Electoral Reform Philosophies Poll

I posted this on r/EndFPTP to gauge where different people’s preferences between 3 opposing goals voting methods for electoral bodies should have:

I considered the traditional 2 axis type of chart between utilitarianism/majoritarianism and other axis’s like simplicity/complexity and geographical/ideological representation, pragmatism/idealism, Thiele/Phrag/Monroe, as well as other axis’s but I found that this triangle between utilitarianism, proportionality, and majoritarianism was the best fit.

Thoughts? Where would you plot yourself on it? Is there a better diagram one could use to summarize the different preferences of electoral reformers in a 2 dimensional matter? If you were to create a quiz to gauge where people fall on this triangle similar to the political compass quiz, what are some questions that might help accurately gauging where somebody falls on this triangle?


I replied on that poll, but hadn’t notice you had posted it.

I think maybe what you mean by “majoritarianism” is what I want, but that is not the word I’d use. I don’t think the concept of “majority” is meaningful in a context when there are more than two candidates.

I think I want the term “game theoretical stability.” (let’s abbreviate it “GTS”) GTS vs. utilitarianism is kind of the difference between a Condorcet method (especially “aggressively Condorcet” methods like Stella-Toby: Does this sequential variation of STAR exist? ) and plain old Score.

I have regularly used an analogous voting concept to represent this concept (median vs. average when voting for a numerical value: https://pianop.ly/voting/median.html ), but a few days ago @cfrank reminded me of Vickrey auctions (sells to the highest bidder at the 2nd highest bid value) and how they compare to Dutch auctions (sells to the highest bidder at the highest bid value). Same thing. While it isn’t voting per se, Vickrey is GTS, Dutch is not. It is very much analogous.

Almost everyone new to the subject likes the non-GTS ones because they seem more intuitive. GTS methods seem to discard important info. We go round and round on this, but some people seem to understand this insight that dispensing with certain data, very explicitly and early in the process, is an absolute necessity. Otherwise it becomes a game of rock-paper-scissors, where you are trying to guess how other people will vote, and they are trying to guess how you will vote, ad infinitum. GTS methods (including with auctions, just replace the word “vote” with “bid”) don’t have this situation.

I don’t know of a term for it other than “GTS,” but I wish there was one that captured it better. Obviously it isn’t “majoritarian” because that word doesn’t apply to these very similar situations but where “majority” makes even less sense.

As for proportionality, I kind of wish that wasn’t in there. It doesn’t apply to single winner elections, and seems to go in with the assumption that there are discrete parties – as opposed to all voters lying on a multidimensional spectrum. I’m just not a party person. :slight_smile:

Majoritarianism is often extended to refer to Condorcet winners when there is no majority winner and a smith set winner when there is no Condorcet winner. The most majoritarian people prefer Condorcet methods and the most utilitarian people prefer pure rated methods like approval voting and score voting. Though like utilitarian the concept is a gradient and some people who lean majoritarian just want the voting method in question to pass the majority criterion, or Condorcet loser criterion, or distribute votes in such a way that it feels like there is always a “majority winner”.

Well then none of these methods are truly GTS since it’s impossible for a voting method to be immune to strategic manipulation. The best a voting method can do is always encourage semi-honesty (where there is no reason to rate/rank B>A when you prefer A>B) in a 3 candidate context and even then only purely rated methods like approval, score, and mj can pull that off.

When voters are strategic and have accurate information (continuous polling), approval voting (and as a result, score voting as well) interestingly enough has a Nash equilibrium at the Condorcet winner (which seems to be the best you can do when all voters are maximally strategic) when one exists: https://rangevoting.org/CondAppConflict.html Condorcet methods on the other hand can fail to elect an honest Condorcet voter when voters are strategic (https://rangevoting.org/CondStratProb.html), so at-least in the case where voters are maximally efficient strategy calculating computers approval voting is more Condorcet then actual Condorcet methods.

If by GTS you mean methods that try to make it so voters don’t have to think about strategy at all, then for me it was the opposite. I was originally more of a fan ranked pairs, Schulze, and minimax, but eventually came around to pure rated methods after realizing that they were only trading vulnerabilities to simple semi-honest strategies to strategies that can be more risky and complicated but also more destructive (ex. https://rangevoting.org/NESD.html) when they are known, by either the average voter or even just different political organizations/infrastructure that have the ability to affect which candidates get enough attention to be viable.

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Sure in the same sense as not all buildings are seismically safe because you can always imagine an earthquake large enough that can take them down.

I think the black and white thinking behind “all voting systems are imperfect” is why we mostly still have plurality.

Of course no system is perfectly immune. How many times do we have to say we understand this?

That doesn’t mean that some aren’t way better than others. And I’d really, really like to see how you plan to strategically manipulate some of the methods such as those I’ve mentioned that are very strongly condorcet (that choose the condorcet winner if there is one, choose one from the smith set if not, and in choosing that one from the smith set, normalize any score votes so any incentive to “pre-exaggerate” is minimized since it does it for you)

Seriously, how are you going to game it then? Can we do some practice votes here and you can try?

