: total number of pairwise preferences over all candidates. That would be sum of the entire row of a candidate. Candidates who are ranked equally to other candidates on more ballots would benefit. However, that's an unreliable metric generally and is really only useful for tiebreaking. So basically my conclusion is that both approaches are correct and should give you the same results, at least for Ranked Robin (not including the 3rd degree tiebeaker).

@isocratia yes I understand the definition of the method you described. But what I mean is, what does the second phase and the two-phase-approval ballot introduce that could not be encoded with just the one phase and an ordinary approval ballot?

@isocratia does there need to be more than one phase? Why not have a single phase and remove candidates without sufficient support before a restricted proportional approval?

@sarawolk yes more or less a thought experiment, trying to address some dissonance between the possibility of a Condorcet winner having low support and a support (approval) winner being different from the Condorcet winner even when one exists.

In this case, I mean that a candidate is either supported or not supported by a voter according to the support cutoff of their ballot. I’m using the word “support” rather than “approval,” because I don’t think approval is an appropriate word philosophically (or mathematically). The positive emotional connotation of “approve” is all that bothers me. “Support” seems more emotionally neutral and has a mathematical meaning that aligns well with what is happening in the system, for example, “the support of a distribution.”

https://en.m.wikipedia.org/wiki/Support_(mathematics)

The quantity of support of a candidate is simply the number of voters who formally support that candidate on their ballot.

Here is another attempt at a modification. In sequence, if there is a Condorcet loser, they are eliminated. If there is no Condorcet loser, a candidate with the least quantity of support is eliminated, with ties broken by rank runoff if possible. Repeat until one candidate remains.

Right, at a glance this detail makes the system not viable or practical for scaled or official elections, imo.

Also, there are a number of ways to find the top two candidates, (Borda, Condorcet, IRV, etc..) Quantity of support isn't explicit enough.

Another point is that a given voter's support cut-off (ie. Approval Threshold) is absolutely relative to the other options. It's not a concrete thing.

What is the intention behind the proposal? Just a thought experiment?

@sarawolk I do understand what you mean, the issue being that on a ballot, candidates may not be lined up in order. One could indicate the ranking position at which support begins. Rank order ballots in general are another topic.

I’m not pining for this or any related method, I’m just trying to think of possible “reasonable” ways to combine support and ranking that are distinct from existing methods.

The prospect of combining the two though begs the question of how exactly to do so, and the ones I’ve considered introduce several somewhat complicated tactical dilemmas, so I’m not sure it’s any kind of promising direction.

@psp_andrew-s

2CV now ensures, unlike any other proposed system, that the winner will, under all circumstances, be one who received at least 51% of 1st or 2nd choice votes.

A voters 2nd choice may be as good as their favorite or almost as bad as their last choice. There's no way to know, so ensuring a majority of 1st and 2nd choice votes is meaningless. Also, in any election where you can support multiple candidates there could be multiple majority supported options. The key is to find the one with the most support by looking at strength of support and/or number of voters who prefer them, ideally both.

I think we've already gone in circles about your other responses in previous conversations so I won't repeat that again here.

@cfrank How would you propose doing a ranked ballot with a support cutoff? This sounds simple but I'm not visualizing an elegant or simple way to do that.

@paretoman I’m actually not sure I understand precisely what you mean. Could you elaborate more with a small example?