Accommodating Incomplete Weak Rankings with N Ordinal Scores
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For a rank-order ballot, voters will ordinarily be faced with an N-by-N grid where N is the number of candidates. That can obviously be a lot of information to record if a voter is demanded to indicate a total strict ranking of all of the N candidates, so as @rob and others have mentioned it's a good idea to try to accommodate incomplete rankings.
Incomplete rankings are no issue if Condorcet methods or certain other voting systems are used, but certain modifications have nice properties (in my opinion) when a ranking/score spectrum of all the candidates is somehow constructed. For example, considering positional dominance can help to make Condorcet methods responsive to broad supermajorities rather than slim majorities, which can moderate compromise rather than enabling divisive majoritarian candidates to win without reasonable concessions to the minority whenever possible. (I am thinking of a consensual quasi-Condorcet method that I think seems to do surprisingly good things.)
This kind of modification would still be possible when the same N-by-N grid is used and voters are simply allowed to mark candidates equally and also to leave slots blank, and where no mark to a candidate is by default the lowest score/ranking. This lets voters indicate a complete strict ranking or a weak ranking if they want to. However, wiggle room in the ranking process may cause the score spectrum to become an arena for tactics, since the same incomplete ranking can be indicated by many distinct ballots that may have different effects on the score spectrum and therefore on the election under such a modification.
Otherwise, inference rules for completions of incomplete rankings can be instated, but that increases the complexity of the method and probably won't ever be more than a hypothetical prospect, even if the inference rules are sensible and beneficial to voters.
I don't know if the "strategic noise" really matters very much if the incentives are such that bullet voting, burial and strategic nomination are ineffective, but it is sort of intellectually bothersome. This is a similar issue as with the potential for bullet voting or min-maxing in cardinal Condorcet, which doesn't seem to be all that bothersome to folks. Then again, the Condorcet method is majoritarian, and that's what I'm trying to find a way to escape. What do you guys think?
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@cfrank said in Accommodating Incomplete Weak Rankings with N Ordinal Scores:
Then again, the Condorcet method is majoritarian, and that's what I'm trying to find a way to escape. What do you guys think?
I think you should not try to escape majoritarianism when designing a single-winner election method
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@andy-dienes thatās sort of counterproductive, and I wholeheartedly disagree. Majoritarianism is a significant factor influencing the formation of a small number of large combative political parties, which is also the main cause of political deadlock. Congress operates on supermajorities and double majorities, and when representatives are split down the middle thereās not much chance for anything significant to happen in terms of public policy thatās beneficial to the electorate. Instead the representatives get to point their fingers.
I think the whole concept that majority rule is inevitable and possibly even a good thing is hugely misguided. Historically it has pretty much always been viewed with contempt by intellectuals, like John Stuart Mill, Alexander Hamilton, Tocqueville and Plato, and I think for very good reason. Majorities are good at some specific things, like guessing the weight of a cow, but consensual government isnāt one of those things.
The only significant historical supporters of majoritarianism I can think of are demagogues and borderline demagogues, hence the term. The rationale is usually just a dogmatic assertion that anything other than majority rule is āundemocratic.ā While majoritarianism may help voting systems themselves achieve a degree of rigidity and stability in the sense that tactical voting is prevented from being inadmissibly effective, majoritarian governments are much less stable and less effective than broad consensual supermajority governments. If a bill gets rushed to the finish line one year, four years later itās rushed to the shredder.
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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Regarding whether or not systems should or should not "escape being majoritarian,"
@cfrank said:thatās sort of counterproductive, and I wholeheartedly disagree.
Forgive me if you've answered this before, but I still don't understand what you mean by majoritarian in this context.
As I see it here, https://en.wikipedia.org/wiki/Majoritarianism, they seem to say it is a two party government (not a voting system per se, but a government structure), where votes come down to approving one side or the other, and -- being only two choices -- the majority is elected.
While I agree that any election system should choose the majority when there are only two choices (and I think all of us agree on that, right?), I am very much against that sort of "binary choice" situation. So based on my understanding of that article, I am a as hard-core anti-majoritarian as they come.
But you refer to typical Condorcet compliant systems as being too majoritarian for your taste, and I don't understand that. To me they seem to be the polar opposite of that sort of majoritarian. They should encourage centrists to run, and should tend to elect them (if they are otherwise liked). They should not be subject to Duverger's law, so a de facto two-party system is not imposed by the voting system. So, while Condorcet pairwise logic does tend to have lots of separate majorities happening within it, its final result usually should be a candidate that is not on one side or the other, and therefore not divisive.
