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

[A Former User]

@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.

[A Former User]

@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.

[A Former User]

@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.

[A Former User]

@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.

[A Former User]

@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.

1. "outlier" is a more generalizable and clearly-defined concept than "minority"
2. "equal power to move the results toward their preference" is a more generalizable and clearly defined concept than "equal representation"
3. 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

[A Former User]

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

They just seem very vague and hand-wavy, and they don't generalize well to situations with nuance and real-world messiness.

I don't think it has to be hand-wavy whatsoever---it's just how we tend to talk about it here. Try looking at definitions like Proportional Justified Representation. Very formal.

[cfrank]

@rob I think something we agree on, although we might express the concept differently, is that what it means to be properly or adequately represented in government or in general, whether absolutely or to any given degree, is not fully clear. To me the meaning of representation appears to hinge on the meaning of consent, which is heavily social. A functional definition or acceptable proxy of that social concept to apply to voting is basically a pillar of the discussion here.

Correct me if I mistake your view when I suggest that you are more or less alleging that agreement on a “reasonable” procedure is in itself an acceptable proxy for consent to representation, and you have illustrated your conception of what constitutes a reasonable procedure with analogies and well-defined criteria such as Condorcet compliance—Because such a procedure is reasonable, then if any such procedure is agreed upon, problems relating to adequacy of representation are effectively solved. Is that accurate?

If so, then I think this is one instance where we disagree. To me, adequacy of representation is an outcome issue, and explicitly not a procedural one. In my opinion it is highly dependent on context whether a single winner method is appropriate to achieve representation of any degree, even if it is for example a Condorcet method. A simple poll on the quality of representation voters receive from government officials on something like a “very poor,” “poor,” “fair,” “good,” “excellent” scale could formalize those feelings in any case. I would be very surprised if a PR system did not outperform a single-winner system in such a poll almost always.

Single-winner systems are still necessary for the delegation of distinct executive roles, but I don’t think they can be very effective in establishing good representation. And the more I think about it, the more merit I feel in @Andy-Dienes’ comment about single-winner systems and Duverger’s law.

[rob]

@andy-dienes I looked at the Wikipedia article, and didn't see the things I discussed above defined.

Specifically, what is meant by "representation"? I would be interested in a definition that is generalizable, such as to situations where voters might have nuanced views on multiple issues. Same with "majority" and "minority". The words as I understand them only apply to very specific scenarios which I would consider unrealistic, such as binary choices.

I do notice that, on electowiki, it says "In the case of non-partisan voting, the definition of proportional representation is undefined". That seems to be getting at what I am trying to say. I take it further, as I find this assumption that parties must exist and be considered a prerequisite to be.... how do I say this? Offensive? Maybe that's too strong. But I don't like it and it doesn't align with my way of looking at group decision making, in the abstract.

Here's the best analogy I can come up with right now. Say I am looking at cars, and want one that is economical to drive and minimally damaging to the environment. And all the terminology used for comparison includes terms like "miles per gallon" and "smog rating" and such. And I keep asking, "why are you assuming it must use gasoline and be internal combustion?" They've basically painted themselves into a corner with their terminology, so they can't even evaluate electric cars -- at least not on the same criteria-- because they've made a bunch of (very limiting) assumptions up front.

That's how I feel about this assumption of parties, and the usage of terms like "representation" and "majority/minority" that only make sense with the assumption of parties (and seemingly with a bunch of other limiting assumptions as well, such as that each voter and each candidate is perfectly aligned/centered within their party).

I see parties (as opposed to special interest groups) as being mostly-unfortunate by-products of some electoral systems, not prerequisites to electoral systems. I'm not saying they must go away entirely or anything like that, but I don't think we should take them as a given, or define concepts around them, which PR seems to do.

[rob]

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

Because such a procedure is reasonable, then if any such procedure is agreed upon, problems relating to adequacy of representation are effectively solved.

No I don't think that is an accurate way of stating my view. It's not whether the procedure is agreed upon, anyway. I think some methods are better than others. I hate to keep saying "Condorcet compliance" because as we all know that isn't perfect itself (although it is pretty good). But we want something that minimizes vote splitting.

