While people aren't likely to cast votes that are perfectly related to utility, I still see scores as more akin to utility than to something like money, where the increase in utility drops off the higher up the scale you go.

So what I'm saying is that I see a 5 and a 0 as in the same ballpark as a 3 and a 2, rather than the 3 and 2 being preferable for equity reasons.

How good score voting is generally is a separate debate obviously, but where it gives the same tie as a pairwise method, I don't see any reason in principle to prefer one result over another. But as a tie-break, it's probably fine to choose the result you might consider less divisive.

An interesting follow-up question would be whether you would consider divisiveness over score where there isn't an exact score tie (but is a pairwise tie still) or whether it's only useful as a tie-breaker. You could, for example, reduce C's score of 3 to 2. That way, the pairwise result is still a tie but on average scores, A and B are now marginally ahead of C despite being more divisive. Is there still an argument to elect C?

Well, it partly depends on what you do with equal ranks or incomplete ballots. If an unranked candidate is scored as 0 then a 4-3-2-1 system would be different from 3-2-1-0. But if it's done in a more sensible way, they would be equivalent.

@multi_system_fan It's quite interesting, although allowing more than one round of voting changes things quite a lot, and there are probably also other alternatives that might be as good or better.

I don't think you could apply it to the metric being considered in this thread though.

Yeah, I mean ChatGPT has some big holes in its ability (as I've complained about), but it's also a bit scary what it's capable of sometimes. I don't think anything we can do is off limits in principle to a ChatGPT type thing.

Well, aside from that, I think Arrow's Theorem is overstated in terms of its importance anyway. Pretty much all ranked-ballot methods fail IIA and if they don't they are unreasonable in some other manner. This has been known for ages anyway as it is a logical consequence of the Condorcet paradox.

So Arrow's Theorem was no great paradigm shift in our understanding. It's a non-event if you ask me.

@rob Well I'd be happy for you to run it if you think you can do good things with it. I definitely think this is a better forum for discussion anyway than the Election Methods mailing list (which is very 90s), although persuading all of those users over here might be difficult.

@robla said in Paradox of Causality from Arrow’s Impossibility Theorem:

Kenneth Arrow absolutely deserved his Nobel Prize, because Arrow's Theorem was (and is) a big deal. The exact choice of criteria was beside the point; what Arrow did was describe a few "common sense" criteria and then showed them to be mutually exclusive.

But my point is that we already knew that. Amongst Arrow's criteria is IIA. And that's the one that always fails in reasonable methods. It's not like some methds fail this, others fail that. How many methods are there that are just dictatorships, for example? It's IIA all the way. Arrow's Theorem can be reworded in plain English as "With a few reasonable background assumptions, any reasonable ranked-ballot voting method fails IIA." And that has been known for centuries. Arrow just dressed it up differently.

I suppose he's used that assumption because a hereditary monarch is essentially a leader arbitrarily picked, like in random winner (as opposed to random ballot). But this is obviously very simplistic. When you have an all-powerful monarch versus some other system, the entire political and cultural landscape is likely to be very different and that isn't modelled by this.

I've been looking at this and I don't think it is the best. One (minor) problem is that when you're summing the scores, for voters that haven't had any candidates elected and also gave a score of 0 to the candidate in question, you get 0/0. Obviously you just need to count it as 0 to get it to work, but it can make one suspicious that there are problems lurking beneath.

But the main problem is that it fails scale invariance. Well it passes in a multiplicative way as it is defined on the wiki, but not if you add to the scores.

For example, if everyone scores 1 to 10 instead of 0 to 9 (so just adds 1 to every score), you can get a different result. KP + SPAV (also known as Sequential Proportional Score Voting or SPSV) passes this. I know it might seem unsatisfactory to "split" the voter with KP, but in terms of passing criteria, it seems to do the job.

@wolftune I'm not sure this is just an Allocated Score thing. I think that sequential methods that start by electing the candidate with the highest total score and go from there are always likely to have this sort of thing happen. Non-sequential methods may avoid it more easily, but that's obviously more expensive computationally. The other option is to not go by total score.

