Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?

I would expect every single-winner method to be subject to Duverger's law

cfrank

@andy-dienes I see, interesting. I’ll have to learn more about multi-winner systems. Are there any you like in particular?

@cfrank Pretty much anything proportional is good. That include party-list, STV, and a few approval-based PR rules.

I am currently working with the folks behind STAR to design a proportional method they can promote. My preferred option would be TEA but there are a number of design options on the table.

rob

@andy-dienes What about something like anti-plurality? Seems to me it should have the opposite effect. That is, it encourages factions to nominate more, rather than fewer, candidates (since that would split the "negative votes" which would work in their favor).

Maybe there are different incentives, that still result in parties forming, but to me the whole basis of Duverger's Law is vote splitting (specifically the kind of vote splitting that results in similar candidates harming each other), so if you remove that effect I can't see how Duverger's Law would apply.

(obviously I'm not a fan of anti-plurality, but.... For and Against isn't so bad. It should negate most vote splitting, since it combines plurality with anti-plurality.. I still don't like it because, like Approval, it incentivizes following the polls)

@rob I don't see Duverger's law to be a statement so much about the number of candidates as it is about the number of social cleavages / political parties.

It's true that stuff like anti-plurality or Borda are highly susceptible to clone (teaming) strategies, but I think this will still manifest as only two parties each nominating as many candidates as they can. Each party will still prefer "anybody on my side" over "anybody on that side"

rob

@andy-dienes said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

I don't see Duverger's law to be a statement so much about the number of candidates as it is about the number of social cleavages / political parties.

I'm not sure what you mean by this. Are you saying that the number of social cleavages exists independently of the voting method? (If so, I guess I'm not on board. I think the number of social cleavages is artificially introduced by the voting method)

As I said I'm not a fan of anti-plurality, but mention it because it causes the exact opposite incentives as plurality. If it causes some sort of effect, I'd expect it to not fall under Duverger's Law.

Also, you don't really need a party to nominate multiple candidates from the same general faction (such as under anti-plurality). The main thing parties do under plurality is discourage candidates from running if they are likely to split the vote. You can't really do that effectively without an official organization. (and sometimes they still fail to do it, such as the Democrats failing to get Nader to simply run as a Democrat and be subject to being eliminated at the primary).

In any case, a system like For and Against should balance the two opposing incentives. So even if you say parties would still form under anti-plurality to do the opposite of what they do now (i.e. add rather than eliminate candidates), this effect would not be there under a system where similar candidates have a neutral effect. (whether that be For and Against, Approval, a good Condorcet method, etc)

These are some old (7 and 10 years, respectively) things I posted about it on Quora, aimed at a mainstream audience. I'd be interested in whether you (or anyone) disagree with the gist of them. They remain representative of my core thinking on the subject, and frankly, the reason why I'm here.

https://www.quora.com/Whats-so-bad-about-plurality-voting/answer/Rob-Brown-13
https://www.quora.com/How-could-we-fix-the-root-problem-s-in-US-politics/answer/Rob-Brown-13

They both use this graphic I made, which I kind of like for explaining the artificial polarization that I think is caused by plurality's vote splitting:

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

Are you saying that the number of social cleavages exists independently of the voting method?

Pretty much yeah. Social & demographic affiliation drives policy preferences much more strongly than the other way around. This is known sometimes as the "funnel of causality." It has been studied from a couple different angles by various political scientists but maybe the most notorious work is Democracy for Realists by Achen and Bartels.

Remember an election is about much more than the tabulation algorithm. There are months and months of campaigning with different social groups pooling resources (donations) and sorting into different camps. For pretty much any voting method, more money for campaigning and more popular support ----> higher chance of winner. Duverger's law is more about this process of partitioning voter space into two camps like this before the election even happens, regardless of the selection algorithm used.

If more than two parties are desired, there's pretty strong evidence to believe that can only be obtained by proportional representation. Condorcet, approval, IRV, and whatever else would be a great improvement to our democracy, but I do not think any would give us more parties represented in government.

While it is true that Nader was not a major party candidate, but was likely the Condorcet winner, I do not think this is a counterexample to Duverger's law, since we do not know how the positions & endorsements of the parties would have changed under the counterfactual where a Condorcet method was used---that is to say, one of the parties would likely move to wherever Nader was! My expectation is that better single-winner voting methods make a two-party system perform better and make parties more responsive to voters, but I do not expect to see more parties.

rob

@andy-dienes said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

Duverger's law is more about this process of partitioning voter space into two camps like this before the election even happens, regardless of the selection algorithm used.

I've always seen Duverger's Law defined specifically as related to voting method. "Duverger's law is a principle which asserts that plurality rule elections structured within single-member districts tends to favor a two-party system". Plurality being a key factor.

