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Comment by glafayette | Hacker News Reader

This is great news! CGP Grey has a great series on voting schemes for anybody who is interested in learning more - https://www.cgpgrey.com/politics-in-the-animal-kingdom

Also, not to be too self-promotional, but I also made a simple site for running polls using Ranked-choice voting. I was surprised that it was tricky to find a nice SurveyMonkey-esque site that did Borda Counts and Instant Runoff voting so I made my own. Hope some other voting geeks can enjoy it - https://poller.io

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I think it is unfortunate that Instant Runoff Voting (commonly called Ranked-Choice Voting, though it is not the only system for counting ranked ballots) is getting all the buzz these days. Someone posted this link to a very nice explanation, complete with spiffy simulations, then deleted their comment: https://ncase.me/ballot/

Approval Voting is much simpler to implement and use than IRV, and much less prone to produce anomalous results. More discussion can be found here: https://electionscience.org/

I think the Marquis de Condorcet got the entire field off on the wrong foot with a conceptual framework in which voting is about expressing preferences between candidates. Voting theorists have tended ever since to think in terms of preferential voting. The result is an unconscious bias to the effect that a voter's evaluations of the candidates tend to be roughly evenly spaced: that the gap between their first choice and their second is roughly equal to that between their second and third, etc. You can hear that bias, for example, in this statement from FairVote.org:

[A]pproval voting [has the] practical flaw of not allowing voters to support a second choice without potentially causing the defeat of their first choice.

It's true in AV that if you vote for two candidates, your ballot contributes equally to the potential victory of either; you don't get to say which you prefer. But calling this a "flaw" assumes that you couldn't be somewhat indifferent between those two candidates, at least relative to the degree of your dislike for the other(s). That assumption is pervasive, albeit implicit, in the arguments I have seen made against AV, and it is indeed nothing but an assumption.

A much better conceptual framework is to imagine an N-cube, where N is the number of candidates, and each voter's position as a point in that cube. Then the problem of designing a voting system becomes that of identifying which corner the mean of the positions of the voters is closest to. In principle a voting system could allow each voter to supply a real number in [0, 1] for each candidate, and we could simply add them up and see which is largest. In practice it makes more sense to quantize the space to some extent. Score Voting gives the voter a set of possible values, e.g., integers in [0, 10]. Approval Voting boils that down to the bare minimum of {0, 1}. (My opinion is that once the electorate is large enough, there is little benefit to allowing more than two choices; the greater quantization noise of AV gets averaged out.)

Armed with that, we can now look back at the preferential systems. Is there a way to interpret a preferential ballot in the N-cube framework? Yes, there is. We cut the unit N-cube up along diagonal hyperplanes; for instance, in 3 dimensions (i.e. for a 3-candidate race), the X=Y plane, the Y=Z plane, and the X=Z plane. This gives us 6 prismatically shaped regions. We compute the barycenter of each — the center of mass, under the assumption of uniform density — and look at their coordinates. These turn out to be permutations of [1/4, 1/2, 3/4] — a linear sequence. In short, what falls out of this exercise is equivalent, modulo linear transformation, to the Borda Count.

So the Borda Count optimizes for the case in which the voters' positions cluster near the barycenters of those regions: where their evaluation of the middle candidate, in a 3-candidate race, is about halfway between those of the other two. If you listen closely to the arguments presented by preferential-voting advocates, you can hear them assuming that this is likely to be the case. But there's no reason it should be, and in practice I haven't observed that it tends to be.

Let's not belabor the bottom line here: any form of voting produces better results than winner-take-all/FPTP, whose only benefit is sheer simplicity of implementation (which was crucially important, once upon a time; these days, much less so). What matters at this moment in history is getting off of FPTP, and I'll throw in with whatever scheme has the most momentum. Even if that means different states end up with different approaches, that's fine--maybe that's even great (laboratories of democracy and all that).

It deeply frustrates me to see essays like this written without saying in big bold words at the top "Id take almost anything over fptp" People not deeply familiar with the voting system world see this stuff and think to themselves "Wow. I guess there's no best voting system." Rather than what they should be thinking: "Oh wow, we have the worst voting system that forces bipartisan politics, we're burning alive from the inside AHHHHHHHH"

So before we get into comments like "If the primary reason you fail a criterion is simply because your voting system just says more about a voters actual preferences, thus creating the potential for conflict, it is a weak failure when compared to a voting system that avoids that failure by simply lacking that information."

