SP Voting: Explanatory Video

rob

@cfrank said in SP Voting: Explanatory Video:

Majoritarianism is easier to establish but more divisive

Do you consider Condorcet compliancy to be "majoritarian"? It's lots of little majorities. That is, it doesn't care how much you beat someone by, just that the majority picked you over them.

But I don't consider it even close to divisive, to me it is the opposite.

I do think, though, if you wanted to reward candidates for being even less polarizing than a Condorcet candidate, you could do that in a fairly straightforward way. A simple one would be IRV, but instead of basing the elimination on least first choice votes, base it on most last choice votes. Another would be something like STAR, but in the first round weighting the scores based on having a small standard deviation. Any number of mechanisms could attempt to identify non-divisive candidates and promote them.

Anyway, you continue to use the term consensualism and the way you defined it seems like how I would describe a Condorcet-compliant election. (or one that selects the median preference for thermostat setting or the like)

cfrank

@rob I think we have discussed the thermostat situation before in some detail, I think actually that SP Voting with different temperatures or temperature ranges given as candidates would be superior to the median method, since it would be able in a sense to take into account the direction of desired compromises for the voters in addition to their top choices. Maybe somebody in the office has severe OCD and hates the number 73, and they would be fine with any number on the thermostat other than that one and don’t even want one close by. How could they express their preference and have it taken into account?

I know you are trying to boil down the complexities of voting into a simplified model, but I think it’s worth considering methods that can begin to actually take more nuanced complexities into account.

I think Condorcet methods are decent most of the time but they have issues in my opinion, the main one being that they are majoritarian methods. If there is an election between A, B, C and D, and exactly 51% of voters score candidate A as their top choice, then A wins, independent of whether B is scored as the second choice by 100% of the electorate, and A is scored last by the other 49%. That doesn’t make sense to me, that sounds like a bad thing and definitely is divisive. In contrast I think that SP Voting would very probably arrive at candidate B in this kind of situation, or maybe even C or D depending on their placements in the rankings of the whole electorate, which is significantly less jarring to me.

For example, looking at this:

ABCD [30%]
ABDC [21%]
CBDA [40%]
DBCA [9%]

who do you think is the most reasonable choice, and why? I think B is the most reasonable choice, and that’s because B was ranked at least 2nd by 100% of the electorate, and I would rather have a candidate with broad and strong appeal be elected versus a highly divisive candidate like A.

Basically SP Voting requires majoritarian candidates to achieve a super-majority in order to beat out candidates with broad bases of support, and the level of supermajority needed to beat out a broad-based candidate increases with the size of that candidate’s base.

rob

@cfrank said in SP Voting: Explanatory Video:

That doesn’t make sense to me, that sounds like a bad thing.

I have noticed that seems to be almost everyone's first reaction to it.

But the further you stray from that, the more you incentivize insincere voting and strategic nomination. It is game theoretically stable, and nothing else is.

Same with temperature thing. Sure, there are ways of dealing with special cases like someone hating the number 73 in a real world office. (although when describing the situation in the past, I have often laid out some assumptions such as that everyone prefers a number closest to their preferred value over one further)

But if you are going to handle it with a vote, and you think there is something better than "everyone pick your favorite temperature, and we'll choose the median," .... yeah, not much point taking the discussion further than that.

cfrank

@rob you seem to already have all the answers figured out, so why haven’t you thoroughly convinced all of us yet?

SP Voting is also resistant to tactical voting, and there simply is a superior method to solving your thermostat dilemma than choosing the median, which I have already described. These constitute two counter-examples, one to each of your unsubstantiated claims, which you are free to dismiss without reason if you like.

rob

@cfrank said in SP Voting: Explanatory Video:

so why haven’t you thoroughly convinced all of us yet?

You want me to hypothesize as to why I haven't convinced you specifically? I don't think I want to go there.