I also don't like using the term "adequacy of representation" because I still don't feel that "representation" is fully defined in a generalizable way. We could be voting directly on an issue. Or if we are voting for, say, president or mayor, which aren't "representatives" per se. (I might be more interested in their competence and charisma than whether they are advocating for particular issues that I care about)

I guess I just prefer we stop using the word "representation" as if it is a measurable thing, at least until is it defined in crystal clear terms that aren't dependent on such things as the existence of parties. I think there are better ways of describing what we are after.

@cfrank said:

A simple poll on the quality of representation voters receive from government officials on something like a “very poor,” “poor,” “fair,” “good,” “excellent” scale could formalize those feelings in any case.

I'd think that is too subjective and too much slop. Some people are bad compromisers, and will rate the results as poor if they didn't get exactly their way. And if the poll has any influence on how things play out, you have incentivized them be "squeaky wheels" and exaggerate their dissatisfaction.

I think a better way of measuring how well a system works is trying to measure whether each voter has equal "pull." This is why I would tend to use a "voting for a number" (or "voting for an N-dimensional point) scenario as a benchmark, where each voter is assumed to have a single-peaked preference. A "median seeking" method is what I'd want. If it truly is median seeking, it would be game theoretically stable and meet my idea of "fair." If that means "adequate representation" (in a case where you are electing representatives), ok, but I find the terminology both vague and not generalized enough.

(and you just aren't going to be able to measure this stuff meaningfully unless you try to minimize extraneous variables and make it a "pure" situation. Think of it like an engineer testing a car engine on a test bench rather than in a car driving down the road. Voting for numerical or geometrical candidates is always going to lend itself better to analysis)

What I am saying is that, to the best I can see, a median-seeking method would achieve all the important ideals of PR (e.g. all voters get equal say), even in elections where there are no parties involved. You just wouldn't use terms to describe them that refer to parties or that assume that voters and candidates fit into neat little groups.

Regardless, bringing it back to Duverger's law. Let's set aside human candidates for an example, that just complicates and obscures.

Say you've got a club that gets together regularly to see movies, and you vote on the movie. It's easy to see how, under choose-one, you are likely to have "parties" form, starting with people just saying to one another "hey, let's agree to vote on the same sci-fi special-effects extravaganza, so we we aren't stuck watching a lame chick flick". So you end up with the action-movie party and the chick flick party (or whatever, but it should tend to converge on two over time). That's all you need for Duverger's law to kick in.... a system that splits the vote and incentivizes people to defend against it by teaming up.

Do you think that would still happen when ranking the options? Would people bother teaming up? I don't see how it would. The incentive to do so would be vanishingly small, especially if using a method that minimized any spoiler effect / vote splitting (e.g. median seeking / Condorcet compliant methods).

If you think it would still be susceptible to Duverger's law, please explain how you think that would play out.

[rob]

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

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.

One reason to split them by geography is simply that it is already done currently in most existing legislative bodies in the US. So my argument there isn't that geography is the best way, but simply that it already is in place and is therefore hard to change. I think putting a ranked method in place is a lower hanging fruit, because it requires the least change. Also, it applies to offices such as President, governors, mayors, and a whole ton of local offices.

My argument is that a good, median seeking method (Condorcet compliant, blah blah blah) would solve the problem just as well as using PR. (and probably better, especially if you are talking about party-list PR) It has the advantage in that it works fine when the numbers are small enough that you can't really get things proportional (e.g. Wyoming only has one representative in Congress, so what can you do there? What about senators where there are two per state? )

I guess the idea is that if you have 3 offices to fill, and the voters are an equal balance of liberal, conservative, and libertarian, it is just as good to elect 3 centrists as it is to elect one of each ideology. A liberal voter, instead of being represented by one of the three office holders, could be said to be represented by 1/3 of each office holder.

And of course, if there aren't a nice even division of positions that matches the number of offices, this system still works. And of course all the candidates aren't just going to be exactly in the center and clones of one another, but at the extreme, yeah.... centrist candidates that represent everyone.