We should always first, and last say: "I'd take nearly anything over FPTP"

And anyone not doing this is not helping. As someone who has lived through 3 failed voting reforms in my province, I need to make it painfully clear to those not doing this. You are NOT helping.

I don't know whether you'll see this belated reply, but anyway: I have had some sympathy with your position, as you can see in my sibling comment, BUT as I read more about IRV, I am actually coming to disagree. Look at this page, especially the chart near the bottom: https://electionscience.org/library/approval-voting-versus-i... What this says is that in simulation, given mostly tactical voters, IRV doesn't do any better than PV (FPTP). This surprised me, but I'm starting to see why, as the rest of that page explains.

Here's another: https://www.rangevoting.org/TarrIrv.html The most telling argument here, I think, is that a century of IRV hasn't freed Australia from two-party domination.

Another page with simuations: http://zesty.ca/voting/sim/

What voting reforms have been attempted in your province?

I wouldn't take IRV over FPTP. We've done it in the past and switched back. It also doesn't solve the problem. All it does is slightly increases the VSE but doesn't accomplish much else. IRV isn't great at allowing a new party to appear when major parties diverge from voter consensus.

This isn't something you take several steps towards the right direction. If we take a step and it doesn't work, people are going to stop stepping in that direction and look for other optimization methods. You have to make a large enough step that the loss function actually decreases.

Out of curiosity how long did you have it for? Because voting reform can not fix the damage of a legacy of FPTP the moment it is instituted, it's going to take 4 or 5 elections before

1. the public figures out how it works

2. parties start appearing that arn't getting crushed by other network effects

3. that an understanding of what a strategic vote looks like in the new system is widespread and existing parties start playing the new game.

And since election cycles are often something like... 4 years. You'd need a voting system in place for maybe 20 years before anything positive would start to happen, and that would apply to any voting system put forward.

Like. These systems are for the far flung future of the country. Not... next election.

It was not national, but some cities and states had it for awhile.

As to the time frame: remember that Australia has had it for 100+ years. They are dominated (>80%) by 2 parties (even though they have the MAJOR advantage of proportional representation through their parliament). One can say similar things about Ireland, though the domination isn't nearly the same and there are 3 strong parties (they use a variant of IRV called STV).

But remember that neither the math nor the 100+ year experiment has shown that IRV won't collapse into a two party system. You'll find plenty of references through this thread and sources as to why if you search for "approval" (and "monotonicity criterion"). The thing is that the problem is rather complex. We don't just want it so you don't waste your vote, we don't want that to happen with ANY candidate (favorite betrayer criterion). We want other parties to rise up with no disadvantage. We want our voting to be expressive (STAR and score are substantially more expressive that IRV). We want high voter satisfaction efficiency (VSE) -- IRV doesn't do much better than FPTP. We want the system to be resistant to strategic voting. And we want the voting system to be dead simple. Frankly IRV doesn't fit these criteria. Approval fills every category but isn't extremely expressive. Score and STAR are at worst approval voting and at best much more expressive than ordinal (ranked) systems.

But basically everything you're pointing out is well acknowledged and I won't challenge it. More what I'm suggesting is that Hasan and CGP Grey didn't do their research but drove the hype. There is no optimal system for voting, unfortunately, but there are pretty dang good ones. When the experts say cardinal, I'm going with that.

Yes, I tend to agree with this. Even so, I think Approval Voting deserves more buzz than it's been getting.

As I like to say: "I approve of preferential voting, but I prefer Approval Voting" :-)

Agreed. There are numerous alternative voting systems out there, but I would say "The best alternative to FPTP is the one that has the strongest chance of happening".

With that in mind, I think it is worth looking at which voting reform proposals have been rejected before, and what argument their opponents used. My impression is that cost and complexity tend to be the biggest persuaders, so strategically it makes sense to support a voting system where the ballot marking and counting processes are as familiar as possible.

