Double Proportionality

FULL TRANSCRIPT:

INTRODUCTION:

Hello everyone! My name ist Stephan Kyburz. And this is the 45th episode of the Rules of the Game podcast. Welcome back to the show!

How can an electoral system achieve proportional representation with electoral equality of all citizens and strong ties to their local environment, when at the same time multi-seat electoral districts strongly vary in size with some being very small and others very large? One answer to that non-trivial question is double proportionality. Its two types of apportionment make sure that every vote is counted with the equal  weight, while keeping overall proportionality intact. 

Now this may sound very complicated and technical to you and surely enough double proportionality is not very well known – probably not even among political scientists. But since I am from the Canton of Zurich in Switzerland, this system is relevant to me and my fellow citizens, and I feel honored to discuss it with its designer, Professor Friedrich Pukelsheim. 

The Canton of Zurich was the first to introduce this type of electoral system in 2006 to elect its 180 members of parliament. Friedrich Pukelsheim achieved to become a well-known name in Zurich, as the electoral system is nicknamed “Double Pukelsheim” or Doppelter Pukelsheim in German, a term that was invented and used by the minister of justice of the Zurich government back then to make this new electoral system more approachable.

Double proportionality has achieved success beyond the borders of the Canton of Zurich and is now used in a number of cantons in Switzerland. And it is likely to spread further. There were even discussions around using it to elect the members of the national House of Representatives, the National Council. Furthermore, Friedrich Pukelsheim has made some propositions to use it to elect the members of the European Parliament.

Friedrich Pukelsheim is Professor emeritus of Mathematics at the University of Augsburg in Germany. He got his doctoral degree in 1977 from the University Albert-Ludwigs University in Freiburg, and a Habilitation in 1982 from the same University. Still in the same year he became professor of mathematics and he has over time developed a special interest in the mathematical intricacies of electoral systems. Throughout his career he had research stays at the universities of Stanford, Cornell, Penn State, the London School of Economics and Political Science, among many others. Two books that treat the design of proportional electoral systems are Proportional Representation – Apportionment Methods and Their Applications, first published in 2014, and one in German: Sitzzuteilungsmethoden – Ein Kompaktkurs über Stimmenverrechnungsverfahren in Verhältniswahlsystemen, published in 2016. You can find all of his contributions on his website. You find links to all references in the show notes.

I am your host, Stephan Kyburz, and this is the forty-third episode of the Rules of the Game podcast. I am a political economist with a PhD in Economics from the University of Bern in Switzerland. And I previously held positions at the London School of Economics and Political Science and the Center for Global Development.

You find a full transcript of this episode on my website rulesofthegame.blog. Please send any feedback to rulesofthegame.ddi@gmail.com. If you like the podcast and want to do me a favor, please give it a 5-star rating. If you’d like to support my work, consider buying me a coffee at buymeacoffee.com and you find the link to it on my website rulesofthegame.blog. 

Without further ado, please enjoy this conversation with Friedrich Pukelsheim.

DISCUSSION

Stephan Kyburz: Friedrich Pukelsheim, welcome to the Rules of the Game podcast. I’m very happy to have you on the show.

Friedrich Pukelsheim: Herr Kyburz, welcome. I’m very happy to be here.

Stephan Kyburz: It’s great to be here, actually, in Zurich, we meet in person, which is kind of for me also the exception. So that’s great to have you here in Zurich.

Friedrich Pukelsheim: And the sun is shining. It’s a wonderful day. So we’ll have a wonderful time.

Stephan Kyburz: Yes, I’m sure about that. So my first question is always what is your first memory of democracy?

Friedrich Pukelsheim: Well, I don’t think I can tell a spectacular story. What I do remember is that in class, at high school, we had elections to elect a class representative of which I had the honor to be one at some time. We had a school council. And after high school I decided to study mathematics. Mathematics is more or less void of political engagement and ideological problems. I do remember though that as a PhD student, my first journey outside the country was to Poland and I realized that Poland has a different political system than we have. In mathematics, we had no problem talking to each other. But political topics were absolutely no no, taboo, were not addressed. And out of this latent interest for our own societies, at some point in the late nineties, I decided to offer a seminar to our students who are going to become school teachers on the mathematics of electoral systems. And that’s how I stumbled into the subject. I noticed during the seminar that I do not know very much about the topic. So it was a very productive result of this seminar. And then I got involved with it further and further and followed the topic in the later years.