@andy-dienes said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

but I do not think any would give us more parties represented in government.

I'm not after more parties.... I don't like parties. (not this kind, anyway) I'd be just as happy to see more independents elected than just members of some party other than Democrat and Republican.

I'm after parties becoming less dominant, less tribal, less associated with people's identities, less vitriol between them, and so on. If they still exist, fine, but if they exist in a way that results in what we've seen in the past 7 years (including widespread election denialism, conspiratorial thinking, etc), that's bad.

Regardless I don't see PR/multi-winner having much impact in the US, since it would require too many structural changes to happen, at least in national politics. I see the momentum being better methods for electing single winners.

@andy-dienes said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

While it is true that Nader was not a major party candidate, but was likely the Condorcet winner,

Wait, Nader the Condorcet winner? I've never heard that. Perot might have been in 92, but I saw Nader as being further to the left than Gore, and therefore unelectable under any system. I saw Nader not as a counterexample to Duverger's Law so much as a counterexample to parties being able to pressure ideologically similar candidates to either join their party (and be subject to elimination at the primary stage) or to not run at all. He resisted that pressure. Whether or not he regrets it, I think not many would want to be in his place.

The fact that, for instance, Bernie Sanders didn't run as an independent in years since shows that that pressure still exists following Nader.

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

Regardless I don't see PR/multi-winner having much impact in the US,

I definitely don't agree here but I think Matthew Shugart among other preeminent political scientists can probably defend the idea more eloquently than I can

Open letter to congress to end single-member congressional districts and adopt proportional representation

Emergency electoral reform OLPR for the US House

Wait, Nader the Condorcet winner? I've never heard that.

Sorry, brain fart, you're right. Gore was likely Condorcet winner. I'll use the "I couldn't read yet when that election happened" defense

rob

@andy-dienes Regarding PR/multi-winner, I don't disagree that multi-winner would be far better than the status quo if adopted, but I just don't see it being adopted widely any time soon, at least not in places where it would change a lot. I'd think you'd need to adopt RCV (or approval or STAR or whatnot) before multi-winner in most cases.

And multi-winner doesn't apply to things like president and governors and mayors, so there's that. (notice that even presidential elections are no longer entirely choose-one.... in Maine they are already using RCV for presidential elections, which admittedly has weird implications: https://www.votingtheory.org/forum/topic/182/what-are-the-strategic-downsides-of-a-state-using-a-non-fptp-method-for-presidential-elections )

I looked at those articles, and what seems missing is a realistic path from here to there. I see things like "this fix would require only an act of Congress," which, by using the word "only", strikes me as incredibly naive of the current state of affairs.

cfrank

@rob only an act of Congress, only the same requirement for a declaration of war! Lol.

Hopefully local legislatures steadily incorporate PR, I think certain state governments are just as farcically representative as the whole nation.

rob

@cfrank Note that one definition of "Act of Congress" is:

(idiomatic, US, chiefly colloquial) Authorization that is extremely difficult to get, especially in a timely fashion.
Does it take an act of Congress just to get a stop sign on a corner?

But yeah, PR is fine as long as it isn't party-list based, which really rubs me the wrong way. I like more general solutions. One thing I like about about single winner is you can learn about it and use it for voting for all kinds of things that aren't political.

Most of the stuff that talks about PR comes off to me as people are grasping at straws to use black-and-white logic to describe things that intrinsically lie on a spectrum. Like, you don't have "representation" unless "your party" has a member in there. To someone who considers themselves an independent, that simply doesn't compute.

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

To someone who considers themselves an independent

Do you think that if there were, say, 10 parties, that none of them would be likely to closely match your desired platform?

rob

@andy-dienes said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

Do you think that if there were, say, 10 parties, that none of them would be likely to closely match your desired platform?

Maybe, it's hard to know. Does this apply to both national and local elections?

I think the biggest issue for me is that people are assuming that they don't have representation if no one from their single, specific party is elected, and to me that is just silly black and white thinking. And I think it’s destructive to the goal of getting better voting systems out there, when people think that if you don't have this ideal (which I think is based on a fallacy), why bother? Since it doesn’t apply to all offices (some are single winner by nature), it isn’t a full solution. It’s twice as much that we have to educate people about.

And of course there's also the issue of, what if I agree with some candidates on all their policies but I don't like them as a person? Maybe I don't think they're very smart or eloquent. Maybe they agree with me on all the policies but they prioritize them differently than I do. When I vote for humans, I can factor that in.

I just don't understand why introduce this extra layer of indirection into the process, while persisting the idea that everyone has to have a tribe, or fit neatly into a box.

It reminds me of ordering cable, where I can’t just pick the channels I want and pay a reasonable price for that. They make me pick one of several “packages”, which is just annoying. It also reminds me of high school with all its little cliques.