Here is my vote simulator which uses 2d "ideological space" to determine how much each voter likes each candidate.... while it doesn't do any Condorcet methods, it shows how other methods tend toward the Condorcet winner if the voters are somewhat strategic and informed. (orange voters are more informed than blue voters) Only choose-one picks a non-centrist candidate, the others elect a candidate very near the median. Regardless, none of these (other than choose-one) really have anything to do with "majority," at least not in the "greater than 50% sense)
So what makes a Condorcet-compliant method majoritarian to you? If I understood this, I'd probably have a much better understanding of your proposals.
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@rob the majority criterion is what makes a Condorcet method majoritarian. A slim divisive majority can force their candidate to win the election despite them being ranked last by everybody else. I donāt like that at all, and thatās what makes me have less confidence in the Condorcet criterion in general. I think that in many cases the Condorcet winner can be a more broadly consensual and centrist option, but I donāt know why not try to find the broadly consensual and centrist option more directly rather than take the Condorcet winner as a proxy, especially when we can see instances that the Condorcet winner is not the intuitive winner just by considering what it would mean for a divided population to come to a reasonable compromise between majority and minority.
My thinking is also that the majority criterion and majoritarianism in general can give groups the incentive to forego local interests in order to conglomerate into larger groups to secure political power. It might not happen as quickly as with something like choose-one, but Iām not confident that it solves that problem. At the same time this is a philosophical problem for me and I want to understand how it can possibly be solved, not just for state and national elections but for collective decision procedures in general. There are other systemic issues like barriers to entry, information disparities, corruption and media that I think can make the diagram you shared less applicable to real world situations. I may be wrong, but in any case I would rather have the majority compromise with the minority, even and especially when the members of the majority are strategically blocked together.
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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@cfrank said in Accommodating Incomplete Weak Rankings with N Ordinal Scores:
A slim divisive majority can force their candidate to win the election despite them being ranked last by everybody else.
especially when we can see instances that the Condorcet winner is not the intuitive winner
My view on those instances is that they are contrived to make the Condorcet winner seem unintuitive, but that doesn't make them "wrong."
Let me try to explain why I tend to think that, despite them seeming unintuitive, they still produce the "correct" results.
Let's reduce this to a two candidate election, to keep it simple to illustrate a concept. (I'll account for three or more in a bit)
Say the voters' honest opinions of the candidates are as follows (as to whether they absolutely love, love, like, are neutral toward, dislike, or despise them)
51% like Alice and are neutral toward Bob.
49% despise Alice and like Bob.Intuitively, maybe Bob should win. He's got a bit fewer people who like him, but at least he isn't despised by anyone.
But this is problematic because it would have to give more "pull" to Bob's voters. It also is problematic because any system that would elect Bob would, by nature, encourage insincere voting... people will start insincerely saying that they despise Bob and absolutely love Alice (or whatever way the voting system affords for them to express their view), to try to swing it their way. This is pretty easy to see in a two candidate election, of course.
So any majoritarian system (including a Condorcet method) would elect Alice. It would simply ignore the difference between "despise" and "neutral".... only considering whether one candidate was preferred to the other, and disregarding "by how much."
My position is that that is exactly how it should behave.
I think most of the examples with more than 2 candidates that are designed to seem unintuitive are basically extensions of this. Condorcet systems ignore "strength of preference", because as soon as you try to include that, you introduce other problems, such as vote splitting, strategic voting incentives, strategic nomination incentives, and the fact that voters that have more extreme positions "move the needle" further in their preferred direction, compared with those with more moderate positions.
My thinking is also that the majority criterion and majoritarianism in general can give groups the incentive to forego local interests in order to conglomerate into larger groups to secure political power
I would expect the opposite with regard to majority criterion. (I can't say for "majoritarianism in general" since its not clear how that is defined beyond majority criterion) Majority criterion seems necessary if it is going to be (mostly) immune to the effects of irrelevant alternatives / vote splitting / strategy / etc. The more immune to those things, the less incentive to conglomerate.