As a concrete proposal, I suggest a system where people fill in ballots exactly as in FPTP, and the results are counted in exactly the same way, but then the candidate with the least votes gets to reassign their votes to another candidate of their choice, and so on until one candidate receives a majority of votes.

So the losing candidates get empowered to speak for their voters? An interesting suggestion, but I think the voters would prefer to allocate their votes themselves — this is what IRV is.

The fear is that an incremental improvement that doesn't solve the major problem (the inability for a more representative party to gain traction) will cause people to revert back to FPTP.

The justification for this is that America did exactly this (not at a national level). As well as that Ireland and Australia are still dominated by two parties, and Australia has had IRV for 100+ years.

Sometimes incremental improvements are actually a step backwards. Specifically when people get over hyped and put too much faith into it.

But I also have to ask, if we already have a better tasting cake and it costs as much as the plain cake, why not take the better one? It isn't more expensive and doesn't take more work. It is just better.

My criticism of RCV is more basic: in RCV, ranking someone too high can in some cases cause them to lose. That's really weird, and we probably shouldn't use any voting system that has that property (i.e. it fails the monotonicity criterion).

Problems generally arise when there is a third candidate who is competitive with the other two. Generally, it's safe to vote for your preferred candidate if they're either in a strong position and will probably win or they have no hope of winning. In between those poles, you might be harming your candidate if you put them first in a 3-way (or more) contest.

Approval voting solves the third party spoiler problem better than RCV does, and it doesn't introduce any weird new problems. Therefore, I think it's a better option than RCV for anyone considering a switch from first-past-the-post. (Range voting and STAR voting are also pretty good.)

Perhaps I am suffering a failure of imagination, but in what circumstance does "ranking someone too high .. cause them to lose"?

Edit: Found this[0] talking about it; what remains unclear to me is whether this should be seen as "this hurts my candidate" over "this result better reflects the electorate".

[0]: https://www.youtube.com/watch?v=JtKAScORevQ

That's an example. One can argue about whether the "bad" candidate should have actually won in that scenario, but what's strange is when you have a situation where the "good" candidate would have won if only some group of voters hadn't put them first.

I think at the root of it is that removing the candidate with the least number of first-place votes is kind of an arbitrary way of eliminating candidates. Maybe that candidate should have been eliminated, but maybe they were an ideal compromise candidate, tolerated by most voters even if not their first choice.

Perhaps RCV might be significantly improved if one were to eliminate by borda count instead of least-first-place-votes, but that's not the system that's been advocated widely in recent years.

I spent some time looking at voting systems, and also in attending a conference on voting systems 15 years ago.

Elections require a few things - one of them being transparency. Another is trust.

Thus while elegant mathematical solutions such as the one you presented, may be more accurate, they are also impossible for the lay man to understand. And for journalists to explain. For many this erodes the transparency,leading to mistrust.

This is the core reason why simple, but explainable approaches are preferred.

That's the best argument for Approval Voting. It's very simple: you just vote for or against each candidate independently. The votes are tallied, and whichever candidate has the most votes wins. It's much simpler than IRV with its multiple rounds. It's even simpler than Plurality Voting (aka "FPTP") because it doesn't require you to pick a single favorite.

Anyway, I'm writing for the HN audience here, not for general consumption :-)

Not sure where to post this, but does anyone know why RCV is getting so much attention in voting reform efforts? Approval voting seems so clearly superior in UX and performance characteristics that I'm confused it isn't even getting discussed in a lot of places. RCV is on the ballot in our district and I felt compelled to vote for it but I didn't feel totally comfortable with it because it seemed like approval voting wasn't even discussed.

My hope is that this might be a foot in the door to moving to approval (the voting machines would be able to handle either) but my guess is there might also be less of a chance of doing so if there's already been a change.

People have strong preferences for one candidate over another. Approval voting takes that preference from voters, which instinctually seems like a very unattractive system.

E.g., let’s say I’m a “moderate” in the US in 2008. I would like either Obama or McCain to win but I have a strong preference for Obama and I do not like any of the third parties. Approval voting doesn’t allow me to express this very common preference.

s/Approval/STAR (or range)? At worse these are approval, at best they are more expressive while still being substantially simpler than any ranked method (which requires multi rounds). I'd argue that STAR and range are more expressive than ranked because you can actually specify how much more or less you like a candidate than another. You can't express this in a ranked system.