Stephan Kyburz: And we know that it developed, you did more and more research on it and that’s also what we’re gonna talk about today. And yeah, as a mathematician, I think it’s really kind of the exception to have worked so much on electoral systems and the mathematics behind it, which is really technical often. And yeah, today we want to discuss the double proportional representation and electoral system that has been used in the Canton of Zurich since 2006. And we will go behind the story, how it came about but maybe to begin with, in kind of simple terms, what is the idea or method behind electing parliaments with a double proportional representation system?

Friedrich Pukelsheim: The idea of double proportionality is to realize two goals of representation: to represent citizens as subjects in their local environment, in their regional district where they live and to represent them as subjects of the electorate with a political persuasion that is with a vote that is given to a certain party to support that party. So double proportionality kills two birds with one stone. We have a geographical representation of districts which is of interest in those cases where the electoral region is subdivided into districts like in Switzerland Canton is subdivided in constituencies and it represents the political split or division of the country by means of the votes which are tallied for particular parties. In many polities, in many countries, it is in fact of great interest to achieve both. And double proportionality serves both purposes and therefore it is called double proportionality.

Stephan Kyburz: Thanks a lot for this first explanation. And you became very well known in Switzerland, I think probably every politician knows your name, Pukelsheim. But also a lot of people know your name, especially since 2006 when the Canton of Zurich adopted an electoral system or a method of double proportionality that you suggested. Now the system became known as the Neues Zürcher Zuteilungsverfahren, or New Zurich Apportionment Method, and it was approved and implemented in 2006 and it was nicknamed “Double Pukelsheim”, “doppelter Pukelsheim” in German. Please share with us you the story behind how you got involved in this evolution of the electoral system of the Canton of Zurich and how it became known as the “Double Pukelsheim”.

Friedrich Pukelsheim: Well, social science has a theorem or insight to the effect which is actually called Stigler’s Law of Eponomy. Stigler Gesetz der Namensgebung which says that no scientific discovery is named after its original discoverer. And so one of these examples is the “Doppelte Pukelsheim”, the “Double Pukelsheim”, “double Pukelsheim” was not invented by myself. The true discoverer is Michel Balinski, an applied mathematician. In the end in Paris, he grew up in Geneva, spent much of his life in the United States. And his applications to mathematics included the analysis of mathematical systems in which of course he proposed, together with his student Gabrielle Demange in 1987 double proportionality. As for me, I started publishing a little bit later, not before 2000. And I placed a paper in the Spektrum der Wissenschaft which is a journal of public science in Germany. It’s actually a clone of the Scientific American and there’s also a French clone, Pour la Science and in Pour la Science, Michel Belinski had a paper exemplifying double proportionality with the elections for the parliament in Mexico. Now the editor of the German journal then asked me, because we were in contact anyway because of my paper, whether I would be willing to translate the paper of Michel Balinski for the German journal and I said yes. And that paper explained and demonstrated double proportionality. And so that’s how I got to learn the details and the power that is behind this method. By the way, the experience to translate somebody else’s work into German, in this case, was quite remarkable from my point of view. I found it extremely difficult because as a scientist, I’m used to using my own words, my own phrases and it’s me who decides how to present the subject. And now I was suddenly bound to reproduce what Michel Balinski had done. I had to somehow stay close to his words and his wordings. That was very strange, very difficult I found, and I decided never to do a translation again. But this one which I did translate then was very productive or very useful for me, because shortly after this, I got a telephone call out of the blue from Christian Schumacher who was on the telephone from Zurich, calling to find out whether I had some suggestions for an electoral problem which they were facing in Zurich. And he had found my name and papers on the internet and he had noticed that I was working on electoral systems and whether I would have a suggestion what to do. So the problem he explained in Zurich was that they had the political representation as usual. But there were also these districts which needed to be represented because this was the expectation of the local people. I think not only in the Canton of Zurich, but all over Switzerland, it’s very important to have this local representation dimension visible and whether I would have an idea what to do about it. And I said, well, the idea is on my desk, it’s in the paper by Michel Balinski. That’s the way how it could be done and it needs to be adapted to the Zurich environment. So we got to Christian Schumacher and I met a couple of times and later then it was presented to the parliamentary committee who was in charge of the dossier and presented it to the Canton Parliament where it was accepted. In the beginning, we called the system, or we named the system the double proportional divisor method with standard rounding, which makes a absolute sense. Reasonable because it describes the technical steps that make up the system.

