SP Voting: Explanatory Video

rob

@cfrank said in SP Voting: Explanatory Video:

I don’t think a binary view of consent matches up with how consent operates in reality, which is always conditional: if I can’t have this, I would consent to having that instead, and so on.

Ok, fair enough. That sounds like what I'd call a "fair compromise".

Regardless of the semantics, you do emphasize that a lot, and the whole philosophy surrounding it, presumably to contrast it with other systems.

I still want to know why your system accomplishes this better than what I'd call a "median seeking" system (which would tend to elect the median choice if applied to something like voting for thermostat setting), such as one where voters rank or rate the candidates and it chooses the Condorcet winner if it exists (and does something reasonable if not).

However @rob I still don’t know why comment when you have not watched the entire video, and haven’t taken the time to understand how the method operates. The entire video explains in detail how the method operates and why it operates the way it does.

It's 47 minutes long. I tried but got frustrated when it didn't explain where it was going and, well, just all the mixing of philosophy and math. I spent a good twenty minutes trying to find where you just explain what it actually does. Can you point me to that part?

If you don't want my feedback because I didn't invest that much time, ok, but one thing I've learned from doing UI work (etc) is that if someone gets frustrated and gives up when trying to use my stuff, I'd actually want them to explain to me why.

cfrank

@rob I think this system is sort of a “median seeking” system. In fact, if a candidate sits on exactly (or near) the Qth quantile on all of the distributions, their fitness metric will be exactly (or near) Q.

So actually, I would say that this method is a “better than the median” seeking system, since its baseline for evaluating candidates is more or less always with respect to the centers of the distributions, which are by construction indicative of profiles of middling, typical or generic candidates.

rob

@cfrank Ok, well good. What do you mean by "better than the median" though?

To me, median is the ideal, but if yours does something else I am interested in what. I am aware that some think that average is a "more utilitarian" result while median is "more majoritarian," but of course the further it deviates from median, the more it incentivizes exaggeration (as well as giving those on the extremes more power than those nearer the center).

cfrank

@rob the distributions indicate how frequently candidates achieve certain levels of support from any given fraction of the electorate. As a candidate’s profile is “lifted up,” this means that more and more voters are giving that candidate higher and higher scores. The only way a candidate’s profile can raise up across the board is if they receive generally high scores or rankings (relative to the norm) from a very broad majority (again, relative to the norm).

rob

@cfrank Is it fair to say that you, in addition to tending toward median, it additionally rewards candidates for having fewer low votes? Or maybe rewards them for having a smaller standard deviation? Either of those might be described as "aggressively centrist".

However either of those could be implemented fairly straightforwardly (certainly without the "changing the formula based on previous elections" part), but you have something that appears quite complex and presumably have a reason for that.

cfrank

@rob not necessarily, it doesn’t have much at all to do with the standard deviation of their score distribution or rewarding candidates for having fewer low scores in a conditional way. The metric is computed and the highest metric wins.

The metric is just a weighted sum of the candidate’s quantiles in each distribution, and the weights are chosen so that majority power is tempered against broad consensus and vice versa in a logically consistent way. My purpose for this system is to find a middle ground between majoritarianism and “consensualism.” Majoritarianism is easier to establish but more divisive, broad consensus is harder to establish but (obviously) less divisive. I have the intuition that trying to go for some intermediary would lead to better results.

As for the distributions, they are not required to update, that’s just an additional feature that might possibly improve future election results by enabling higher responsiveness to future compromises. The distributions could just be fixed as uniform order statistic distributions or something. I think that’s more arbitrary than data-driven distributions.

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.