The phrase "one person, one vote" is also the root of much mischief. While we certainly want everyone to have equal influence over the outcome, the fact is, in a race with more than two candidates, you're always voting for some of them and against others. With two candidates, this fact can be glossed over, because you're always voting for one and against the other one; there are no more possibilities. But with more than two, "one person, one vote" suggests that you should only be able to vote for one of them, overlooking the fact that this forces you to vote against all the others. You're still casting N votes about N candidates; they're just subject to the rule that only one of them can be affirmative. In that light, it is clear that the rule is utterly arbitrary.

The correct motto, I submit, is "one person, one candidate, one vote". Approval voting falls directly out of that. Every AV ballot has the same amount of influence over the result as every other, because they're all points on a hypersphere whose center coordinates are all 1/2. That is, they all represent points equally far from the point of indifference.

in quantitative marketing, the equivalent sort of discussion centers around revealed preferences and (choice-based) conjoint analysis. because of that, i'm partial to score voting with something like a 7-point scale (e.g., absolute best, good, acceptable, average, unenthusiastic, unfit, absolute worst).

but for any of this to matter, we need more than 2 choices, so the bigger issue is breaking the stranglehold of the two-party system (either by getting rid of parties, or adding many more legitimate parties to the fold), which also means we need serious campaign reform (which the supreme court seemingly opposes, and might oppose even more soon).

They both have similar problematic red boxes.

https://en.wikipedia.org/wiki/Comparison_of_electoral_system...

Unfortunately CGP Grey is wrong. RCV (IRV) has been used in Australia for 100+ years. Ireland uses it. We've already had it in America. We've done enough experimenting. The thing to get excited about is Approval and STAR. Let's interested try cardinal voting systems instead of ordinal. They are also substantially simpler.

What about "Path Vote" AKA the Schulze method?

https://en.wikipedia.org/wiki/Schulze_method

"The Schulze method (/ˈʃʊltsə/) is an electoral system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners. The Schulze method is also known as Schwartz Sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), the beatpath method, beatpath winner, path voting, and path winner.

The Schulze method is a Condorcet method, which means that if there is a candidate who is preferred by a majority over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied."

Condorcet methods get discussed a lot but they are pretty complicated. I believe that they are discussed because they maximize VSE, such as Schulze. I'll reference my comment in this thread because the VSE link has what I'm talking about. The problem is they are less resistant to strategic voting (though much better than IRV and plurality). But let's just keep it dumb and simple with cardinal systems. Approval is dead simple and gets you pretty much all the way there on most of the criteria. If you want to add a little bit of complexity, STAR makes things even better because it gives you some more specificity (and slightly improves upon score/range). Every time we talk about electronic voting everyone always brings up the matter of simplicity, well, that matters here too. With approval and score you're literally just creating a matrix. STAR you have two rounds (top two from the previous round). Ordinal methods are pretty complex and much more prone to mistakes because of such. You don't need a PhD to understand approval (it is actually how I solve the "where should we eat" problem).

[0] https://news.ycombinator.com/item?id=24563236

Schulze has a very nice geometric interpretation, but I should get off my ass and get the working paper ready to be released first.

Let's be real: plurality is trivial, approval is dead simple, score is easy, IRV is so so, Schulze is complex. That is, in determining the winner.

In plurality you just count the number of votes. Largest number wins. max(sum(votes)

In approval you just count the number of approvals. Candidate with the most approval wins. (max(sum of columns(votes))

Score you actually have to create a matrix!

IRV you have recursion!

Schulze you have both and graph theory!

I just don't see the appeal. Sure, it has a slightly better VSE than STAR if everyone is voting 100% honestly (that condition is a key part!) but it just isn't appealing when you consider other criteria. Especially when we talk about simplicity. Approval is essentially trivial but also has a lot of other criteria going for it. How much does VSE matter? Especially if you still aren't combating spoilers (I'll give you that Schulze does better than IRV at spoilers).