Stephan Kyburz: It’s an accurate description.

Friedrich Pukelsheim: It’s an accurate and informative description, but it is not very easily sold to politicians in a committee. So when we presented it to the committee, we decided we would have something which has more local “Colorit”, sounds more acceptable to local people and we called it Neues Zürcher Zuteilungsverfahren, New Zurich Apportionment Method which we actually also chose because when you reduce it to its initials, it’s NZZ. And the NZZ, which in this country is the “Neue Zürcher Zeitung”, and not the “Neue Zürcher Zuteilungsverfahren”. And the NZZ immediately noticed this play of words and commented on the procedure quite favorably. So it was in a way a success. And when I think it was in the final debate in the canton parliament, when the system was presented by the Minister for the Interior and Justice, Markus Notter at the time, that in his speech, out of a spur of a moment, he termed it “Doppelter Pukelsheim” and probably got a reaction that everybody smiled or laughed and noticed that this was successful. So the punch line actually is due to him. I still have to ask him when it happened, how he got the idea or whether it was suggested to him by a third party, I don’t know. So in Switzerland, it’s called “Doppelter Pukelsheim”. But meanwhile now, as time goes by, it’s more or less called Doppelproporz, which is also meaningful and it explains the system much better than “Doppelter Pukelsheim”.

Stephan Kyburz: Yes. But it’s definitely an exciting name for it and it probably made it, you know, more known or people were more curious about it. I’m sure about that. Because, of course, “Neues Zürcher Zuteilungsverfahren”, New Zurich Apportionment Method, you know, still sounds very technical and even though the big newspaper in Zurich, the NZZ was probably also having a smile on their face. It’s still the name evolved to become more practical in a way, right? But what was your first reaction when you heard “Doppelter Pukelsheim”?

Friedrich Pukelsheim: Oh, as a German, you think of “Doppeltes Lottchen” and you think of, it sounds funny. It sounds amusing. So I was amused. My wife was amused. The Children were amused. Everybody was amused and I think it was an ingenious strike by Notter. It’s a very dry subject, electoral methods and the change of the electoral law, the law of political rights. And so it was an ingenious twist by him to use this name.

Stephan Kyburz: I think it was, it was definitely a great idea to make the name sound exciting or interesting or funny or whatever, you know, people make of it. And now in the meantime, a lot of other cantons in Switzerland have also adopted the same system. I guess that makes you feel really reassured, right, that the system is also practical, that it’s used and many cantons have adopted it.

Friedrich Pukelsheim: Yeah, that’s really surprising. And of course, it’s very satisfying that the system is realized as so strong and so satisfying, and so serving the needs that political activists and active politicians feel in this country that it has spread to other cantons. Almost like a pandemia, but a positive.

Stephan Kyburz: Yeah, exactly. Yeah, I think the system has been a great success and a lot of cantons, I mean, there is Schaffhausen, Aargau, Zug, Nidwalden, Schwyz, Valais, Uri and Grisons they all have adopted the same system. And it really shows that it’s not only in mathematical terms or in electoral terms a success, but also practical in a way that now a lot of cantonal parliaments use it. And even at the national level, there were some discussions, right, for the national parliament.

Friedrich Pukelsheim: Yes, that’s true. It’s of interest on the national level because there we have the same understanding that the cantons want to preserve their identity. So regional representation in Switzerland is very important also on the national level. And outside Switzerland, we have other political constructions or unions, units like the European Union, where this simultaneous contribution of regional provenance or member state provenance in case of the European Union and political subdivision both play a role. Germany, of course itself, is another example, we are a federal state. So we have 16 states. But in Germany, it’s a bit different because each state gets so many seats that a distortion of the proportional effect is not really visible. And so there’s no need to amend the system. In Switzerland, the situation was a bit different because some of the electoral districts or constituencies were getting so small that they only were assigned one or two representatives. And if you only have one Schnitzel and three Children, it’s very hard to find a proportional solution that everybody is happy with.