Among the candidates that you prefer to the current winner, find the one whom is the closest to beating the winner pairwise, give that candidate a maximum rating, give the winner a minimum rating, and give all other candidates ratings in between the two.

Also, by in “give all other candidates ratings in between the two”, I mean give them a score less then (not less then or equal to) that closest rival and greater then (not greater then or equal to) the current winner. This means that if you like a candidate less then the current winner or like a candidate more then the closest rival you chose, you have to be dishonest (you can’t just be semi-honest).

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Is proportionality in conflict with utilitarianism? Normally we discuss systems that give higher utility versus more majoritarian systems, such as Condorcet.

But what is the most utilitarian way of electing people to multiple positions? It can’t be assumed that you can just add up the utilities for the candidates had they been elected individually.

I see it as a slightly separate discussion (see my post above), but proportional systems don’t have to imply parties.

I vote 100% Proportionality ofc.

I see what you are trying to do here and I like the idea but I do not think this works. Take the Three Telos Model of the political spectrum. Each corner represents an approach to problem solving so more of one implies less of another. With this you are trying to force three of the major advocacy things into a ternary plot and I do not think it works for a few reasons.

Utilitarianism and majoritarianism are two approaches to aggregating desires. They do have a natural trade off with one another and can sort of be considered opposites. If you look at the three telos political model none of the three points have their opposite. For example, the traditionalism/conservatism does not have a progressivism vertex to oppose it. Instead progressivism is more of an ideology where it is a mix of the other two vertexes. I think this is what you would want to do here. So choose either Utilitarianism or majoritarianism as a vertex and not put the other.

Although now that I think about it, both Utilitarianism and majoritarianism are solutions not the rejection of a specific solution like progressivism. So maybe they should both be points with the third being GTS or mathematical stability. Something like free from issues like participation and nonmonotonicity. I do not know what to call it so I am going to call it robustness. Then your three telos/axioms for theory are Majoritarianism, Utilitarianism and robustness. The majoritarian corner would have STV and IRV. On the line between Majoritarian and Robust you would get Condorset methods. The Utilitarian corner might be Score/SMV/SSS. RRV would be more robust but less utilitarian than that. STAR would be right in the middle. Does that work? We could then put different methods into this triangle.

Proportional Representation is a totally different issue. Solving it is somewhat independent to the other problem so I do not think it can fit into the same ternary plot. Also, proportional representation is not really a thing. It is a metric to be measured on the results of an election if it is anything solid. Otherwise it is about approaches to getting high ideal representation. There is a clear trade off between partisan proportional representation and local/regional representation. This has been discussed on this forum a lot. There is also the third approach which is the non-partisan multi-member riding approach. I think the best word for this is likely justified representation. So then you could have Partisan Representation, Local Representation and Justified Representation as the three corners. The various party list systems would be in the Partisan Representation corner. Single member district systems would be in the Local Representation corner. Justified representation would be the types of “PR” systems we normally talk about here. MMP would be half way between local and partisan. I am not sure this works perfectly but it at least makes the choices more clear. I also think Balanced Representation and Proportionate Representation need to be incorporated as well. This is a tricky one because in a partisan system the members of parliament are only intended to represent party adherents.


I think what you said is reasonable, but I just wanted to point out that the location on the majoritarian/utilitarian spectrum is conditionally coupled with game theoretic stability—i.e. majoritarian systems are usually more stable, while utilitarian systems tend to be less stable, so I don’t know if that space makes much sense either. The points of the triangle should be more or less independent.

At the same time, there is the so-called “paradox of democracy,” which is when superficially utilitarian systems lead to unambiguously majoritarian outcomes due to strategic alignment, which some might consider to be tyrannical and oppressive of minorities.

In my opinion, what we want is a balance between majoritarianism and utilitarianism, and a simultaneous balance between representativeness/expressiveness and simplicity. I’m not sure what else we would want that is independent of those two things. Maybe theoretical versus pragmatic?

This is interesting, but also seems to imply that there is always a tradeoff, which I’m not sure is true.

Ranking all candidates, compared to scoring all candidates, might be approximately equally expressive, given a particular granularity. So if there are 10 candidates, and I can score than 0-5, is that more or less expressive than being able to put them in full rank order?

I would argue that scoring them 0-5 is easier on the voter, whether or not it is more expressive. “Easier” is sort of a subjective user experience question more than a math question, though.

I tend to think that there is a theoretical limit that must be traded off. It’s sort of computationally necessary. If you want to capture an amount of information, of whatever sort, your model has to be complex enough to represent that information in some way. Of course, you can do badly on both fronts, but that’s easy and clearly nobody reasonable wants that lol.

You can measure the complexity of a string, for example, reasonably well using the Kolmogorov complexity model. Even that depends on the computer programming language you select as your standard, though. So you’re right, complexity is subjective. Or rather, I think it’s more generally correct to say that complexity is relative.

I see it as far less of a computational issue (I mean, computers are fast), than a ballot complexity issue. For instance, I’m happy to normalize score ballots using floating point values (or maybe integers that range from 0-255 or something), but we might only take 0-5 from voters because otherwise the ballots get complicated.