Come on, just look at the wikipedia page for the Schultze method. There are matrices, graphs, and stuff. That might be fine for a technical community like Debian, but for a society filled with average Joes and Janes, not so much. Democracy needs trust, including the average person being able to understand how something as fundamental as voting works.

That's one of the main reasons my favorite is approval voting.

To expand on your point: there is one specific point that CGP Grey gets wrong in his IRV/RCV videos, which is that he says the system is not worse than first-past-the-post in any way.

On the contrary, FPTP adheres to the monotonicity criterion, which means you can't harm your preferred candidate's chances of winning by voting for them. In RCV, you actually can cause your preferred candidate to lose by ranking them too high in some situations.

As far as I know, approval voting is strictly equal to or better than FPTP on any reasonable voting system criterion, which I think makes it a better option. Also in its favor is that it's simpler and doesn't tend to eliminate compromise candidates who weren't anyone's first choice. Range and STAR are also both good systems.

What criteria is Approval not better than Plurality? Only one I can think of is simplicity (although I'd argue that plurality is only slightly simpler).

But approval doesn't have the favorite betrayer like ordinal (RCV/IRV/Condorcet) does. As far as I'm aware, cardinal systems are all like this. They are much more resistant to spoilers.

> I'd argue that plurality is only slightly simpler

I've actually heard it argued that Approval is simpler (for the voter) because all valid FPTP ballots are valid in Approval, but not the converse. There is definitely some benefit to a system that makes invalid ballots less likely (although that doesn't guarantee that the voter's intention is captured).

The difference in complexity for counting ballots, however, should not be understated. For elections with a paper trail, if you are putting each ballot in a single pile with other similar ballots, then Approval voting can require hundreds of piles. This can delay the process and add to the cost. Jurisdictions which rely on electronic vote counting can avoid this, but that introduces its own trust/legitimacy problems.

> I've actually heard it argued that Approval is simpler (for the voter) because all valid FPTP ballots are valid in Approval, but not the converse.

Voting systems can actually be optimal in two candidate systems. It is when you introduce more candidates that things get complex.

> For elections with a paper trail, if you are putting each ballot in a single pile with other similar ballots, then Approval voting can require hundreds of piles.

This would be poor counting. You need the same number of ballots as FPTP. You just sum multiple columns instead of a single column. The process isn't much different. This is actually the major advantage of approval over even other simple but better systems like score or STAR. It is dead simple to count and understand. Compare any of these to IRV/RCV (what the post is about) and they've got huge complexity problems. But Ireland is able to handle the many rounds of counting you need for IRV and they do it with paper ballots. Remember that Ireland and Australia already have IRV and I'm pretty sure Australia didn't have computers a hundred years ago. (I don't advocate for IRV btw)

> This would be poor counting. You need the same number of ballots as FPTP. You just sum multiple columns instead of a single column.

I'm not saying you need more ballots to implement Approval voting, I'm saying that FPTP has the nice property (when counting paper ballots) that the votes can be put into piles, where the weight of each pile is roughly proportional to the number of votes for the candidate whose votes are in that pile.

Of course, FPTP votes aren't actually counted using measuring scales, but the fact that this isn't possible with Approval voting is an indication that "just sum multiple columns" is a slightly more laborious and error-prone step than you make it sound, at least for humans counting paper ballots (which I believe is a necessary property of trustworthy elections).

Oh I see what you're saying. But I will point out that they successfully do IRV with paper ballots which includes many rounds of moving said ballots around. You wouldn't have nice piles with Approval, but it wouldn't be too hard. You're always going to have to add a little complexity to get benefits. The thing though is that Approval is the least amount of complexity we can add, and it gives surprisingly a lot of benefits. Maybe sorting would be a little more straight forward with Score or STAR voting since you can bin them on the highest score. These do have more benefits too and are actually preferred over Approval.

I think you're in agreement with me, unless I somehow said something backwards. I think that approval is equal to or better than plurality (FPTP) in every criteria I'm aware of.

