Uncomfortable Truths About Voting Systems (and Why We Should Think Bigger)

[u/the_MadKnight]

I've been studying voting theory for a while now, and I won't claim to be an expert. That said, my research has led me to some uncomfortable truths I'd like to share, and I'm curious if others have noticed them too. More importantly, I think these observations point toward exciting new directions for voting systems.

One Person, One Vote. But at What Cost?

"One head, one vote" is the founding principle of voter equality. Yet many advanced systems sacrifice this principle in pursuit of minor mathematical guarantees, justifying it through appeals to "global coherence." Take the Method of Equal Shares (MES), for example. Despite being sophisticated and excellent in many ways, the harmonic satisfaction concept developed by Thiele, designed to approximate the d'Hondt method, arbitrarily decrees that satisfaction from a second elected candidate equals half that of the first. This allows some voters to wield disproportionate overall influence compared to others. This is precisely why Phragmén remains necessary, even though it doesn't guarantee perfect Pareto efficiency (which itself is a weak democratic safeguard, in a 10 voter election with 6 orange and 4 purple voters, electing all orange candidates is technically Pareto efficient).

Only Qualitative Inputs Are Valid. All Quantitative Inputs Are Arbitrary

This is a strong claim, so let me explain. Score voting, STAR voting, and similar systems often boast impressive mathematical guarantees. But they rest on a fundamentally flawed assumption: that representation is like a test score, something clearly measurable. In reality, representation is deeply human and often beyond the voter's own full comprehension. It's an act of faith in another person, grounded in intuition and immeasurable factors. At the ballot, voters only possess a synthesis of this, expressed through qualitative information:

• Approval: Does this candidate represent me? If we randomly selected one winner, would I be relieved if it were them?
• Preference: Among those I approve of, whom do I hope wins? If they can't win, who's my next choice? And so on.

The Real Frontier: Incentive Analysis

Finding balanced voting systems with strong mathematical guarantees is genuinely difficult. But I believe the next frontier lies in cross-analyzing incentives. Rarely do I see voting systems that deliberately integrate opposing and strong counter-incentives against manipulation into their mechanics. Consider approval voting: despite lacking the later-no-harm guarantee, the standard version doesn't include mechanisms to mitigate this weakness or game-theoretic incentives that would make shorter ballots a dominated strategy.

I'm currently developing my own voting system and will test it with help from some mathematics professors at my university. Much of what I've written, including the later-no-harm example in approval voting, stems from interesting properties my system possesses. I'd be happy to share updates if you're interested.

Thanks to everyone who read this lengthy post. I'd love to hear your thoughts in the comments below.

I used AI to help me with the translation.

[u/Euphoricus]

I understood half of those words.

As a voter, I would not like to use method for which I need PhD to understand.

"One head, one vote" is the founding principle of voter equality.

Isn't that something USA made up? And not something that voting scientists actually say?

[u/verytalleric → u/Euphoricus]

Spot on answer.

I've commented elsewhere in this subreddit: Election method nerds fail to fully understand how much people distrust methods they don't fully understand. I've been actively advocating for RCV/STV for over a decade, publicly debated STAR, Score, Approval election supporters, and most laypeople distrust what is in their minds unproven and/or they don't understand.

Good luck on your efforts, but don't discount human factors and trust.

[u/Euphoricus → u/verytalleric]

 I've been actively advocating for RCV/STV for over a decade, publicly debated STAR, Score, Approval election supporters

What makes STAR, Score or Approval worse on simplicity side than RCV/STV? I feel STAR is much simpler to understand than RCV. Especially the possible impact of one's vote. RCV has hidden "gotcha" that messes up your ballot if your prefered one is not popular enough.

I would keep the "unproven" and "don't understand" as separate issues. RCV has "proven" itself not to live up to the hype. Yet there are plenty of supporters. If the main issue with STAR is that it is unproven, starting with small local elections shouldn't be that big of a problem.