Stephan Kyburz: Unless you have a good knife.

Friedrich Pukelsheim: Unless you have a good knife. Yeah. Actually I was born in Solingen, I can tell you stories about knives too.

Stephan Kyburz: Yeah, interesting. So to get a bit more technical, so the Cantonal Assembly in Zurich or the cantonal parliament is elected in several districts. It’s 18 electoral districts now and 180 members. And the system that is used is like a proportional system with a 5% threshold in each district. So a party should have at least a 5% vote share in at least one of the districts and maybe we can discuss that later. But the important part is actually that the districts vary in size, right? Some are really small and some are big and they vary between four seats per district to 18 seats per district. If you compare the old system, what was the problem of the old system? And how could you resolve that with a double proportionality?

Friedrich Pukelsheim: Well, the problem of the old system was very well described by the Swiss Federal Court when they said that when a district has too few seats to fill and when the cantonal constitution promises people a proportional system, then the two do not go together because if you have nothing to distribute, you can’t achieve proportionality. And so the problem or the issue was what to do with small constituencies. One way is to resolve them or to amalgamate them, aggregate them together with other districts. This is not really very well received in Switzerland because the local identification of people is very strong. I do not want to be put into one basket with the people next door more or less.

Stephan Kyburz: And the districts also have a geographic sense, right? So like they haven’t been moved in a long time except for the seats. I mean, the number of seats have been changing because of changes in population size. But the geographic units are kind of strict.

Friedrich Pukelsheim: That’s why I prefer the term district. These districts have grown in past history and they are not constituencies in the sense of other words, where these constituencies are being drawn and decided upon continuously for each new direction and where the constituencies by themselves have very little meaning to people. But districts here are regional districts which provide a feeling of life and understanding of these people. And this is particularly visible, for example, in the Canton of Valais where its high mountains, that separate one district, which is one mountain valley through peaks of 3000 Meters from the next valley. And so these people really feel we are living in one valley and we don’t want to be mixed together with the other.

Stephan Kyburz: It’s almost like a compromise between having proportional representation but still being represented by a few politicians that feel connected to the region.

Friedrich Pukelsheim: Yeah. So the goal is to maintain, to preserve this regional representation. But also when the cantonal constitution promises people proportional representation, that the political representation is proportional across the whole electoral region, which is the canton. And it is perhaps all of Switzerland or perhaps all of the European Union, the big unit. And so to achieve both dimensions, geographical representation proportional to population figures and political representation proportional to the vote tally of the political parties. And this is what double proportionality achieves. And at the same time allows to maintain these geographical, historical and socially well accepted geographical subdivisions of the electoral region.

Stephan Kyburz: The double proportionality, the method is divided into an upper apportionment and a lower apportionment. And could you please explain what the upper and the lower apportionment are like in terms that maybe are not too technical but enough so that people can have an idea.

