[godelski]

> Arrow’s impossibility theorem

First off, Arrow's doesn't apply to all systems. You'll need to look into both Gibbard's and Gibbard-Satterthwaite's theorems.

Second off, just because you can't find a global optimization in a highly dimensional space doesn't mean there aren't local optimizations along criteria we care more about. Appealing to Arrow's is a cop-out.

> Approval voting I think is much too tactical and, strictly speaking, worse than IRV. No contest.

You're going to have to back this up with some strong evidence. Approval has higher VSE, is simpler, is more resistant to spoilers and tactical voting.

> IRV lets people express their preferences in a fairly understandable way.

Actually your argument holds true for any ordinal or cardinal system. Cardinal even having more flexibility since you can give two candidates the same score. And in cardinal if you want to rank your candidates, no problem. Better yet, you have better encoding opportunities because you can specify the distance between your ranking instead of the uniform spacing that ordinal systems force upon you. (BTW, given what the person above you wrote, I would assume that they know how ranked voting works and explaining how it is going to come off as you calling them dumb).

[magila]

One big problem with approval voting is that it presents voters with a difficult conundrum: what do you do with candidates you don't particularly like but would still strongly prefer over one-or-more other candidates? If people are too lenient with their approval it increases the risk of someone no one really likes getting elected over someone a majority would have preferred. If people are too stringent you start running into the same problems as FTTP.

Approval voting has some nice mathematical properties, but I think in practice trying to pidgeon hole people's preferences into a binary decision would be a major source of voter frustration and lead to tactical voting.

[godelski]

Fine, go STAR or Score/Range. Honestly I prefer those systems (in that order and I'd argue most people that are pro cardinal systems have that same preference[0]). Nice benefit is that people can bullet vote and we collapse to Approval which is a "good enough" system.

> but would still strongly prefer over one-or-more other candidates?

In fact, this is why I argue for STAR or score. It encodes information for better than a ranked (ordinal) system. In any ranked system you encode your preference with equidistant from one another. Where as when you score you can indicate a much stronger preference.

Here's an example. Let's say I REALLY like candidate A, moderately like candidate B, and strongly dislike candidate C.

Ranked:

A > B > C (with my encoding I'm saying that my preference of A over B is the same as my preference of B over C)

Scoring

A: 10, B: 7, C:0 (with this encoding I can indicate that my preference of A over B is not as large as my preference of B over C. Obviously we are capturing more information here)

Let's just encode information better, I agree. But also let's consider other factors like how easy it is to count the votes (which every cardinal system is going to beat ranked systems).

[0] That same preference where the distance between STAR, Score, and Approval is smaller than the distance between preference of Approval over IRV (e.g. STAR: 10, Score: 8, Approval: 7, IRV: 3, Plurality: 0).

[ad8e]

Small correction: The term "bullet voting" means voting for one candidate only (001000), rather than voting 0 or 1 on each candidate (101011). It is caused by low engagement from the voters, who only take the time to learn about one candidate, their favorite. It has been a problem for approval voting in practice, and it is unclear to what extent it affects score methods in practice.

I think STAR is slightly worse than Score, is comparable to Approval, is much better than IRV, and is likely better than Condorcet methods. STAR has some odd behavior which can be explored in a 3-person race. Score has less-problematic behavior caused by risk-taking with equilibrium voters (not like voters behave in any way similar to Nash equilibria though, and who knows what the real-world behavior will be).

However, STAR's main benefit may be in overcoming political resistance, if its properties are simpler to convince voters. Majority criterion sounds nice even when it is inefficient. Much like Top Trading Cycles losing to Gale-Shapley in school choice algorithms (excluding Boston).

[ClayShentrup]

There is absolutely no evidence that bullet voting has been a problem with approval voting.

https://www.rangevoting.org/BulletBugaboo.html

> I think STAR is slightly worse than Score

I would say they are probably roughly equal, but the best computer modeling we have shows that star tends to perform a little better.

https://electionscience.github.io/vse-sim/VSEbasic/

> However, STAR's main benefit may be in overcoming political resistance, if its properties are simpler to convince voters. Majority criterion sounds nice even when it is inefficient.