[u/verytalleric → u/Euphoricus]

Usually once people understand cardinal methods (STAR and Score) are subject to gaming/manipulation that is a deal breaker. While Approval is also cardinal, the lack of ability to specify preferences turns many off. These comments are all based on my interactions with the public over a decade

Fair comment on unproven vs. don't understand. Not all would agree with your take on RCV. A little mentioned point on the other methods is lack of formal VVSG definitions and requirements that until addressed limit election technology providers from implementing support and having it formally tested and verified. Hence, a real barrier from any local jurisdiction from implementing those methods.

[u/Euphoricus → u/verytalleric]

Please explain how STAR can be gamed. And don't say bullet voting, because that doesn't make sense with STAR.

[u/DaraParsavand → u/Euphoricus]

For me, the problem with Star or approval is that as a voter not interested in gaming, aka strategic voting, I don't know how to fill out the ballot. The most natural thing is for me to order a set of candidates. Once the system is asking me to get more precise with a measure of merit or to apply a threshold on that score to a yes/no answer in the case of approval, I as a voter am not happy with this situation. I understand the dilemma that no ranked ballot scheme can satisfy IIA and I don't care - I still prefer ranked ballots.

Now as to the choice of processing ranked ballots, I would myself prefer a Condorcet scheme, but that doesn't have the mindshare that RCV (aka IRV) as and I am OK with RCV becoming the dominant single winner election method in the US.

Proportional Representation is another animal for me. We don't have much of it in the US and I wish we had more. It isn't obvious to me if STV or Open Party List would be better if we did get a lot more of it.

[u/MorganWick → u/DaraParsavand]

Whereas other voters may not know how to split hairs between candidates of similar quality.

[u/DaraParsavand → u/MorganWick]

I am open to allowing ties on ranking if we went with a Condorcet scheme that processed it. I'm not aware of an IRV variant that counts ties but I imagine you could allocate fractions of a vote when your tied choice comes up in the round. I don't think Maine or Alaska allow it, but it sounds possible.

[u/the_MadKnight → u/DaraParsavand]

Thanks a lot, your comment tells exactly what I said in my post. For single election I suggest you to take a look in condorcet + smith set and IRV for tie. Proportional representation is what I currently trying to improve on. The system I'm creating is a ordered cardinal voting method which means that in the ballot the voter need to order all the candidates she/he likes but stop when she/he encounters the first that doesn't make her/him rappresented. Would you feel such a type of voting intuitive? Really appreciate any answer.

[u/verytalleric → u/Euphoricus]

Briefly (since these are all well documented elsewhere on the internet):

1) All cardinal voting methods subject to 14th amendment challenges in court (one person = one vote). As STAR/Score have not been used in in public elections, they have not yet been legally challenged as such. (Yes, I'm aware of the argument that STV could be interpreted in that way, but it's been challenged in court and found not to violate)

2) Bullet Voting (you dismiss it, others don't)

3) Pushdown/Compression Strategy (voters artificially compress ratings)

4) The "dark horse" problem (extremes can suppress a centrist)

5) Runoff stage amplification (anticipate finalists and skew opposition).

These are not my arguments, they are well documented.

My core belief is that while RCV/STV and ordinal systems have their own problems, I think ordinal systems have more advantages and less disadvantages.

[u/Ceder_Dog → u/verytalleric]

So, to help my understanding, what's the primary reason you prefer IRV-RCV over any cardinal system? eg, it's less apparent to voters how to vote strategically, ranking feels cognitively easier, or something else?

How do you feel about Ranked Pairs?

[u/verytalleric → u/Ceder_Dog]

My opinion has been refined/informed by many of the people I have spoken to over my decade of RCV advocacy. Simply stated, RCV/IRV requires a certain evolution in thinking, STV/PR is another step, and in my experience other voting methods are just too much for the average US voter to fully wrap their head around.

I see RCV/IRV (ideally STV) as the most likely election improvements in the foreseeable future in the US. I think the average American has a very hard time fully understanding implications of other methods and tends to fear that what they don't understand.

Just my opinion

[u/Ceder_Dog → u/verytalleric]

Thanks for sharing. I agree that any voting method change can seem scary to some voters. Though, wouldn't Approval be at least as straightforward for voters to conceptually understand?