@jack-waugh said in Revisiting Quadratic Voting:

@cfrank https://votingtheory.org/archive/posts?where={"topic_id"%3A541}

Also this.

It seems like something that someone would make up, tell a few people about and they'd go "Nah". Arbitrary and pointless. I mean, why should your vote be worth more if you vote for more candidates?

@masiarek That's quite interesting, but converting ranks into scores like that rests on some dubious assumptions. So I don't think the score and STAR results are valid.

Also, I haven't read the paper so don't know how they technically define that criterion, but it doesn't pass it as it's worded in English. Say we have:

35: A>B>Everyone else
33: B>A>Everyone else
32: Everyone else>B>A

Under IRV, B will win this election. That doesn't pass "majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose."

@masiarek said in Condorcet, IIA, monotonicity in RCV IRV:

IRV is the only voting method to satisfy ordered majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose.

I'm not sure that this is even a good thing. If there are two candidates who might win - A and B - why should only people who like A and B get any say in who is elected? Someone might dislike them both, but still much prefer one to the other. I see this as a bad criterion.

@sass said in Ranked Robin Disadvantages -:

As I've thought about it more, if there's a Condorcet Winner, then cloning is irrelevant under Ranked Robin, making it an unreliable strategy.

It's not just about strategy though, as said above. A potentially "wrong" result could still happen by accident.

Also, basically all Condorcet methods fail Participation. It comes with the territory.

Yes, it's very hard for methods to pass it in general. So relative to other Condorcet methods this doesn't count against Ranked Robin.

Moreover, focusing on pass/fail criteria is the issue that caused voting enthusiasts not to achieve real-world progress for 200 years. The question is not "Does this method pass this criterion 100% of the time?"; the question is "How well does this voting method perform on this metric in practice?". Considering that cloning is only helpful under Ranked Robin when there's no Condorcet Winner and that scaled elections without Condorcet Winners are incredibly rare and difficult to predict, I see it as a nonissue.

I agree that overall performance (however one might measure it) isn't necessarily the same as just how many criterion boxes you can tick. However, if a method does fail a criterion, it still doesn't look good if there is another method that is as good elsewhere that also passes this criterion.

And just to set the record straight, I think Approval and Score are great methods. I absolutely support them and would be very happy to see their use in public elections.

That's good. I think they and Condorcet methods have merit.

@Toby-Pereira I was on mobile, so the link didn't copy properly. Here's the section discussing frequency of ties:
https://electowiki.org/wiki/Ranked_Robin#Frequency_of_ties

OK thanks, but I'm not seeing anything to suggest that a three-way cycle would not be the most common tie.

I need to clean up the electowiki page, but the Equal Vote site on Ranked Robin is a much better reference:
https://www.equal.vote/ranked_robin

Thanks for the reference.

@cfrank said in Ranked Robin Disadvantages -:

@sass I appreciate your perspective. However, if the power is concentrated in parties rather than in individual candidates, then election packing is a perfectly valid concern for methods that fail independence of clones. We can’t judge a voting system by the economic landscape reinforced by a different system, it needs to be recognized that market forces will lead to adaptation. I think, personally, that independence of clones is a far more important criterion than participation, for example, since for the most part voter activity is individual whereas party and media activity is more centralized. I would like to see how the members of this forum rank the various criteria in importance (in terms of having a “high probability” of compliance).

I think something like ranked pairs is an excellent single winner system, even though it fails participation. I also think approval voting is excellent, even though it fails the Condorcet criterion (but gets close in a sense). On the whole, my thinking is that proportional representation with some clever system of checks and balances to mitigate block formation would be even more excellent.

On criteria, I would say that participation is very important, or at least it would be if it wasn't incompatible with so many methods. But this is one reason why I like score and approval - they both pass it. What else does? Borda - well that's awful. Then you have Descending Solid Coalitions. and Descending Acquiescing Coalitions. Oh and First Past the Post. Of them, I would say only score and approval are reasonable methods.

But generally, monotonicity and independence of clones are "cheap" enough that I think there's little excuse not to have them.

@jack-waugh said in Condorcet Score:

@cfrank, Ouch!

OK, then, how about this one?