But I haven't seen many (if anyone other than you) that disagree on the basic idea that median for numerical vote and Condorcet for discrete candidates is the most stable method in a game theoretical sense. At least, no one who knows a bit of game theory, Nash equilibria and such. Regarding Condorcet, I think this paper does a superb job at making the point: https://hal.inria.fr/tel-03654945/document

Key quote out of its 343 pages:

the search for a voting system of minimal manipulability (in a class of reasonable systems) can be restricted to those which are ordinal and satisfy the Condorcet criterion

If you think that using SP voting for temperature as described is better than median, well, I guess all I can say is I'd be interested in if there is anyone else who is similarly sold on it. (or if they are sold on it for human candidates, for that matter)

I have heard people initially argue against median for temperature, but every last one of them quickly acknowledged that it couldn't be beat, and especially that you can't gain any advantage by insincerely stating your preference under such a vote.

Although I guess all bets are off if we are trying to accommodate people who are allergic to the number 73.

@cfrank I appreciate the concept of Lijphart consensus but I do not think it really applies at this level of detail for the mechanism. I view that meaning of "consensus" as much more abstract, answering the questions

do voters understand and trust the political process
do voters feel like they are able to participate fairly in the political process

I do not think somewhat vague notions like that should be used to decide the exact inner workings of the voting method; instead I would use Lijphart consensus to guide an approach to questions more like "what is the structure of my government" or "which government officials should be publicly elected" or "who gets to vote."

By the way in more generality this kind of statistic can be called an L-estimator where @rob would use the L-estimator on a single point (median) and someone like Warren Smith would probably argue for the (uniform) L-estimator at all points (mean). If I am not mistaken, @cfrank your argument somewhat boils down to the claim that somewhere between the two is better than either extreme. The correspondence is not exact because I think when Rob says "median" he is referring to more like a median in the latent preference space like e.g. a Tukey median, and here Connor I think you are referring to a median as in literally the median score, like Bucklin or Majority Judgement would find.

Nonetheless, personally I think I am in the "median" camp, but viewed that way your claim seems at least not unreasonable. I would still encourage you to try to attach less philosophy to your argument and just treat it like a mechanism design problem. Use the philosophical arguments to decide what you want the mechanism to do, and then just normal math & engineering approachs to design the voting rule to achieve that goal.

Also just very concretely to address the proposed rule at hand: I do not think a rule that does not reduce to majority when there are only two candidates will ever be politically viable (or appropriate). I feel the same way about regular Score as well.

cfrank

@rob you really have quite a habit of engaging in straw man fallacies. But sure, if you would like to illuminate your perspective as to why you have not convinced me specifically, please be my guest.

The reason that median and Condorcet methods are “game theoretically stable” is that they sacrifice consensus building power for simplicity. Being stuck at a suboptimal equilibrium doesn’t make a system good, and Condorcet methods are certainly vulnerable to burial tactics.

Obviously there is nobody else currently “sold” on SP Voting, Rob. Condorcet methods have a good 237 years of publicity on SP Voting.

@cfrank said in SP Voting: Explanatory Video:

you really have quite a habit of engaging in straw man fallacies

OK stay civil please

The reason that median and Condorcet methods are “game theoretically stable” is that they sacrifice consensus building power for simplicity. Being stuck at a suboptimal equilibrium doesn’t make a system good, and Condorcet methods are certainly vulnerable to burial tactics.

No, this is neither true nor is it why they are considered game theoretically stable. There are actual mathematical reasons which can be stated and proven quite formally. It has absolutely nothing to do with "publicity;" probably far less than 0.1% of people have ever even heard the word "Condorcet"

Here are[1] a few[2] published articles[3] to get[4] you started on[5] the topic[6]

cfrank

@andy-dienes I am considering the median in the same sense as Rob, as he and I have discussed this before in some detail. I am talking about the “median candidate,” which in the sense of SP Voting happens to be a candidate who achieves a fitness metric of approximately 1/2. Such a candidate would achieve a typical profile in terms of the distributions chosen for the system, which can be driven by relevant data.