Friedrich Pukelsheim: Yeah. The lower apportionment is the apportionment of the seats per Wahlkreis (electoral district). This is something which was done in the past separate evaluation per Wahlkreis (electoral district). The upper apportionment is the new and first step. How it starts. Upper apportionment means that the vote tallies of the political parties are evaluated across the whole electoral region. So the whole canton enters as one unit, people from a small district have the same weight of vote, the same option to contribute to the final result as people from a more densely populated. So this upper apportionment guarantees electoral equality among citizens for everybody in the canton. And at this upper stage, this global stage or cantonal stage, there’s no distinction by regional provenance. So in terms of evaluating votes for political parties for political persuasion, we have a very good achievement of electoral equality of citizens. That is the big achievement. And this is the point that was criticized by the Swiss Federal Court. When you do it separately per district and some districts are small and some districts are large. So now we have two dimensions, we know how many people live in the district. That’s the regional representation. And we have at the end of the election day, we know how many seats every party deserves. That’s the political division. And these two dimensions are brought together in the sub-apportionment, Unterzuteilung, the second step. And it is possible to achieve this, that parties on the cantonal level get a total number of seats that fits the first calculation. And in each district, the parties that stand for election there with a total of their seats exhaust the number of seats that this district has been assigned. So the second step where these two dimensions come together is a bit more complicated because you have to view the full results subdivided by district and party that gives as we call it a table with rows, rows represent the districts, columns represent the parties. And so a table for many people is a bit overwhelming, but that’s the price to pay. If you are more sensitive to the input, you have to do a little bit more work to get a sensitive output. And that’s happening at this stage. The upper apportionment is nothing new. That’s done as always, except that there’s a little change there which makes it even more equal in terms of electoral equality that it was used before. Because the old apportionment method that has a long tradition in Switzerland is named by Hagenbach-Bischoff. Eduard Hagenbach-Bischoff was a physics professor in Basel who promoted the system of Victor D’Hondt, who was a law professor in Belgium. And  Hagenbach-Bischoff said very explicitly, he does not want to have the system called after him. But people didn’t listen to him so they called it Hagenbach-Bischoff. And in most other countries, it’s called the D’Hondt system. It’s a divisor method with rounding downwards. That’s when you change your Swiss Francs into Euros. And you get a conversion rate from the bank and then there are small remainders and you always round them down, then the party that wins is the bank and not you. And this has been changed to the divisor method with standard rounding, which is named after André Sainte-Laguë. Saint-Laguë was a mathematics professor in Paris. And he said that standard rounding is better and that’s the way now we convert currencies because the fractional part after you have applied,the exchange rate is rounded downwards when the fractional part is smaller than one half and upwards when it’s bigger than one half. So both parties sometimes win. That’s the Proporzglück, the proportional luck. And sometimes lose when it’s smaller than one half. That’s Proporzpech, but it’s equally the chances of being lucky or having “Pech“ unlucky are equal. It’s a fair way to resolve these rounding problems.

Stephan Kyburz: And I think the system checks a lot of boxes that we want to have checked, right? And, and a big or, or a real advantage is also that we have full, full proportionality at the whole cantonal level.

Friedrich Pukelsheim: At the whole level of the electoral region involving every person who goes to vote, of course. In fact, it’s very important to understand this notion of electoral equality, which is very demanding. And when you read these decisions of constitutional courts or the Swiss Federal Court, they always spend a few pages to explain this. Because it’s really, I find it more or less very intriguing and almost unbelievable because our democratic societies actually rely not on equality but on inequality. One is talking like myself and you are listening, we are very unequal, we are unequal in very many other respects when we stand side by side. And in our family, one of the most successful phrases when educating the children when they were still small, was the phrase “every child is different”. Because even a small child senses that in this statement, there is a promise of equality because every child is taken for herself or for himself. And in the same way, our democratic societies actually blossom and bloom from being that we are different subjects. But for the purpose of a parliamentary election, we are all equal. It has taken a long time to understand this type of electoral equality. And so talking of electoral equality is also from my point of view of mathematics a bit strange because equality is a relation. You need at least two pieces to compare. How can one election be equal? I mean an equal election which is a standard term for these constitutional jurists is a very strange composition of words. So equality needs a reference set of many several subjects which can be compared. And for an election, there are at least three reference sets. One can think of one is the people who go to vote, the electorate: many thousands, hundreds thousands or a million. Then there is the set of members of parliament who are being elected. They are the objects, they are the people you and I elect. We are the acting subjects and we elect the members of parliament. And then we have a representative democracy for the next four years or so. The members of parliament are those who rule and decide and we are the objects. Anyway, the first reference set would be the electorate. The second, the members of parliament. And the institutions that mediate between the many electors, the many citizens and the few representatives are political parties. And as always in our societies, institutions develop a living of themselves and an understanding. They are very strong. And so political in many ways, political parties come first to mind when talking about elections, but in terms of electoral equality and constitutional principles, they come last. The first are the voters, the electorate and the second are the members of parliament. They also have the right to statutory equality. They are all equal. There is not a first member and a second member, they are all equal. They are all equals in parliament. And the political parties actually from this point of view come last. Although in practice, I realize they come first and in political science, they come very first. Political science is a science of investigating these institutions and voters come very late then. So anyway, that’s a very fluid and difficult and demanding notion of equality. And so double proportionality secures electoral equality among the voters among the citizens who vote and that’s their day and their promise by the constitution that they are treated equal.