Yes you’re right. But still I think that increasing ballot complexity can improve the representativeness of a system if done correctly, while simplifying ballot complexity can tend to reduce it. This gets back into the psychological overwhelm factor. There should be a “sweet spot” that most people generally like, where they are content with the amount of information their ballot takes into account and with how little effort they had to put into compressing that information into a specific format. Which I’m basically treating as a computational problem, however inappropriately.

But how much effort people are willing to put in to a ballot for whatever payoff in representation they get for filling one out is probably an important/subjective issue. For example, with FPTP you get what you pay for. It may be a non-issue though for more reasonable systems.

I’d like to see a ballot set where doing that will get a better outcome vs. scoring them honestly.

My guess is that if you can produce such a ballot set, it would be some combination of highly contrived (e.g. unnaturally clustered into discrete groups), an extremely close election, an extremely small number of voters, and where the voter in question seems to have a near magical ability to predict with absolute perfect precision how others are voting.

Here’s the latest CodePen where you can try to create such a ballot set if you’d like: https://codepen.io/karmatics/pen/ExKZVjM
I believe the most GTS method there is Stella-Toby, so if you can demonstrate any reasonably real world ability to game it as you suggest, I’d be impressed.

Consider yourself challenged. :slight_smile:

Keep in mind that “more data” doesn’t necessarily equate to “more complex for the voter.” If we were doing online voting (say voting for the domain name for a forum :slight_smile: ), using the bottom interface for entering ratings isn’t significantly harder, and might actually be cognitively easier, than using the stars as on top.

Screen Shot 2020-08-26 at 9.45.43 PM

With the full range between 0 and 100, it allows you to fully capture subtleties that, if you try to express them with stars, you have to futz around with them more. Given that the more GTS a method, the more it must use rankings rather than ratings, you might want to be able to give one candidate a 70 and another a 72, while with stars you have to either rank them identically, or use up another “slot”, so getting it right is more work. Ultimately, it’s probably less brainwork to just use the sliders.

But the sliders represent significantly more data. To the voter – even one who is happy to be quick and dirty and sloppy – that’s not really an issue, since sliders are super quick to use.

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Yes, for sure, but there are other practical considerations. How do we make sure that the elections are secure using something like virtual sliders, or using computers at all? That’s a question for another topic but it seems like an important one.

Yeah well as I’ve said before, I’m not here to only talk about political voting.

Ultimately though, I think the larger the number of voters, the less it matters whether you capture a high granularity. When we had 18 people voting for 11 possible domain names, the granularity actually was significant and may have affected the outcome. With a political election with thousands of voters, 0-5 should be fine. Certainly better than approval, which only has 0-1.

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I just copied this example (happens to use the same strategy that I suggested for your method with giving A a 5, C a 0, and all others something in between) and applied that example to your method:

Honest votes:

# A B C D
6 5 2 3 0
2 2 5 3 0
3 3 5 2 0
2 2 0 5 3
2 2 3 5 0
5 2 0 3 5
1 3 0 2 5

C is the Condorcet winner so she wins automatically.

Where the 6 A>C>B>D voters are strategic:

# A B C D
6 5 2 0 1
2 2 5 3 0
3 3 5 2 0
2 2 0 5 3
2 2 3 5 0
5 2 0 3 5
1 3 0 2 5

There is no Condorcet cycle and all the candidates are in the smith set. All the votes are already normalized. A has 64 points, B has 43, C has 49, and D has 42. A wins.

Since you presented me with a challenge, I will return the favor. Can you find an election where for some group of voters, it takes less honest votes to change the election to a result that is more desirable for them then it does votes using the strategy I presented for gaming your method? If such examples are rare (if not non-existant), why would voters want to vote honestly as opposed to using that strategy? Are you up for the challenge? :slight_smile:

So here is the ballot you are suggesting (in a format that can be pasted into the CodePen):


6: A[5] B[2] C[3] D[0]
2: A[2] B[5] C[3] D[0]
3: A[3] B[5] C[2] D[0]
2: A[2] B[0] C[5] D[3]
2: A[2] B[3] C[5] D[0]
5: A[2] B[0] C[3] D[5]
1: A[3] B[0] C[2] D[5]

strategic (replace first line with this):

6: A[5] B[2] C[0] D[1]

I notice that it works to get A rather than C in some methods, but not in others (Cardinal Baldwin and Toby’s Condorcet/Score Hybrid still elect C).

And yes it works by causing there to be no Condorcet winner (A and B both end up 2 pairwise wins), then C wins under certain methods.

My best test for it being “unnaturally contrived” is to see if the strategy works with any “blurred” ballots. (these are made by a picking a few ballots at random, averaging them, and then normalizing them) If I add even 3, the strategy seems to never work. That suggests to me that the likelihood that someone could predict that this might work, and that it would be more likely to give them a positive outcome compared to a negative one (such as them accidentally causing B to win) is pretty tiny. And it is all hinging on it being razor-thin pairwise margins between three candidates.

So, I don’t want to dismiss it outright, it is interesting, but my feeling is that it isn’t something that would cause a real world problem. I’ll have to look more closely as I have time… (which I don’t right now sorry) but I do want to build tools to hammer on this kind of issue.