@Keith
Thank you Jack & Keith for humoring me while I educate myself and float ideas on voting methods. Let me explain my background. I am working on an open primary ballot initiative in Oregon, and our group is at loggerheads in deciding how run an election. We did agree that since primaries tend to have low turnout, more than two candidates should be advanced to the general election (we settled on Top-4 like Alaska).

We are constrained by the state constitution which says that voters “may vote for one person under the title for each office. Provision may be made by law for the voter’s direct or indirect expression of his first, second or additional choices among the candidates for any office.”

I’m not too worried about the primary election itself. Even plurality voting would likely produce four acceptable candidates. But looking at the popular menu of election methods for a 4-way single-winner election, none of them is appealing. Range and approval voting (and variations thereof) have the same flaw as plurality voting: if voters only pick one candidate, then the candidate who is the most opposed by a majority of voters could end up winning. For that reason I favor methods that ensure some level of majority support for the winner. However ranked-choice voting with instant runoff (RCV/IRV) does not reward a candidate for being nearly everyone’s second choice (proponents rationalize this flaw by claiming it to be a desirable feature). I also don’t like the complexity of RCV/IRV in a time when many voters are being told that elections can’t be trusted.

I came up with the “Vote for 2 then Instant Runoff” method as a way to include voters’ second choices in determining who would reach the runoff, while allowing voters to choose between “friend betrayal” and “later no harm” as a resolution of Arrow’s impossibility theorem. I mentioned this idea to someone promoting a different method, and they suggested that I post it on this forum. I still think it is not a bad way to run an election, but it is a bit awkward formatting it into a ranked-choice ballot.

I then started wondering if there was a way to guarantee majority support without having a runoff. That led me to the “Successive Rank Voting” proposal that I now realize is just a form of Bucklin voting. I’m surprised that Bucklin voting never popped up in any of my internet searches. Evidently it is not good to force voters to choose candidates they don’t like, so I’m abandoning that idea.

However, Bucklin voting does seem like a logical way to count successive ranks, so I now favor combining Bucklin voting with an instant runoff if no candidate achieves a majority. The runoff can be achieved using a ranked choice ballot by distinguishing between approved and non-approved candidates in the rankings. See http://www.classicalmatter.org/Election Science/BAIR Voting.pdf . This admittedly wouldn’t qualify as a “new method”, except perhaps in the details of vote tabulation. But I still appreciate feedback.
That’s my story. Thanks for indulging me in this discussion.
-Robert

@Jack-Waugh I mean that partisan voters will rank their candidate first and the main opposition last. So one (or both?) of the top contenders is likely to be eliminated early.

@Jack-Waugh Coombs has some appeal, but I think it has a similar problem to the coercive Bucklin voting that I considered before: voters will not rank their lower choices honestly.

@SaraWolk Sorry I haven't had time to formulate an answer to your replies, and even this reply will be minimal.
One comment I have is that it IS possible to ensure a majority if all voters express a preference when there is no harm (to more favored candidates) in doing so. The Portland election used plurality voting and allowed write-in candidates, so it was not a true runoff between two candidates. I think RCV/IRV would have produced a majority. In what sense do you mean that IRV does not count every ballot in the runoff?
I would like to know your criticism of the last method I proposed:
http://www.classicalmatter.org/Election Science/BAIR Voting.pdf
It is Bucklin voting for three rounds, and if no candidate has a majority then there is a "true" runoff between the two most approved candidates. By "true" runoff I mean that every voter may express a preference without risk to more favored candidates.
I think your arguments against later-no-harm do not apply if the voter can choose between later-no-harm and no friend betrayal.

@Keith said in Successive Rank Voting:

This is a fair point. Some voters may hate both the STAR finalist and then should have given them both a 0. This is guaranteed to be a minority of voters since the two finalists are the top two utilitarian candidates.

How is that guaranteed to be a minority of voters? If voters bullet vote among four popular candidates you could have a winner with 26% scores of 5 and 74% scores of zero. This is an extreme example, but you could relax the bullet voting quite a bit and still not have a majority winner.
I take your claim seriously that bullet voting might be unlikely. But as I mentioned earlier, I worry about worst-possible scenarios. If an initiative gets on the ballot, it will be attacked by pointing out potential bad outcomes.

@Jack-Waugh The problem with any method without a "later no harm" option is that voters have an incentive to avoid showing any level of support for opposed candidate, even if they don't oppose them all equally.

@Keith said in Successive Rank Voting:

However, what if there are two candidates where 90% of the public view as identical? Deciding based on the preference of the 10% makes sense. STAR voting does prevent the case of the winner being most opposed by a majority. The only way this could happen is if they score the most opposed the same as everybody but their winner. This is why people do not bullet vote. Bullet voting will hurt you. There is no incentive to do this.

You are assuming that if voters oppose two candidates enough to score both of them zero, then they have no preference between them. I don’t think so. I think the incentive to give both candidates a score of zero is that they don’t like either of them. But they still may hate one more than the other. Also, candidates have an incentive to encourage their supporters to bullet vote. The only way to know for sure if there is a preference is to allow a “later-no-harm” option (which voters can leave blank if they truly don’t care). You expressed concern that this would lead to “tyranny of the masses”. That is always a possibility. But the only thing worse than" tyranny of the majority" is "tyranny of a minority". I think a good election method should at least prevent that.

@Jack-Waugh I considered a similar runoff scheme using Borda count as the elimination criterion. But it comes back to the question of whether voters approve or disapprove their lower ranks. Voters shouldn't be expected (or required) to rank candidates they don't like unless there is a "later no harm" option. And if ranks are left blank, the winner may not have a majority of votes in the final round.

@Keith
If all you care about is that your favorite wins and you do not care about any compromise then you should bullet vote.

I am glad we agree on that point. The reason I am interested in open primaries is that there is not enough compromise in politics these days.

Majority support is that the candidate who is preferred by the majority of voters wins. It is implied that this is the majority of voters who have a preference.

This is where we disagree. I interpret “majority” as meaning over 50%. The “majority of voters who have a preference” would be a plurality. I worry about the worst-case scenario of the election winner being the most opposed candidate of a majority (>50%) of voters. STAR does not prevent that.

That is not just a bad idea because ranking is bad but because you are forcing people to show FALSE preference.

Unless the candidates are clones, I expect all voters to have some preference, whether they express it on the ballot or not. If they really don't have a preference, then they could randomly rank one candidate above the other without any regret. I see no harm in forcing voters to express a preference between near-equally-supported candidates. Requiring unequal ranks or scores also prevents voters from “voting for more than one candidate”, which is unconstitutional in my state.

@Jack-Waugh As far as I know, there is no case law establishing a precedent for what is acceptable and what isn't. But I wouldn't want to jeopardize an open primary initiative with any method that looks like "voting for more than one candidate". Since ranked choices are specifically allowed, the safe thing to do is to have voters rank choices and treat those choices as discrete ranks.

@Jack-Waugh The mechanics of it look good, but I suspect it is too complicated for the general public. I had to read the instructions very carefully to interpret your example. I worry that even adding an "approval" button to ranked-choice voting might be too complicated.