You're definitely correct on this.

[ad8e]

Out of respect for you taking the time to respond, I will elaborate my claims more specifically. My assertion regarding bullet voting is isolated to elections where the voting body cannot be bothered to engage carefully, because they barely care about the race. In addition, the drawbacks must be then compared with other voting methods, which may face the same bullet issue in equal measure. The bullet voting comparison I am making is between Score and Approval; I think Score will face less bullet voting than Approval does.

A typical example where bullet voting should occur is a down-ballot election. Examples of low-engagement elections at https://en.wikipedia.org/wiki/Approval_voting#Other_organiza... bear out that these elections degrade in behavior to plurality. However, it can't be determined just from this behavior that IRV or Condorcet would do any better.

> https://www.rangevoting.org/BulletBugaboo.html

1-3 have major engagement from voters and I do not expect approval voting to suffer unduly from bullet voting. 4, an alumni association, should. However, the question then becomes, what about other voting methods? Because if the voter has weak information on the other candidates, he may simply bullet vote under all voting methods. In this context, Score needs testing. Voting values between 0 and 1 would give a much better idea of how voter engagement is affecting their votes, rather than their second choice always collapsing to zero. This is why I claim that it is "unclear to what extent it affects score methods in practice". Granular cardinal scores in even one such election would mean a lot for determining voter behavior.

I do not support FairVote's arguments and consider them dishonest. Notice that in my original post, I carefully describe bullet voting as a consequence of low engagement, which is supported by past real-world low-engagement elections. This is very distinct from FairVote's arguments, which are not sophisticated and demonstrate a willingness to make blind claims. The distortions that FairVote argues for require more justification than they give.

> https://electionscience.github.io/vse-sim/VSEbasic/

I don't believe much in that simulation. While I agree with your characterization of it as the "best computer modeling" in voting theory, it would still be considered a fatally flawed paper under the standards of most fields, and I faced some heavy obstacles when trying to analyze it. I think this field needs more/better academics. I described some of my objections at https://news.ycombinator.com/item?id=27612876

[ClayShentrup]

> In addition, the drawbacks must be then compared with other voting methods, which may face the same bullet issue in equal measure.

A robust cross-system analysis shows that approval voting is more robust to strategy than almost any other method. Most ranked voting methods, for example, fail the favorite betrayal criterion.

https://electionscience.org/library/tactical-voting-basics/

[ClayShentrup]

1. Extensive game theoretical analysis, and even computer modeling, has shown that approval voting resists tactical behavior better than virtually any other voting method.

https://electionscience.org/library/tactical-voting-basics/

There's even an entire book focused on the game theory and tactics of voting methods, which advocates score voting, approval voting being score voting on a 0 to 1 binary scale.

https://electionscience.org/library/tactical-voting-basics/

Approval voting elections have been successfully held in 2020 and 2021 in Fargo in St Louis respectively, and there were no indications of voter confusion or anything like that.

https://electionscience.org/press-releases/st-louis-voters-u...

[klodolph]

I disagree that cardinal voting is understandable. It’s how we rate restaurants and review products on Amazon, and I don’t think it translates to an election with multiple options.

The issue here is not just how logical humans “homo economicus” behaves, but how actual voters behave.

Not really interested in engaging with the rest of this comment right now, but suffice it to say that I don’t think you’re accounting for human behavior in practice, which is messy and illogical. I don’t think it’s reasonable to say that I’m appealing to Arrow’s impossibility theorem as a cop-out—I’m saying that since we don’t have a game theoretic solution the the problem, we should look at the actual behavior of imperfect, irrational humans as the deciding factor.

[godelski]

> I disagree that cardinal voting is understandable. It’s how we rate restaurants and review products on Amazon, and I don’t think it translates to an election with multiple options.