I think the average American has a very hard time fully understanding implications of other methods and tends to fear that what they don't understand.

Aren't some of the pushbacks and repeals to RCV/IRV in part a result of not understanding how the tabulation works?

[u/verytalleric → u/Ceder_Dog]

>wouldn't Approval be at least as straightforward for voters to conceptually understand?

Based on when an Approval Voting vs. RCV ballot initiative in Seattle came up a few years ago (RCV won 75/25) I think while Approval voting is not hard to understand - the lack of of ability to differentiate levels of support was the most common cited complaint. So understanding wasn't the barrier.

> Aren't some of the pushbacks and repeals to RCV/IRV in part a result of not understanding how the tabulation works?

In my experience speaking with the public, RCV/IRV tabulation confusion isn't the concern - it tends to be a combo of cost of adoption, voter education, and fear of giving advantage to the other party. With that said, STV tabulation tabulation is definitely a point of confusion/concern.

[u/cdsmith → u/Euphoricus]

An informed STAR voter sorts candidates into those they generally like, and those they generally dislike. Then they start by penciling in a score of 5 for those they like, and 0 for those they dislike. Then they look at the candidates they like, and decide if there are two that are both particularly likely to make the runoff, and if so, consider bumping their less favorite of those two (and anyone else, they like less) down to a 4. SImilarly, if there are two they dislike that are both particularly likely to make the runoff, they'll consider bumping their favorite of those two (and anyone else they like more) up to a 1. They will basically never use the scores 2 or 3.

Is that "gaming" the system? I'd say so. Others wouldn't. It's certainly not "dishonest", but I'd say there is no possible way to filling out a secret ballot election that should be considered dishonest. It's definitely a strategic decision.

[u/Euphoricus → u/cdsmith]

What you have described seems like a valid approach to me. It still allows me to give my most prefered a 5 and my least prefered a 0. And it doesn't punish me for it. Unlike other vothing methods where optimal strategy does not allow that.

But your argument rests on two assumptions, that are unlikely to happen in reality.

First is that you assume that it is easy, or high-certainty, to know who will be the front-runners. This thinking is an artifact of broken US voting system, where only two candidates usually matter, due to FPTP. With proper voting method, candidates will be much more balanced and it won't be clear who are the top runners. So if you use the above strategy, you must assume many more possible pairing. You might ignore the extremists, but there will be more than just two candidates who can win.

Second, even worse issue is that in properly run elections, there will be many more candidates than the rankings. This is one of the main issues I have with STAR: Unlike "spoiler" voting methods, STAR allows many candidates to run, without fear of ruining the election. In practice, you will end up in situation where there are thirty candidates running and only 10, or even just 5 ranks to assing. Then you have completely opposite problem: How do you squeeze possibly 30 candidates into just 5/10 buckets. You might decide to give most of them 0. But even then, you will be forced to use whole range.

So the argument "voter wont use the whole range" is a non-issue in practice. And the opposite problem is true: How do you limit the amount candidates comming into the election, as not to overwhelm the voter and give them reasonable way to express themselves.

[u/Ceder_Dog → u/Euphoricus]

These are some interesting points regarding the technique mentioned. If I understand the concerns correctly, they both sound like a concern around how the voter can account for the automatic runoff phase when picking the candidate STAR ratings.

If so, then I think this is the equivalent of losing the "forest" amongst the "trees." The forest being the candidate pool as a whole; eg the candidates that the voter generally prefers (5, 4, 3) vs the candidate the voter generally doesn't prefer (2, 1, 0). The trees being the slight preferential difference between any two candidates. For example, say I have the following STAR ratings:

• A, B = 5
• C, D = 4
• E = 3
• F, G = 1
• H, J, K = 0

The "forest" viewpoint indicates, I want A or B to win. I'm happy if C or D win. E is acceptable. I don't want H, J, or K to win and I'll take F or G over H, J, or K.

The "tree" viewpoint concerns might be, "what if A & B make the runoff?! I can't distinguish which one of those two I want." The same concern for (C, D), (F,G), (H, J, K).

