Also, I haven't read the paper so don't know how they technically define that criterion, but it doesn't pass it as it's worded in English. Say we have:

35: A>B>Everyone else
33: B>A>Everyone else
32: Everyone else>B>A

Under IRV, B will win this election. That doesn't pass "majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose."

@masiarek I really like a new method that takes some time to understand. It's called a dodgson-hare synthesis
see http://jamesgreenarmytage.com/dodgson.pdf
Abstract: In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists, and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method: a variation on Dodgson’s procedure for use in public elections, which allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve the most persistent cycles. Given plausible (but not unassailable) assumptions about how candidates decide to withdraw in the case of a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations which count how often each rule is vulnerable to coalitional manipulation. In the special case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw.

Maybe it would make sense to regard a canonical preference matrix as having only an upper triangle. However, for software, I think it is convenient to represent it using the whole matrix.

@masiarek it’s common to consider the plurality/choose one algorithm as operating on rank ballots, it just counts the number of first place rankings of each candidate and chooses the candidate with the highest count. The tallies are just those first-place counts. In these cases, since the lower rankings don’t matter for the outcome of the method, the ballots usually serve as indications of true preferences, or in contrast, as examples of tactical voting, usually to mitigate vote splitting.

In this example, you can see that under plurality voting, the two top-right voters would benefit by tactically raising C above B against their actual preference, essentially colluding with the lower four voters. In a sense, B would have spoiled the election for C. This is vote splitting and Duverger’s law in action, and ultimately the reason we have two huge honking awful parties.

It also demonstrates how Condorcet methods are resistant to certain kinds of tactical voting. In the example, C is the Condorcet winner and A is the Condorcet loser. In an election that may fail to elect an existing Condorcet winner, the majority who prefers the Condorcet winner to the alternative has a tactical incentive to collude and form strategic ballots to secure their preference.

Unfortunately this may be a slim or non-existing majority, but the hope is that it’s a broad one.

@jack-waugh It's fairly well known that approval and score voting pass Independence of Irrelevant Alternatives in a technical sense. But if you added/removed candidates, then voters would likely change their score/approval threshold, so in practice they would still fail IIA.

I can't see a proof that it is additive. I can't see a proof that it is Frohnmayer balanced. If a system isn't both of those things, I don't know how to convince myself that it accords equal influence to the voters regardless of how many or few candidates the voters oppose. And without equality, I fear that the monied interests can find a strategy within the system to confine the voters to a Prisoner's Dilemma and thereby prevent them from having any effective power over governmental policy.

Let's say there are 5 candidates and a voter bullet votes for their favourite. According to the m-rule (the "good" way), the points would be 1, 0, 0, 0, 0. According to the n-rule (the "bad" way) it would be 4, 0, 0, 0, 0 (or equivalently 5, 1, 1, 1, 1).

But 1, 0, 0, 0, 0 would also be equivalent to 5, 4, 4, 4, 4, which doesn't really seem that good either and is biased against voters choosing not to rank all candidates (rather than being unbiased as claimed by the article).

I've always thought the most logical way is to average the ranks. So if 5 ranked candidates would get 5, 4, 3, 2, 1, then bullet voting should give 5, 2.5, 2.5, 2.5, 2.5.

@toby-pereira On a ranked ballot you can't show if a 2nd choice is as good as a 1st choice or as bad as a last choice. In practice, ranked methods have to constrain how many candidates can be ranked. There are a few different ways you can look at it, but here's why I think it's the most expressive on the table (excluding cardinal methods with a bigger range)

the ability to vote on every candidate no matter how many there are, The ability to show preference order The ability to show degree of support on a 6 rating scale.

FairVote claims that "RCV" doesn't have a spoiler problem. It most blatantly does.

FairVote claims that your ballot will help your 2nd choice if your 1st choice doesn't win. False, & FairVote knows that.

FairVote says that it isn't known whether Condorcet has a spoiler-problem.

No, actually MinMax(wv), & then Smith//MinMa(wv) were introduced 35 years ago, & their strategy-properties were well studied & well-known at the time. It was known even then, that the wv Condorcet methods, which also include Schuilze & RP(wv) meet Minimal-Defense, & that truncation by only one faction can't take the win from a CW.

Those things have been well known among Condorcetists for 35 years. No, Condorcet(wv) doesn't have a spoiler problem,

But FairVote has a dishonesty problem.

@lime I don’t think any of the points are actually valid except the last one, with the addendum that Democratic representatives are just as likely to stall or derail voting reform efforts, because they also benefit directly from lack of accountability to public interests.