I disagree but also don't see this as a problem. If you rank candidates you still get the majority of the desirable properties. Rank with non-equal distances, even better. Hell, it isn't even bad if you bullet vote (that's just approval voting). Investigating non-optimal ways of voting under any voting system is an extremely important analysis. So for the voter there is no problem. I'm also kinda put off that you give real world examples of humans using cardinal methods and then claiming that we can't understand it (HN is using cardinal voting...)

But we also have to consider the counting of votes side of "understandable." Plurality is pretty damn easy, and this is clearly why we use it. Approval is almost as easy (just just sum multiple columns). Range/Score isn't much harder. Then STAR introduces 2 rounds of counting. Then we look at IRV and we see that we have tons of rounds. This isn't typically so bad in a presidential election where there are realistically about 4 candidates, but that complexity increases real fast elsewhere. Just watch NYC. There's going to be at least 5 rounds (probably more). This is far more complex. We only have to look at Arizona to understand why this part of the "understandable" question is important.

[justinpombrio]

For anyone like me who hadn't heard of Gibbard's theorem, it's actually even simpler (and more depressing) than Arrow's theorem. To quote Wikipedia:

For any deterministic process of collective decision, at least one of the following three properties must hold:

1. The process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome;

2. The process limits the possible outcomes to two options only;

3. The process is open to strategic voting: once an agent has identified their preferences, it is possible that they have no action at their disposal that best defends these preferences irrespective of the other agents' actions.

https://en.wikipedia.org/wiki/Gibbard%27s_theorem

----

So basically, it's impossible to completely eliminate strategic voting. No matter the method: ranked vs. cardinal vs. anything else you dream up can't help.

[godelski]

> it's impossible to completely eliminate strategic voting. No matter the method: ranked vs. cardinal vs. anything else you dream up can't help.

I think this comment is a defeatist at best and deceitful at worst. Just because there is no global optimization does not mean that all optima are equal. We can in fact have optima that are better than one another (including all optima we know about!). This is a common feature of highly dimensional solution spaces.

The big issue here is that not all criteria are weighted equally, by desire of effectiveness. So we find an optima where we optimize features that have a large weights and care less about optimizing features with small weights. By doing this we can compare systems in their desirability and select the best ones. This is not cause for throwing up your hands and giving up.

As an example: cardinal systems, when compared to ordinal (ranked) systems, are more resilient to strategic voting and simpler (both for the voter and for the people tallying the votes, aka transparency). The cost? Slight decrease in maximal VSE. BUT if we look at the min, mean, median, or modes of VSE given different strategies cardinal system outperform ordinal (aka, desirable). You can see this by comparing with this chart[0]. For example with STAR0-10 we have maximal VSE of .983 and minimal of .912 (actually this makes it strictly better than plurality!). But if we look at our best ordian, RP, we see RP has a maximal VSE of .988 and minimal of .870. So on terms of maximal there's a 0.005 difference but on minimal there's a difference of 0.042! We can easily tell here that STAR is much more resistant to strategic voting than RP (Shulze is even worse!). Doing the same for IRV we see .07/.115 (max/min comparison of STAR0-10 vs IRV on VSE).

So we can compare. We can select better methods. But is there a ''perfect,, solution? No. But don't let the lack of the ability to create a perfect system detract from the ability to compare systems. Not all is lost.

[0] https://electionscience.github.io/vse-sim/vse.html

[justinpombrio]

> I think this comment is a defeatist at best and deceitful at worst.

Wow, very HN! I don't actually mind very much, but seriously, consider applying the principle of charity?

I agree with you, and did before you wrote this comment too! Hence my use of the word "completely". I was just surprised that strategic voting couldn't be completely eliminated; before yesterday I expected that you could, in exchange for losing other nice properties. Of course being impossible to eliminate completely doesn't mean it shouldn't be minimized.

[pksebben]

according to Wikipedia:

>Gibbard's theorem states that a deterministic process of collective decision cannot be straightforward, except possibly in two cases: if there is a distinguished agent who has a dictatorial power, or if the process limits the outcome to two possible options only.

.. it also mentions that gibbard's is specifically about irv.

All that aside, I can't understand the idea that we only get to change things once. My understanding of history is at odds with the concept.

