SP Voting: Explanatory Video

cfrank

This is a system I have proposed numerous times before, but I think it has required a more detailed explanation. This is a somewhat lengthy video (apologies) where I try to make the case for this kind of system. In principle it can be watched on higher speed. If you watch it and consider the arguments I make, I would appreciate your feedback and any suggestions.

Youtube Video

rob

@cfrank I was hoping that in the intro you'd give some hint as to how this, above any other decent system (say STAR or a Condorcet compliant system, whether ranked or cardinal ballot), makes it more consensual. (a word you often use to describe it)

I think of the concept of consent as being a binary, you either give permission or you don't. I'm not clear on how that applies to voting.

You may have seen previously that I like to try to use the simplest example I can imagine first, such as voting on something other than human candidates. I find this is effective so we have a baseline we can agree on before moving to the more complex and messy situation of human candidates that may exist in a vaguely defined multi-dimensional ideological space.

For instance a group of friends voting on which restaurant to go to or which movie to see. Or even better, voting on a numerical value like the temperature to set the thermostat to, or the monthly dues of a club.

Does the word "consensual" apply to those sorts of elections? Do you still see it as a binary, or do you see it as I do, where it is simply a case of some people being more happy than others with the outcome?

With the example of temperature (such as in a office shared by 100 workers but only one thermostat), would your system work effectively for that? Say you nominate a dozen possible temperatures, and vote using SP voting. Would the words you are using to describe it (such as "consensual") still apply?

Finally, I'll admit I didn't watch the whole thing (I mean, 47 minutes..... sorry) but I really did try to find the part where you explain what the method actually does. Like, step by step, how it tabulates the result. I couldn't find that.

I'm not attacking it or anything, I just don't understand what you are trying to do with it, nor how it accomplishes it.

@cfrank I don't mean for this to sound too harsh but I figure you wouldn't have posted this if you did not want honest feedback: I think you are ascribing significantly too much philosophical meaning to scores.

Ultimately a score a voter gives to a candidate is just a number they happened to choose within the rules of the game set before them. (The "game" being the election). I would not go anywhere near as far to say that score represents something as meaningful as "consent." I mean, just consider the case where there are only two viable and popular candidates but you (personally) hate both of them. I would fully expect a voter to grit their teeth and strategically score one of them highly, but this hardly means they "consent" to that candidate in the way I suspect you mean it.

That being said you touch on some useful ideas here. You bring up the topic of positional dominance around the 11:24 mark and this is something people study in the topic of generalized scoring rules, and there is also sort of a one-off paper I found once on a certain kind of generalized Condorcet winner according to positional dominance (this paper I think).

Also purely as a matter of engineering, the metric you propose around minute 18 (bucket into quantiles and then take some uniform mean) might likely work well in some senses, and actually if I am understanding correctly it is pretty similar to something @Ted-Stern has been trying to sell me on with "Top Biased Hare Quota" .

However, I think you do not give enough attention to transparency and understandability of a democratic process. If you are doing something very engineering-y e.g. trying to optimize a load balancer and you want to use some kind of voting mechanism to decide where to send your item, possibly you could use a rule like this as some kind of noise-robustness mechanism.

However, as it stands this is incredibly complicated to understand, especially if you are determined to include the part where the parameters are self-updating from one election to the next. And I do not think it is conducive to a political environment where voters feel like they can trust and understand the system and think that it is fair.

cfrank

@rob some of your considerations are valid, and to @Andy-Dienes I generally use the terms consent and preference when referring to ballot indications in a formal and relative sense. In any case 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.

More generally I am using “consensual” in the sense of Arend Lijphart in his “Patterns of Democracy,” where a “consensual democracy” is one that responds primarily to broadly shared public opinion as contrasted with a “majoritarian democracy” which primarily responds to the opinions of a majority.

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.

The purposes of the distributions and the weights used in SP Voting, and the chosen metric, are multifaceted:

It tempers majority power against broad consensus in a logically consistent way;
It treat generic candidates as noise and promotes compromising behavior in the electorate;
It partially disentangles voters from the prisoner’s dilemma of supporting a “lesser of evils” candidate;

In addition, it can be adjusted with a STAR-like modification, and can accommodate rank or score ballots.

All that I am trying to accomplish is to build a very good voting system that addresses the concerns that I have when I consider voting systems that I have already investigated.

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.