Stephan Kyburz: Before double proportionality, the equality wasn’t really given as well because more votes were quote unquote like lost in small districts, right? Because in small districts, we had only a few seats where proportionality doesn’t yield as good of results as we want. And double proportionality resolves that.

Friedrich Pukelsheim: Yeah, absolutely. In small districts when there are only two seats or there are even districts in Switzerland in Schaffhausen, Buchberg-Rüdlingen, that have only one seat, you can’t achieve proportionality. So voters who vote for a party of whom they know that their candidate will not win more or less have no say in the election. And now this is changed so that every vote contributes to the final result. And that achieves the electoral equality, also for people who live in small districts.

Stephan Kyburz: The system itself is, as you say, like mathematically to calculate the results and to adjust the seats, the seat apportionment across districts to reflect really the voters’ choice, there is an algorithm used, a computer algorithm programmed to adjust the seats. Did you feel like in the last few years when it was implemented, was that like a problem? Or was there any kind of questioning of whether this would all yield the results we wanted?

Friedrich Pukelsheim: Well, technically, mathematically, it’s safe. It’s not a question. The result is being produced by these computer programs or algorithms or ways how to calculate it. Sometimes it’s not well received that you need to involve a computer which I can understand. But my attitude is that our current elections need a computer anyway. And you get the result by the push of the button so you wouldn’t even notice that it’s so easy mathematically to do it that you don’t notice that the machine spent some time finding the result. And my other reaction is that, yes, I was afraid that it may not be accepted from the political level. But as I said, with Christian Schumacher, when I first appeared before the parliamentary committee who was in charge of it, I was led into a room and here sat these 20 members of the Zurich parliament who were members of the committee. And all of them had a laptop in front of them and were looking at the screen of the laptop. So I thought, well, this is not going to be a problem. They know how to use the virtues of modern technology. And even a simple election where you do not have double proportionality but simple proportionality is done by a computer nowadays. Nobody, of course, yes, you can do it with pencil and paper if you can divide two numbers, which is more and more difficult for the younger generation, but nobody would do it anyway. So using the computer is not really an issue anymore.

Stephan Kyburz: Yeah. And once, as I understand, once the results are obtained, it’s easy to check them, right, with a calculator?

Friedrich Pukelsheim: That’s the other big pro that I try to communicate. It’s difficult to find the result. But once the result is reported and the key numbers that produce these results are also reported, it’s very easy to check. So it’s laborious, “das Ergebnis auszurechnen”, to find the result, but it’s very easy to verify the result, “das Ergebnis nachzurechnen”. And all that the public really is concerned about when they look at the minutes of the electoral commission of election is that you can check the result that 30 years ago, this was done correctly and you can do it just by looking at these numbers and looking at the key figures, key numbers that gave the result. 

Stephan Kyburz: And that is important for trusting the system and you know like really confirming that it’s working really well.

Friedrich Pukelsheim: Yes, I think so. And actually the way how to calculate it is not uniquely determined, as we say in mathematics, this is an algorithm. Everybody knows that when there is one algorithm, there are actually two and three and four. And I think we have implemented in our academic research program 20 algorithms to find out which one is fastest, which one is safest and which one has this property and other properties. But in fact to carry out or to write an electoral software for a particular canton or situation, you only need one algorithm and then you are happy. And the algorithm that functions is in fact a repeated application of the algorithm which you would use in a normal one dimensional case. It may be necessary to apply it 14 times or perhaps 29 times. So the only help that the machine provides is that boring, long winded iterative, repeated calculations are done by a machine much better than by a human being.

Stephan Kyburz: Yeah. Yeah, totally. Especially in these times, the 21st century, right? And so did you feel some other backlash or people found disadvantages of the double proportionality?