Ultimately I am against tribalism. Maybe having ten tribes is better than having two tribes, but it’s still tribalism.

Maybe someone can tell me what PR would give us that single winner -- but selected with a good method such as a Condorcet compliant one -- doesn't.

@rob said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

Maybe someone can tell me what PR would give us that single winner -- but selected with a good method such as a Condorcet compliant one -- doesn't.

The ability to represent in government minority groups who are not a majority in any particular geographic location. This is commonly known as the "Massachusetts Problem," named after the difficulty of drawing districts in MA to give Republicans adequate representation.

rob

@andy-dienes And what I'm saying is, the terms “minority” and “majority”, when used as you just did, are essentially meaningless. Maybe a better way to say it is, they don’t hold up under deep scrutiny. I would argue that looking at things that way makes it harder for people to arrive at anything approaching a consensus, because it ignores those in the gray area / middle ground. In other words, it is a “false dilemma”, i.e. “an informal fallacy based on a premise that erroneously limits what options are available.” ( https://en.wikipedia.org/wiki/False_dilemma )

Would you be willing to give an example of a “minority group” as you use it above? One that is well defined, and appropriately sized (say, somewhere between 5% and 30% of the population) such that party-line PR would be effective for dealing with it.

Am I in a minority group because my ancestry is 100% from the British Isles? Normally I’d think I’m as majority as they come in terms of my ethnicity, but technically less than 10% of the US population has such pure Anglo ancestry. But if you simply change where the dividing line is, and divide people into white vs non-white, now I’m comfortably in the majority. (the US being about 75% white)

And I think this applies to all groupings and issues. Jack mentioned abortion as one that is inherently black and white (i.e. pro-choice and pro-life, with little in between). Pro-lifers are apparently in the minority by that way of looking at it. But you can very easily change it to “those who support some degree of restrictions on abortion” and “those who think there should be zero restrictions on abortions”, and you get a different group as the majority. ( https://www.votingtheory.org/forum/topic/244/are-there-any-issues-that-have-no-reasonable-middle-ground?_=1664296838846 )

I could go on. Ok I will.

Temperature. If you divide it into “those who like it below 72 degrees” and “those who like it above 72 degrees”, the former is the majority. Change the dividing line to 69, and now the majority shifts to the other side. Speaking of minority and majority here is obviously unhelpful, if the point is to decide what temperature to set the thermostat to.

Guns. There is a middle ground there too, so again, the concept of majority and minority doesn’t make sense:: https://www.ajc.com/news/opinion/opinion-yes-there-middle-ground-guns/2GrspjlI1AhT56V0aNKf6L/

Military interventionism. There are people who think it is appropriate for the US military to get involved in foreign situations in limited cases for humanitarian purposes, but otherwise should stay out of foreign conflicts. Middle ground.

Police. There are people who think that police brutality and racism is a real thing to be taken seriously and addressed, while agreeing that having police is overall a positive and that calls to “defund” them are not helpful.

And on and on and on.

So my argument is, if you get rid of the “majority” and “minority” terms, and think in terms of everyone having preferences that generally tend to lie on a spectrum, the arguments for party-based PR don't hold up. (when compared to "median seeking" voting methods for electing individual candidates)

Re: the “Massachusetts problem”.... you probably aren't surprised that I suspect that the root of the problem comes from the implied assumption that people neatly divide into Republican and not-Republican. I think that is an artificial distinction that has arisen (mostly) as a side effect of centuries of choose-one voting methods. As soon as you step back a bit to view people as individuals, whose views and preferences lie on multiple spectrums (and of course may or may not correlate to varying degrees with those we consider “Republican”), the problem -- if it is still a problem -- looks a lot different.

@rob

Voter candidate choice tends to be driven by demographic factors and social pressure significantly more strongly than it is driven by any romanticized idea of policy or ideology.

If you pick basically any minority group based on ethnicity, income, ability, age, profession, religion, nationality, etc. etc. you will find that not only are they underrepresented in the legislature, but that it can be difficult to draw single-winner districts at all such that these communities could get a seat, even if one were to intentionally set out to do so.

Splitting seats up by geography is one way to guarantee some amount of diversity, but doesn't it seem to you like sort of an arbitrary axis along which to slice people? Why not split seats up by income level? Or gender? PR lets voters choose which of these axes they lie on matter most to them.

cfrank

@rob I think you could consider two groups of people such as those who have reasonable confidence that they are "adequately represented" in government, versus those who have reasonable confidence in the opposite direction. Then maybe there’s also some middle zone of suspicious, uninformed and misinformed people, and you could lump them into the mix. But I think we want to make the first of those groups as large as feasible and the second of those groups as small as feasible.