However, I don’t believe I am using an L-estimator for SP Voting.

Also, Arend Lijphart is definitely talking firstly about governments that are responsive to supermajorities rather than slim majorities or pluralities, which is what motivates the balancing principle of SP Voting that majority power should be tempered against broader consensus.

cfrank

@andy-dienes I am aware of the game theoretic and computational complexity literature on voting methods. Publicity in this context is relative to the voting theory community, and I was in no way intimating that publicity has somehow contributed to the fact that Condorcet methods are game theoretically stable. I was saying that Condorcet methods have more support in significant part because they are well-known and well-studied.

If you take a survey of various voting systems, you will notice a triangular spectrum of behavior between (1) game theoretical stability, (2) consensuality in the sense of Lijphart, and (3) computational simplicity. Each of these three properties seems to be somewhat at odds with the other two. In order to be game theoretically stable, systems tend to restrict ballot expressions and reduce the information that can be utilized from the electorate, which reduces the ability to come to a broad and relevant consensus. To build broader consensus, more information from the electorate is necessary, which reduces both stability and simplicity since voters will have more avenues for expression and therefore for tactical voting. Since stability and consensus building are at odds, a system will become more complicated as it attempts to reconcile the two.

@cfrank said in SP Voting: Explanatory Video:

(1) game theoretically stability, (2) consensuality in the sense of Lijphart, and (3) computational simplicity. Each of these three properties seems to be somewhat at odds with the other two.

I think we're unlikely to agree regarding this statement. A rule like Minimax is both strategically stable and extremely simple, and I would certainly "consent" to using Minimax for political elections. Unfortunately I cannot say the same about SP voting.

cfrank

@andy-dienes that is not the meaning of consensualism in the sense of Arend Lijphart. The voting method must be responsive to a broad supermajority. Minimax is still a Condorcet method, which is explicitly majoritarian.

@cfrank Every Condorcet method is responsive to a supermajority. On the other hand SP is not necessarily, depending on the exact weighting parameters you use. So I will admit I do not see the point you are trying to make.

cfrank

@andy-dienes no, Condorcet methods are responsive to a slim majority. That is what it means to be majoritarian. SP Voting with the weighting I proposed, which is a geometric weighting with common ratio 1/2, is by construction responsive to a supermajority whenever possible, and the strength of the supermajority necessary for a divisive candidate to win will increase with the level of broad support available from among other candidates in the election.

@cfrank
From wikipedia:

In this book, Lijphart defines a consociational democracy in terms of four characteristics: (1) "government by grand coalition of the political leaders of all significant segments of the plural society," (2) "the mutual veto", (3) proportionality, and (4) "a high degree of autonomy of each segment to run its own internal affairs."[10]

In contrast to majoritarian democracies, consensus democracies have multiparty systems, parliamentarism with oversized (and therefore inclusive) cabinet coalitions, proportional electoral systems, corporatist (hierarchical) interest group structures, federal structures, bicameralism, rigid constitutions protected by judicial review, and independent central banks. These institutions ensure, firstly, that only a broad supermajority can control policy and, secondly, that once a coalition takes power, its ability to infringe on minority rights is limited.

These definitions are focused around the design of the democratic institutions as a whole, not individual voting rules. Note that even in this definition properties of a consensual democracy are stated in terms of outcomes e.g. a diverse coalition of leaders and proportionality. These are things that can only be achieved by looking at the structural design at a much higher level than a voting algorithm and I again encourage you to stop letting misapplied philosophy have such a heavy hand in what should be a mathematical problem.

Moreover, of of the main tenets of a Lijphart consensual democracy is the protection of minority interests. Even if you want to effect this in the voting rule itself it needs to be defined and proven much more rigorously; there is far too much handwaving for my taste speculating how SP maybe could or should behave.