[justinpombrio]

> .. it also mentions that gibbard's is specifically about irv.

No, Gibbard's is not limited to any particular voting method. I think you're misreading the next paragraph (and also confusing IRV, which is a particular method, with ranked choice, which is a whole category of methods). Note the distinction between Gibbard and Gibbard-Satterthwaite:

> A corollary of this theorem is Gibbard–Satterthwaite theorem about voting rules. The main difference between the two is that Gibbard–Satterthwaite theorem is limited to ranked (ordinal) voting rules: a voter's action consists in giving a preference ranking over the available options. Gibbard's theorem is more general and considers processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates.

[godelski]

> it also mentions that gibbard's is specifically about irv.

This isn't true

> I can't understand the idea that we only get to change things once.

Those of us concerned about IRV and promoting cardionality actually looked at history. Between 1910 and 1920 40 US cities used Bucklin voting (similar to IRV, slightly better even) and all repealed them[0]. So looking at history we see that people recognized the need for a better voting system, implemented something similar to IRV, saw that it didn't make things better, and subsequently said "fuck it, we'll go back to FPTP because it is easier." (I should also mention that in Australia, since 1949, 90% of Lower House elections, which use IRV, are equivalent to using FPTP[1])

So we're looking at history (and modern times) and saying "hey, this didn't work and actually ended up causing us to take a step backwards. Maybe we shouldn't repeat the same mistake."

I hope this clarifies our differing understanding of history.

[0] https://clayshentrup.medium.com/momentum-e5fd12ffce2a

[1] https://en.wikipedia.org/wiki/Australian_House_of_Representa...

[pksebben]

A little, I think we may have different ideas about what the difficulties were in the early 1900s vs now - I believe that the circumstances are different enough now that broad conclusions about what is and isn't feasible cannot be drawn, but that's just a piece of the puzzle and I think your point deserves merit.

What I would ask, then, is rather than not doing IRV, what should we do, in your opinion?

I'm looking at this as a sort of crisis situation, as our ability to affect our politics is in a state of constant erosion, and the process of capture at work here can only end in systemic collapse - the further power gets concentrated, the more centralized our decision making becomes, and the more vulnerable we become to systemic single point of failure.

I would love to see STAR voting become a thing. I think of IRV in the current context as a proof-of-concept that might show people that we can change the structure of voting. I can't see anyone wanting to go back to FPTP, because I don't really see anyone who thinks it's even remotely working.

[logicchop]

> Cardinal even having more flexibility

I thought Gibbard-Satterthwaite (or maybe just Gibbard's version) applied to cardinal systems as well. This seemed likely to me for some reason, as if an ordinal method could approximate any particular cardinal discretization by just including "ghost" candidates that can be packed (ordinally) between your actual candidates.

[godelski]

> I thought Gibbard-Satterthwaite (or maybe just Gibbard's version) applied to cardinal systems as well.

Correct, but it is also a weaker version of Arrow's (also as Clay points out, Arrow's isn't really about voting[0]...)

> This seemed likely to me for some reason, as if an ordinal method could approximate any particular cardinal discretization by just including "ghost" candidates that can be packed (ordinally) between your actual candidates.

Okay, but this just adds complexity. Cardinal is already simpler than ordinal systems (both for voters _and_ for those counting the votes). There's absolutely nothing wrong ranking candidates in a cardinal system (it's actually pretty unlikely that you'll have the same preference for multiple candidates so this is going to naturally happen). The difference? In cardinal you can better express your preference of one candidate over another (I give an example here[1]). So now we've added "encoding efficiency" to the added benefit of cardinal systems.

Cardinal systems are better than ordinal systems in almost every single way (the only thing I can think of ordinal systems doing better at is that RP and Schulze perform better on maximal VSE, but as I discuss here[2] that is pretty limited as well as unlikely considering strategic voting and the ability to manipulate people exists).

[0] https://news.ycombinator.com/item?id=27598975

[1] https://news.ycombinator.com/item?id=27599324

[2] https://news.ycombinator.com/item?id=27600248