Obviously what constitutes adequate representation to a person is highly individual and depends on values and special interests, but it has a pretty unequivocal normative meaning once hypocrisy is removed. I think the second group is pretty close to what I would consider “the minority,” even though it has nothing to do with whatever fraction of the electorate it constitutes. PR even with parties seems to pretty decently address adequately representing a much larger fraction of the current minority than the present situation could hope to accomplish.

Also, there just has to be some kind of non-compensatory means of narrowing down the pool of candidates. I think political parties and primaries are reasonable and I'm not sure how else it would be done. The problem to me is a small number of large parties with a serious lack of accountability to public interests, not necessarily the very existence of parties. It would be ideal to be able to have a smooth spectrum of choices and the ability to elect based on the candidates alone, but I don’t think that can be accomplished without untenable sacrifices in efficiency.

When it comes down to it, potential candidates need to gain recognition, support and traction with a significant base, otherwise they have no chance of even getting on the map, since there is limited bandwidth. Granular parties don’t seem problematic to me, I think particularly binary ones though just in theory don’t have enough resolution to represent public interests, even ignoring externalities like polarization.

@rob

Just to expand once more:

https://twitter.com/mcpli/status/1574795032967712773

Check out the gerrymandering shenanigans happening down south *right now*

Due to incredibly racially polarized voting, Black voters can get a majority in only a single district. This is not an effect of FPTP vs Condorcet vs Approval vs whatnot---since we are talking about true majorities here the results will all be the same.

Proportional representation means that gerrymandering like this is impossible, or at least significantly more difficult and for less potential impact.

rob

I'll put my TLDR at the beginning, but the rest of this post (which of course I wrote first) supports it in some detail.

"outlier" is a more generalizable and clearly-defined concept than "minority"
"equal power to move the results toward their preference" is a more generalizable and clearly defined concept than "equal representation"
You don't need to bring in parties or multi-winner positions to make sure outliers have equal power to move the results toward their preference

So....

@cfrank said in Are Equal-ranking Condorcet Systems susceptible to Duverger’s law?:

I think you could consider two groups of people such as those who have reasonable confidence that they are "adequately represented" in government, versus those who have reasonable confidence in the opposite direction.

Sorry but I don't understand that distinction. Based on what the voter's themselves have reasonable confidence in? If we can't define the concept in non-vague terms, how would we expect voters to have a reasonable or meaningful perspective on it?

Maybe you could explain it in terms of the temperature example I keep returning to: that is, something where there is a variable value and voter's individual preferences are single peaked. (making it more mathematically "pure" to ease analysis)

If someone happens to prefer the thermostat be set at 69.5 degrees, and 70 degrees happens to be the median preference (and therefore the "winner" under reasonable voting methods, including Condorcet), does that person have more "representation" (*) than the person who prefers 65 degrees?

I would describe the 65-degree person as an "outlier," but minority is obviously not a good way of putting it, since the term "minority" is dependent on a specific granularity/ quantization. Outlier is a concept that can be generalized in a way that "majority/minority" can't.

And I'd argue that both people have equal voting power, since each pulls the result in their preferred direction an equal amount. I'd call that "equal representation", or at least the closest equivalent that can be described in non-vague terms.

And I'd also argue that the exact same effect applies to voting for human candidates (with good, "median seeking" methods such as Condorcet). Example: 10 candidates are running for a position as city budget director. A minority of the electorate, 20%, wants a million dollars a year put into fixing the potholes in the roads. The other 80% want only $400,000 spent on that. Because it is Condorcet, the effect of those 20% is to elect a candidate that wants to spend, say, .5 million rather than one that wants to spend only .4 million (that would be elected if not for those 20%).

(And of course, more realistic is that there isn't really a clear minority or majority, since each person has different preferences. And, there are issues beyond fixing roads that influence voter's preferences. )

The point is, a voter that is in the "minority" (for whatever that means) has just as much influence on the outcome as a voter in the majority. You don't need to bring in parties to help with that. And this is true whether there are multiple candidates, or just one, or where the city is split into districts and each district gets to elect a single representative. It still works. Obviously the fewer candidates that are running, the less mathematically accurate it will be (in terms of picking the exact median budget), but hopefully you see the point here, which is that it should converge on the median, and all voters had equal pull.

I don't see how basing things on whether voters "are confident that they are adequately represented" narrows things down or clarifies anything, though, even if you assume they aren't being hypocritical. It just kicks the can down the road.

You and @Andy-Dienes are for more math-educated than me, but hopefully you can understand why I'd like something a bit closer to being possible to plug into an equation. I don't think the concept of minority/majority, or of "degree of representation" do that at all. They just seem very vague and hand-wavy, and they don't generalize well to situations with nuance and real-world messiness.

* or whatever the equivalent word is when we aren't actually speaking of a multitude of representatives per se