For an example of what I'm talking about, check out this paper[7] where they define a notion of majority power and veto power for a number of voting rules and then analyze existing rules from that perspective. Unsurprisingly, Condorcet rules have in general a stronger veto power (aka minority protection) than Borda, which, being a positional scoring rule, is probably the most similar method in that paper to SP.

cfrank

@andy-dienes
“These institutions ensure, firstly, that only a broad supermajority can control policy…”
This is the primary purpose of those institutions. This is not possible if representatives themselves are not accountable to broad supermajorities.

SP Voting is very different from Borda scoring, which is a cardinal scoring system, AKA a positional scoring rule with fixed weights assigned to each score, whereas SP Voting is not a positional scoring rule, it is a type of ordinal scoring system, which is different. It isn’t the scores themselves that are being weighted, but the quantiles of the candidate in each scoring category.

I can’t single-handedly construct an entire corpus of mathematical work on SP Voting that is comparable in volume with that of Condorcet methods for obvious reasons, not least of all being that SP Voting is a more complicated method that is more difficult to analyze formally. It has to be, since it attempts to reconcile game theoretic stability with consensualism.

Voting is not just a mathematical problem, it’s primarily a social problem that has significant mathematical aspects. Any hand-waving is based on actually testing the method, which I coded up in Python, in many instances, and observing the results. I’ve also written up a document detailing the reasoning behind the method, but I think the video provides visual diagrams that are easier to conceptualize.

rob

@cfrank said in SP Voting: Explanatory Video:

But sure, if you would like to illuminate your perspective as to why you have not convinced me specifically, please be my guest.

I think I said I didn't want to speculate on that, obviously I don't know the answer. It's probably not appropriate to attempt to psychoanalyze you, even with your invitation.

But since you ask, I will say that engaging with you feels like engaging with someone who has invented an spectacularly complicated energy producing machine, complete with pages of mathematical equations, but studiously avoids any attempts to establish a baseline, such as agreeing that the law of conservation of energy is true.

I'm not so much saying you are wrong, as I am saying you have unrealistic expectations as to how much time people are going to be willing to spend looking at the details of what you are trying to sell, given the lack of a simple abstract or summary.

Obviously there is nobody else currently “sold” on SP Voting, Rob.

Well you asked why I haven't convinced everyone of my own views. I think the core concepts don't need me to convince people, since my views are pretty mainstream. But there will always be iconoclasts.

And you are right that Condorcet methods can be shown to have strategic vulnerabilities, which I would characterize as very subtle, just as almost every real world solution to anything has imperfections. Again, that's why I go to the simplest possible examples (voting for a one dimensional numerical value being my favorite) to demonstrate a point and establish a baseline. Another baseline is a simple two candidate election: as Andy notes yours -- like Score -- doesn't seem to distill down to simply electing the majority winner in that case, while I would argue that majority winner is in all senses the correct choice in a binary election. But if we can't agree on that, I don't see why we should waste time trying to agree on something that takes a 47 minute video to explain how it works.

cfrank

@rob the method is not that complicated, and 47 minutes is not very long. It takes upwards of two hours to explain to a typical student how to apply almost any new concept, which is why that’s how long lectures typically last. You just aren’t willing to invest the effort needed to engage with the idea, nor it seems generally with ideas that don’t come flagged with a guarantee to conform with your own mental picture of how things are for whatever reason required to work.

I’ve also given pretty comprehensible reasons, arguments and examples for my opinions about majority rule even in cases of two candidates. Instead of addressing those arguments, you appeal to the stone. That doesn’t make me an iconoclast. If the situation is so clean cut, you should be able to support your point of view with logic.

How my proposal is akin to a perpetual motion machine is well beyond my powers to recognize. You’re just deciding it’s that way without actually looking at it.

rob

@cfrank said in SP Voting: Explanatory Video:

You just aren’t willing to invest the effort needed to engage with the idea

I've spent a lot more time than most people seem willing to spend.

Yes, 47 minutes is long, in my view. This is not a college class, you aren't my professor, and your video does not come with a single recommendation from anyone else but you.