(One criteria you could argue about is later-no-harm; IRV passes, but approval voting does not. It's kind of silly though to say that it's safe in RCV to put lower ranked options below your first choice when in RCV it isn't even always safe to put your first choice first. FPTP adheres to later no harm by not allowing you to vote for anyone but your first choice in the first place, so one could reasonably say that Approval isn't really worse than FPTP, except as a sort of technicality.)

I believe we're in agreement. I was coming to your defense since there seemed to be some confusion among readers who didn't like your extension. Maybe wording?

But yeah, I think on basically every metric cardinal is better than ordinal methods which are better than plurality. The whole IRV push seems odd to me when approval (or STAR) is both simpler, responds better to spoilers (the main concern?), and obtains a substantially higher VSE. I don't think IRV solves enough of the problems to make a meaningful difference (I've brought up Australia a lot in this thread).

I don't know about Australia but in Ireland most elections are done with proportional representation and the method is called Single Transferable Vote in that context (and has different properties). According to Wikipedia only the president (a role with little power) and by-elections are single candidate.

https://en.wikipedia.org/wiki/Elections_in_the_Republic_of_I...

IMO, this is a great way to do it and the proportional representation part is more important than the details of voting method.

STV is IRV (well slight variant: Single Winner STV). Fair Vote has muddled the name by calling it Ranked Choice Voting. This is dumb because there is a class of voting methods where you rank people (ordinal).

Ireland is doing better than Australia in terms of party control.

> IMO, this is a great way to do it and the proportional representation part is more important than the details of voting method.

And I 100% agree with this. The math does too. That's why I advocate so hard for a better voting system. In America we don't have that advantage (I want that too!). But everyone thinks that if we get IRV in Bernie could win. That's not how it works out.

Hey this is great! I've been looking for a decent poll site like this!

Some things I would like:

Could you randomize the initial order to avoid donkey votes?

I'd like it if there was an option to allow invited participants to add their own choices. For communal voting like "where shall we have breakfast" letting people add things would be good.

Also it would be nice to be able to drag some of the choices into a "I'm not voting for this" box or something. Or maybe just start all the options in the "I'm not voting for this" box and let people move them over? Not sure what would be easier.

Anyway thanks for making this.

Hey, thanks for checking it out!

Definitely planning to randomize the order. This is next on my todo list whenever I get back around to this site.

Adding your own choices is tricky UX-wise, because if person A votes, then person B votes and adds a new choice, person A's vote never took the new choice into account. When using this personally with friends, I've just aggressively solicited ideas beforehand to get around this. Definitely not a perfect solution though.

I really like the "I'm not voting for this" idea. Also, that would let you just click your votes in order, rather than having to sort a list. Will explore this idea!

When it comes to learning about voting schemes, I will always link to this: https://ncase.me/ballot/. Interactive simulations comparing different voting methods really tickle the nerd in me.

The conversation in this thread demonstrates why first-past-the-post voting is so hard to replace. There is no consensus on which alternative system to replace it with.

On the contrary, it shows that so many people with differing views share a common goal of replacing FPTP. I'm sure all the people here opposing FPTP would eagerly accept any of the alternatives being proposed, if it had a credible chance of being implemented in their jurisdiction.

The real barrier is that a change to the voting system would have to be approved by a party that is winning under the current system. Convincing a party to agree to any change is much harder than picking one of the many good options.

Also, I hope you don't mind if I mention that your point is eerily analogous to a dictator saying "We can't introduce democracy, because then people would disagree on who the leader should be."

So what's the solution here? Pick a system at random? Hold a vote? Neither seems quite satisfactory.

In practice, the decision-makers within a major party would look at which option would benefit them more than the other major party, and then a commitment to introduce that system would be added to their party platform, with it being implemented the next time they win an election.

For example, if the Democrats were afraid that the Green party would split their vote, they might support RCV. Therefore, arguably, the best strategy for bringing about voting reform might be to vote for the Green party, even if you don't support any other Green party policies, or any Democrat policies.

Are you asking the public or experts? Because I'd argue that a big reason there isn't consensus in the public is they don't even know about cardinal methods. With experts, I think most would approve of any cardinal. But of course nerds are going to squabble. That's what we do.

Amusingly this can be interpreted as that the vote for which voting system to use uses first-past-the-post so first-past-the-post wins.

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