Collect Score-style ballots. If there is a Condorcet winner, elect her. Otherwise, elect the straight Score winner.

I think Smith//Score is better than Condorcet//Score. Condorcet//Score could elect the Condorcet loser.

Or what I was discussing here, which I think is just Landau//Score. But maybe that's getting a bit complex.

@Sass, thank you for your post.

@sass said in Ranked Robin Disadvantages -:

A few things, all.

@masiarek, if I rank candidate A first, candidate B second, and candidate C third, then I know the order I prefer each, but not by how much compared to each other. If I had a 5-star ballot, I might give A 5 stars, B 4 stars, and C 0 stars; or I might give A 5 stars, B 1 star, and C 0 stars. There’s no way for you to determine how I really feel about B based only on my rankings. However, if I start with a 5-star ballot and give A 5 stars, B 3 stars, and C 0 stars, then you know for sure that I would rank A first, B second, and C third. You can always extract a full set of rankings from a set of scores, but usually you cannot extract a full set of scores from a set of rankings. Scores contain strictly more information than ranks; therefore, a score ballot allows voters to express more information than a rank ballot, i.e. score ballots are more expressive.

This only applies if the score range allows for it. A STAR 0 to 5 ballot does not allow for a full ranking of candidates if there are more than a handful standing, so it's not really very expressive.

@Toby-Pereira, you are overestimating the frequency of Condorcet cycles in real-world elections. As more people have studied the question, the estimates have gone down and down.

Additionally, Ranked Robin fails clone independence in the opposite direction of Choose One Voting. This means that to gain an advantage, a party would have to support entire campaigns of multiple candidates who are seen as identical by the electorate. This is so difficult in practice that it legitimately can be dismissed as a real concern. Candidates like to differentiate themselves from each other, electorates do not behave predictably, and campaigns are egregiously expensive. These difficulties are further amplified under a method like Ranked Robin that incentivizes candidates to appeal evenly to the entire electorate (see @Marcus-Ogren’s new paper on Candidate Incentive Distribution).

A party could field two candidates, or if that's not allowed, then essentially get round it by having a B party that's basically the same. These candidates would not want to differentiate themselves from each other because they'd be there as part of a grand plan.

In any case, it's not just about intentional cloning. It's like how IRV fails monotonicity. An IRV proponent might say that it's too hard to vote strategically to take advantage of this, but that doesn't matter. It might affect things anyway. Ranked Robin's lack of clone independence could affect a result, intentionally or not.

Also, if there’s not a Condorcet winner, then there are multiple scenarios more likely than a top-3 cycle that Ranked Robin resolves simply. Check out the electowiki.

https://electowiki.org/wiki/Ranked_Robin

I'm not sure exactly what I'm looking at. It's quite a long article. What's more likely than a top-3 cycle when there isn't a Condorcet winner?

Furthermore, your claim that Ranked Pairs is simple is…absurd. I canvass for STAR Voting, a far simpler method, every day, and it truly is at the limit of what we can expect lay voters in America to digest.

Simplicity actually is the most important factor for a Condorcet method because…it’s a Condorcet method. By that metric alone, it excels at both accuracy and honesty, and is also sufficiently expressive.

Ranked Robin may well be simpler than Ranked Pairs, but I still think Ranked Pairs is a relatively simple method. Plus, the way Ranked Robin is presented on that wiki article, it doesn't look simple. Those 8 levels of when there is a tie - what is going on there? It's horrific.

Also, other than Ranked Pairs, there's also Benham's Method. This is just elect the Condorcet winner if there is one. Then eliminate the candidate with the fewest top ranks and carry on until the is a Condorcet winner. Like IRV except the winning condition is being the Condorcet winner rather than having >50% of the votes. This is fairly simple too and cloneproof.

Or something like Smith//Score.

Another STAR alternative, discussed here is to provisionally elect the score winner. Then see if that candidate is "covered" by any others. If so then provisionally elect the highest scoring candidate that covers it. Carry on until the provisionally elected candidate is uncovered.

Basically, candidate A covers candidate B if every candidate that pairwise beats A also pairwise beats B, and at least one candidate pairwise beats B but not A.