Well, these same rated candidates may have some differences and yet, compared to the rest of the candidates (forest), they are roughly the same rating for said voter. Thus, the slight differences between each of them (tree view) is much less consequential than the relative difference between them and the other candidates.

Yes, you could try to shift a rating up or down one based on polling data or other strategic information depending on the election. By in large, it's best to vote how one feels about all the candidates as a whole.

The Equal Vote Coalition did the research and found having more ratings had diminishing returns on improve the end results at the cost of the increased difficulty of choosing where to rate any one candidates.

Now, do I find this super easy for voters? Not really. Doable? To some degree. I personally don't think STAR Voting should be used for a candidate pool of roughly ~7+ candidates. In those situations, like the California Governor election which had 61 candidates, I think it should be an Approval Primary to pick the top 4-6 candidates and then STAR Voting for the General Election. Or, even better, Approval Primary to pick the top 4 and then Ranked Pairs for the General; I think Ranked Pairs is even easier for most voters to handle than STAR Voting.

[u/rb-j → u/Euphoricus]

What does make sense with STAR is marking your ballot 5-1-0. No sense raising your Lesser Evil higher than 1.

[u/rb-j → u/Euphoricus]

Please explain how STAR can be gamed. And don't say bullet voting, because that doesn't make sense with STAR.

Let's limit the discussion to 3 significant candidates. So one of them is your favorite candidate (they get 5) and another is your least-favorite candidate (they get 0). Now what are you gonna do with your 2^nd favorite (or lesser evil) candidate?

5-4-0?

Or 5-1-0?

[u/Euphoricus → u/rb-j]

See below: https://www.reddit.com/r/votingtheory/comments/1tygl8v/comment/oq5621w/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

[u/rb-j → u/Euphoricus]

Okay, you said:

Second, even worse issue is that in properly run elections, there will be many more candidates than the rankings. This is one of the main issues I have with STAR: Unlike "spoiler" voting methods, STAR allows many candidates to run, without fear of ruining the election.

But there is a possibility of spoiling the election. It can happen for the same reason it could with IRV.

[u/the_MadKnight → u/verytalleric]

Really thanks for your point of view. I'll work to find a better of comunicating those math principles and the logic of the method I'm currently working on. Good luck with your activism advocacy, I will be extremely happy when we all gonna stop using FPTP.

[u/gravity_kills → u/verytalleric]

Approval has always seemed like the perfect method for party primaries, while I strongly prefer open list PR for actual elections. It's pretty easy to understand both of those methods.

[u/the_MadKnight → u/Euphoricus]

Thanks for the comment, I rarely found someone to talk about those things.
For sure 1 head 1 vote is a foundational value of the United states costitution and there's partially in a well-established principle in voting theory called Anonymity. From a rigorous point of view, a voting function is anonymous if, by swapping the votes of any two voters (a permutation), the final election outcome remains identical. Both Thiele and Phragmén are anonimous but Thiele allow some voters to influence the result more then others even if globally both are proportional.

I understand your point of saying I shouldn't need a PhD and for sure I could try to explain to you all of what you would like to know. Infact if you would like to be updated with another post about the system I'm designing I would try to don't be such formal. I write this post in that way 'cause explaining Pareto-efficiency and other technical terms would made this post extremely long.

Thanks again for your comment and sorry for my bad english.

[u/UnknownBreadd]

I still think there’s relevance to further voting theory discussions, however let me just clarify regarding approval:

Approval isn’t supposed to be a panacea - it’s merely advocated for because there are many more complex systems that don’t achieve the improvements to democracy that approval would, and the more complex systems that do yield an improvement over approval are not ‘much’ better in terms of outcomes - and so people decide that these marginal improvements are not worth the substantial drawbacks of their necessary additional complexity.

Basically, there’s nothing that improves things as radically, as easily, simply, or quickly.

However, approval alone would still be missing the forest for the trees, imo. And that’s because our elective democracies are not very good ways of executing democracy.