In related news, it looks like ranked pairs satisfies participation when there are at most 3 candidates in the Smith set (where it reduces to Minimax). See here for why 3-candidate Minimax is participation-consistent. This can fail for Minimax, though, because it fails ISDA.

@lime said in "Problematic" Ballot Exhaustion examples - RCV IRV:

Advertisement: a candidate is declared the winner and starts celebrating; then somebody comes up and explains they've found extra votes for the candidate, and the candidate suddenly loses. End with "Last year, Nick Begich lost the Alaska election because voting authorities thought he had too many votes. How could voting for someone make them lose? Don't let it happen here. Vote no on IRV."

New advertisement idea: circle of dictators at a table, bragging about how they took voting rights away from people and laughing. Suddenly, an Alaska politician stands up: "Oh, we did even better. Get this: if too many people vote for a candidate, that guy loses. Pretty great, huh?" Stunned silence. A man in uniform with a thick German accent: "that's too far." "Really?" "Ja, that's illegal in Germany."*

Voiceover: "When even the Germans are calling your system undemocratic, you have a problem. Vote no on IRV."

*Reference to BVerfG ruling on participation failures.

@michaelossipoff said in Ranked Robin Disadvantages -:

River adds a clause to RP, & loses the autodeterence of wv RP & MinMax.

Could you explain more? How does it lose autodeterrence? I was under the impression that River(wv) was effectively minmax with fewer spoilers.

@lime
Thank you for the clarification.

This brings to mind the question I posed in "STLR - Score Than Leveled Runoff might not be too complex for voters"
Does STLR maintain enough the criterion compliance of Score to justify the STLR's extra complexity?

@lime I see, so this would be used in absence of a Condorcet winner like for a ranked pairs resolution?

I was trying to think about burial but I don’t think my method addresses it quite as I conceived. My reasoning was that, by replacing absolute score differences with their more robust percentiles, burial (and bullet voting) strategies will suffer from severely diminishing returns compared with less risky and more honest ballots. For example, burying a second-favorite below a turkey to support a first favorite probably won’t significantly improve the score percentile provided by that voter to the first favorite’s runoff with the second favorite, but will significantly improve the chances of the turkey winning. This makes dishonest burial more severely punished and risky, meaning that fewer rational voters will choose to do it. Also, the effects of the fraction that do will be significantly reduced, since they will not only be fewer in number, but the magnitude of their indicated score differences will be majorly reeled back upon being replaced by their percentiles relative to the more honest bulk.

At the same time, the method is not restricted to Condorcet compliance, since, for example, it is possible for a [1-sqrt(1/2)]~0.2928… fraction minority of voters to overrule a sqrt(1/2)~0.707… fraction majority as long as the whole minority has the top quantile of absolute score differences and all of them have the same sign. That is the smallest possible minority that can overrule a majority in this method. It’s in one sense a generalized, more flexible extension of some of the reasonable measures we already have in the legislative houses, where for example a supermajority (2/3) is required for certain decisions.

Alternatively, each absolute score difference percentile could be measured relative to the distribution of all absolute score differences across all differences. The data set would consist of N*K(K-1)/2 values where N is the number of voters and K is the number of candidates.

@lime you could also have a persistence diagram that shows the support level of each candidate at every possible cutoff. This produces “score proportion” profiles that indicate the fraction of voters who score each candidate at least a given score. It’s possible to define a dynamic threshold or even an integral across all thresholds.

@gregw said in Top-k primaries might be good?:

@lime said in Top-k primaries might be good?:
(regarding SNTV changes)

reserve a spot for the incumbent. Second, assign seats to parties using a rounded-down Hare quota based on party registration—e.g. if 45% of voters are registered Republicans, and there's 5 candidates on the ballot, 2 of the places go to the first- and second-place finishers on Republican ballots.

I am afraid that this would turn voter registration drives into a major industry. Abuses and mistakes could occur. Misunderstandings caused by language barriers could cause noncitizens to be registered by mistake, they would not know what happened but they could be prosecuted.

Perhaps I exaggerate, but people will pay dearly for any electoral advantage.

Also, a lot of people are not aware of which party the are registered with, if any.

BTW The common term for a payment to an person who gathers voter registrations is called a bounty. So if party R is paying $10 per registration from citizens residing in district x, the bounty for those registrations is $10.

There might be a small advantage to running more candidates (one of them might be a slightly stronger candidate than the others), but I'm guessing this is probably a small effect—generally, all the members of a party will do about equally well. There might even be a slight push in the opposite direction, because running more candidates splits funds and volunteer efforts between them. (Besides running the risk of party infighting.)

My guess is parties won't decide to do unethical things for such a small benefit.