And it has no straightforward summary, and it mixes philosophy, vaguely defined words (that you seem to assume we all agree on their meanings), and hard math in a way that I personally find quite off-putting and frustrating, to be honest.

You don't have to take my advice, but that's what it is. Make a good, short presentation. If your idea is too complex to present the gist of it in a minute or two, I don't think it has a chance of spreading widely. You seem good at math, and this is where I'd suggest you, well, do the math.

@cfrank said:

you should be able to support your point of view with logic.

I believe I have. I believe @Andy-Dienes has as well, since I agree with the vast bulk of what he's said above but didn't feel the need to repeat much of it. (I don't disagree with anything, but some of it is outside my area of knowledge. I've copied below things that I especially agree with and think are well stated) The fact that my logic doesn't connect with you is not necessarily all on me.

I'm getting a bit tired of your attacks, and your accusations of my being too lazy to watch the entirety of your (yes, long) presentations. I approached this diplomatically after spending a good bit of time with your video, if not all 47 minutes. I only made the "perpetual motion machine inventor" analogy when you challenged me with demanding to know why I haven't convinced you yet.

An aside:

One thing I have advocated for (and am working on building result visualizers for) is using the voting methods we advocate for to vote for our favorite voting methods. I will run this here and in other forums such as EndFPTP and maybe election methods mailing list. We can run the tabulation in any method we want (since the ballot data will of course be public), so it would be great if you run the tabulation under SP and post the results, if you haven't made an online tabulator so others can.

But since you are asking such questions as "why haven't you convinced everyone?" I think you should be willing to have it on the ballot, so you can see how many people you've convinced of the merits of SP. I'll happily link to whatever presentation you want -- if you think a 47 minute video is best, that's your call. Maybe a lot of people will embrace it, maybe not, I'm not going to make a prediction.

(below are Andy's comments from above that I 100% agree with)

These are things that can only be achieved by looking at the structural design at a much higher level than a voting algorithm and I again encourage you to stop letting misapplied philosophy have such a heavy hand in what should be a mathematical problem.

No, this is neither true nor is it why they are considered game theoretically stable. There are actual mathematical reasons which can be stated and proven quite formally.

I do not think somewhat vague notions like that should be used to decide the exact inner workings of the voting method; instead I would use Lijphart consensus to guide an approach to questions more like "what is the structure of my government" or "which government officials should be publicly elected" or "who gets to vote."

I would still encourage you to try to attach less philosophy to your argument and just treat it like a mechanism design problem. Use the philosophical arguments to decide what you want the mechanism to do, and then just normal math & engineering approachs to design the voting rule to achieve that goal.

Also just very concretely to address the proposed rule at hand: I do not think a rule that does not reduce to majority when there are only two candidates will ever be politically viable (or appropriate). I feel the same way about regular Score as well.

cfrank

@rob I have read and responded in turn to all of Andy’s comments, apparently you have chosen to repeat them. This is a forum for investigating voting theory. You are the audience who is most liable to actually take a look and to gauge the merits and demerits of the system. The video is less than 24 hours old, how on Earth can it be reasonable to demand external recommendation?

You can get as tired as you like with my “attacks,” which are almost nothing else but drawing your attention to logical fallacies. The system is perfectly well-defined, and so are the principles I am referencing.

The “philosophy” I am using is called logical reasoning, and it isn’t “misapplied.”

“Use the philosophical arguments to decide what you want the mechanism to do, and then just normal math & engineering approachs to design the voting rule to achieve that goal.”

The irony of what Andy recommends here is that this is exactly what I have already done, and the reason your logic doesn’t connect with me is that you have not actually addressed my arguments.

Here is your most recent appeal to stone:

“But if you are going to handle it with a vote, and you think there is something better than "everyone pick your favorite temperature, and we'll choose the median," .... yeah, not much point taking the discussion further than that.”

And this is why I intimated that you are being dogmatic, despite the fact that there are logical reasons for people to disagree with your stance, among them being the arguments I have already drawn your attention to before.