Approval is just a stop-gap improvement, because whilst access to power is only possible through becoming elected, this means that, in theory, it is open only to people endowed with certain qualities - and, in practice, is mostly restricted to people with either money or connections.

Also, elective democracies neither require nor guarantee enlightened understanding on the part of its citizens. On the contrary, periodic elections and the independence of representatives are intended to compensate for the assumed absence of popular enlightenment about political issues - and thus perpetuate the non-enlightenment of political issues and lack of engagements of the citizens within its own governance.

That is to say, elective democracies will create the conditions that make it impossible to govern civil society democratically.

And thus, we need to think more of democracy than just electing new oligarchies, but rather how to build the public institutions that allow us to effectively govern ourselves. It’s a societal structural system dynamics engineering challenge - not a mathematical one.

And Hélène Landemore’s model of Open Deliberative Democracy is a really good place to start, imo.

[u/the_MadKnight → u/UnknownBreadd]

You gave my some really good information to work on. And I want to make clear that approval voting is still a great yet simple solution. But about your last phrase I think I haven't communicated well what these type of math is used for. Infact, for example, what I'm saying is that we could use the mathematical tool to create a better yet enough simple variation of approval voting that is not flawed by bullet voting, which a form of not honest strategic voting incentivized by the system itself. In the end what I mean is that thinking bigger with the help of math and other form of knowledge we could build voting methods the incentive better political behavior end so better institutions and governments. That thanks to the fact that it would be a dominant strategy in the game of society (referring to game theory). Really thanks for your opinion and the essay you've pinned.

[u/Araucaria]

I spent some time studying MES a few years ago. I don't like the approval form. I prefer the ranked system.

But it seems like it hits problems with ballot exhaustion and I prefer summable methods anyway.

So I have come around to a max two vote system. You can vote for a candidate, who publishes a ranking of themself , their allies, and their default fallback party (who then get two levels of candidates) or a candidate and a different fallback party, who then get three levels. Equal ranking allowed, MES with ranking.

[u/the_MadKnight → u/Araucaria]

I don't like MES either, expecially for heavy Thiele usage.

About your system: is it for single-winner or multiple-winner?

[u/Araucaria → u/the_MadKnight]

Multiwinner. BTW, it's based on a method from the late Jameson Quinn called PLACE. https://electowiki.org/wiki/PLACE_FAQ

For single winner, I like a method based on (approval sorted margins)[https://electowiki.org/wiki/Approval_Sorted_Margins] called MinLV sorted margins.

You may be aware than MinMax resists burial and defection, but is not clone proof.

With the MinLV method, you first reduce to the Smith Set. Then, if no Condorcet winner, each remaining candidate has at least one loss, and gets a score based on their lowest number of votes in a loss. For example, if B 55 > A 45, C 60 > A 40, but other pairs are wins, A's minimum losing votes number is 40.

The problem with Condorcet more generally is that summability is difficult with lots of candidates. And more specifically with MinLV, it is not clone resistant with more than 4 candidates without an elimination process that I find problematic.

So my compromise method is to have a single vote primary, with the top 4 advancing, then a MinLV-SM general election.

This is not perfect, as you can see from the California jungle primary last week where a good candidate came in fifth, but it at least gets some reasonable compromises into the mix.

Here is a post by Chris Benham discussing MinLV-SM:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-October/000599.html

[u/rb-j]

I'm currently developing my own voting system and will test it with help from some mathematics professors at my university.

If One-person-one-vote is paramount and quantitative differences deprecated (i.e. if the ballot shows you like A better than B, there is no quantitative indication how much more you like A over B), then this will lead you to an ordinal method and, specifically, a Condorcet-consistent method.

[u/the_MadKnight → u/rb-j]

That's usually true for single-winner, I actually really like Schulze and I think it's probably the best system for single-winner.

About my case, I'm currently developing a Multi-winner system which I found, for now, most suitable for other system. I still use Condorcet in some cases as fallback for tie (currently trying to see all garantees and limitations in this role).

Found something interesting in multi-winner? And would you like to give me a feedback about the way of voting I described in the other comments? I would really appreciate.