And if it was like that, I don't see a lot of gerrymandering. Because if it is centrist candidates getting elected, what is the point?

And sure, you can do that with multi winner or you can do it with single winner (typically by district). I see advantages to both. But what I don't want to do is require there be parties written into the legislation. Someone can be liberal without being in the Democratic party. The point is that the parties should have less, rather than more, importance in elections that they do today. Third parties are great, but so are independents. And parties don't work very well when they try to be both national and local. (for instance here in SF the republican party doesn't really exist in local politics)

[A Former User]

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

My argument is that a good, median seeking method (Condorcet compliant, blah blah blah) would solve the problem just as well as using PR.

Let's return to the example of what's happening in Alabama right now. How would using Condorcet solve the fact that Black voters are a minority in nearly every district, yet are a substantial percentage of the population?

[rob]

@andy-dienes I spent many years in Alabama. Lotta racism there. But there's actually a good number of counties that are majority Black.

But yes I think Condorcet would help just as much or more than party-based PR. Extremists (including racist extremists... Mo Brooks comes to mind) would be less likely to be elected to office. The 27% of the voters that are Black would be able to "move the needle" in their direction, favoring candidates that are less racist and more likely to make improvements on issues such as racial equity and inclusion.

I think with party list PR, you'd be more likely to have both racists, as well as people far on the other side, in the legislature. I'd rather have people on neither extreme. The more polarized the legislature (even if polarized in more than two directions), the more anger and ugliness, and the less progress gets made. And less progress is generally a bad thing for underprivileged groups.

One other thing I should say. Black people are an obvious distinction, because in most cases, you are either Black or not Black, and it is seen as an important part of your identity. Under a PR system, would there be a "Black party"? If not, what good does PR do in this case?

But there are so many ways to divide people. When I was in Alabama, I was employed as a software developer. Software developers are also a minority. I was a dog owner. Dog owners are also a minority. I was over 6 feet tall. People over 6 feet tall are also a minority. Everybody is in tons of minority groups. I'm not trying to be difficult here, I'm just saying, dividing people into discrete groups and then trying to deal with it based on group isn't always helpful. Treating people as individuals, and giving everyone equal pull (as Condorcet methods tend to do) is.

So yeah, I'm curious why you wouldn't think Condorcet methods would help.

[A Former User]

@rob

I do notice that, on electowiki, it says "In the case of non-partisan voting, the definition of proportional representation is undefined".

Electowiki is (largely) written by people who tend not to read academic research, and I would take anything you read there with a grain of salt. PR emphatically does have rigorous definitions---in fact there are multiple. My favorite is Proportional Justified Representation.

Black people are an obvious distinction, because in most cases, you are either Black or not Black, and it is seen as an important part of your identity. Under a PR system, would there be a "Black party"? If not, what good does PR do in this case?

Yes, in the case of Alabama, voters are incredibly polarized across racial lines and we should almost certainly expect to see a Black coalition. I also wish you would not equate PR with party-list PR, because while I do think party-list PR is fine, there are plenty of PR schemes which do not require parties.

That district map you sent is not the one I am referring to, which is being drawn this year and is heavily gerrymandered. It doesn't matter if you use the fanciest Condorcet method in the world when the districts are drawn like this---nonblack voters have a true majority in nearly every district.

Software developers are also a minority. I was a dog owner. Dog owners are also a minority. I was over 6 feet tall. People over 6 feet tall are also a minority. Everybody is in tons of minority groups.

Exactly! Yes yes yes. Everybody is in tons of minority groups---why not let people choose which of these minority affiliations matter most to them, rather than artificially slicing along geographic lines?

Generally speaking, gerrymandering is a form of Simpson's paradox

It does not matter if you find the "median in each district," since depending on how you draw the districts this can give you an overall outcome very very very far from the median of the entire electorate.

In your thermostat example, the median of [30, 31, 32, 70, 70, 70, 70, 70, 90, 91, 91, 92, 92, 93, 94] is 70, but the median of the medians of
[30, 90, 91], [31, 91, 92], [32, 92, 93], [70, 70, 70], [70, 70, 94] is 90.