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@rob I think I mostly agree with almost everything you said, except for that the examples are contrived. I tend to think that trying to including degrees of preference is usually too problematic for tactical voting and that even if āhonest degrees of preference,ā whatever that means, were somehow real and plotted statistically for voters with a given rank-order preference, they would sort of average out and resemble the ranking in some sense anyway, just because I think probably individual people on the whole arenāt really all that special or different from each other in terms of how they experience their preferences.
But I want to ask, putting aside the idea that the examples are contrived, letās say that the sort of ballot activity Iām describing actually occurred in a real election. Without quoting the majority criterion or the Condorcet criterion, but just intuitively, what do you think of the election results?
Continuing on, if what you are saying about the Condorcet winner being a moderate and generally non-divisive candidate is true, then the modifications I am suggesting will almost always elect the Condorcet winner anyway. You can look at that and think, āwhy complicate things then?ā and I understand that point of view. But again, if thatās true, then the kind of modification I am suggesting in terms of finding higher order Condorcet winners or substitutes would almost always only require a single extra check, as in one of the examples I give that you would perhaps consider to be less contrived. So itās a question of whether itās worth it to try to safeguard against a divisive majoritarian victory. I wager you think even the potential benefits arenāt worth the extra complication, but I personally would rather err on the side of safety and look closer to see if the benefits are significant in any way.
On another point, I would be curious to see if any examples could be contrived to illustrate why the kind of modification I am suggesting might lead to results that are not both intuitive and game-theoretically stable. What do you think of the examples I gave?
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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@cfrank said in Accommodating Incomplete Weak Rankings with N Ordinal Scores:
I am suggesting might lead to results that are not both intuitive and game-theoretically stable.
Any instance where the Condorcet winner is not elected is exactly an instance illustrating game-theoretic instability. A relevant notion here is the core, which is exactly the Condorcet winner when one exists.
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@andy-dienes OK, perhaps, but can you please provide an example, and demonstrate what kind of strategic action would be effective to illustrate your example? Thatās what Iām looking for.
Iāve given examples where the modification I am referring to is resistant to both burial and strategic nomination, and the results of the elections Iāve exemplified are pretty well intuitive to me. Are there any examples Iāve given where the result is somehow ābadā in a sense other than not satisfying the Condorcet criterion? And if so, can you please explain why it is bad, with a concrete description of how a reasonable voting tactic could alter the results significantly?
One convincing example is all I would need to see.
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60: A5, B3, C0
40: A0, B4, C5If A doesn't win then the block of 60 will vote A5, B0, C0 in the next election.
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@andy-dienes this is exactly the problem I am trying to address in this post. The examples Iām talking about having given use strict rank ordering and no degrees of preference. They can be found here: consensual Condorcet
The issue Iām trying to address is to maintain the strict order while still enabling a comparison of the ranking spectra in a reasonable way. My question is about how to accomplish that, not about how to give up trying to accomplish it.
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I think trying to enforce strict rankings as a way to patch a method is a 'code smell' if you have heard that term before. If the method cannot handle equal rankings in a relatively elegant way that should be a signal to you that there may be something more fundamental to fix rather than simply disallowing equal rankings.
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@andy-dienes it isnāt a patch, itās a starting point. Iām trying exactly to allow equal and incomplete rankings and to still follow a reasonable analogue of the kind of procedure described. Thatās the very point of this topic.
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@cfrank Any example where the Condorcet winner exists but is not elected is an example where there is some strategic instability.
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@cfrank said in Accommodating Incomplete Weak Rankings with N Ordinal Scores:
You can look at that and think, āwhy complicate things then?ā and I understand that point of view. But again, if thatās true, then the kind of modification I am suggesting in terms of finding higher order Condorcet winners or substitutes would almost always only require a single extra check, as in one of the examples
Its less a matter of ""why complicate things" and more a matter of avoiding situations where people, following an election, regret voting as they did. When it can be shown that a positive result could have been had for some group of people if they had voted differently, that's bad news. It leads to everything from wanting to repeal the system, to parties eliminating candidates via primaries.
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@andy-dienes in this example there are more scores than there are candidates. The same problems remains though when there are only three scores for three candidates, and I can see why this is a significant issue. With the method I described, no matter what the majority does with strict rankings, the middle candidate will win, even if the ballots are
A>B>C [99%]
C>B>A [1%]Which is absurd. And without strict rankings, the majority can guarantee their top candidateās victory by bullet voting anyway. I donāt like it but it is what it is. I think youāve convinced me.