Friedrich Pukelsheim: Disadvantage is perhaps a bit strong but nobody is perfect and nor is double proportionality. The weak point that sometimes pops up is that double proportionality gives a result which is different from treating districts separately. That’s why it is introduced. As I said, it secures electoral equality for everybody in the canton or in the electoral region. But in order to balance the seats that are owed to a political party and the seats that are owed to regional districts for their population, sometimes an adjustment in the table is necessary. We call it a discordant adjustment. When you only look at this particular region, a party may have 1900 votes and another party has 2000 votes which are more votes. But the party with fewer votes, 1900 votes, gets a seat and the party with 2000 votes gets no seat. So this is discordant because as the number of votes going from one party to the other one grows, the number of seats decreases. But you need to look at the whole electoral region in almost all cases. It’s then the case when you look only at the party, then the party with more votes has other districts where it is still more successful. So the seats that they owe go to other districts and not to this district. I don’t know, this may sound confusing. I may not have done it very well, but this is something you can quibble about.

Stephan Kyburz: Yeah. No, I think it’s, it’s important to say that this is done essentially to save overall proportionality.

Friedrich Pukelsheim: When you are very stubborn, a representative of your district, let’s say in the valley, of your valley where you live in, you don’t care about the other rest of the canton. And from that point of view, when you only see your local, your immediate environment, then you don’t care about the advantages of having a system that extends equality also to the people who live far away on the other side of the Rhone or something. But of course, our understanding of a canton or of a parliamentary election of an electoral region is that people in the electoral region are all equal and they should care even if traditionally they didn’t. And modern technology is not only computers, it’s also cars and helicopters, and nobody nowadays lives as remote that he or she is not aware that there are other people in the world and that essentially we are equal democratically, although we are all very different.

Stephan Kyburz: Exactly. And also I feel like, you know, and we have become way more mobile. People are traveling a lot. People are very, you know, probably less attached to their very local community than they used to be. And so like, for me, overall proportionality is definitely kind of the main goal or the priority as opposed to the district.

Friedrich Pukelsheim: Absolutely. I just happened to have spent two weeks vacation in the Scottish Highlands together with my wife, which traditionally were viewed as remote and secluded and a lone country. But people traveled there as tourists as we did. But the local people also travel away from the highlands. And mobility has increased to a point that reflecting it in the political system is more than appropriate. Nobody is by themselves nowadays.

Stephan Kyburz: And I think also for, you know, the double proportionality for Switzerland as a whole will for sure, come up again. I think the current state of affairs is that the national, the federal government wants to kind of see how things go with double proportionality in different cantons. But for me also to achieve higher or overall proportionality of Switzerland would also be a goal of an electoral system.

Friedrich Pukelsheim: Yes, I can see the point. But of course, I’m not Swiss, I’m German. And the last thing I’m going to do is to missionize in Switzerland of what you should do in your country. That’s up to the politicians over here. But right now, the cantons have a very high, important standing. Double proportionality would emphasize the common strains in the cantons. Which after all, the federal government is supposed to represent as we have in Germany, the Bundestag does. But it is a political decision whether you want, whether this is wanted and whether this finds a majority and whether this is implemented and used.

Stephan Kyburz: Exactly, you are not a Swiss citizen, but you are a European citizen. And you’ve done some research also on the European parliament and how it is elected. Do you maybe quickly want to share, you know, what are your thoughts on the European parliamentary elections and maybe what suggestions you have made?

Friedrich Pukelsheim: Yeah, right now, we just are coming out of an election for the next European parliament and the electoral system right now is a patchwork of 27 domestic systems of the member states. And most of these systems are very closely modeled after how the member states elect the domestic parliament. Now for the European Union, there are two issues. One is how to distribute the seats of the European parliament, which in the upcoming legislative period will be 720. How to apportion these seats among the member states, that’s called the composition of the European parliament. So the technical term is composition, “Zusammensetzung des Europäischen Parlamentes”, and up to now this has been decided upon by negotiations behind closed doors. And the wish for the last 30 years in the European parliament was to find a system which is transparent and reliable and which can be used to do it safely so that the usual mobility of the population figures is accounted for. And that when new countries are going to join the European Union, which one can use them to subsume them in the whole system. So this is probably the first topic where hopefully they will make progress in this upcoming legislative period because the wish has always been there, there have been many workshops and hearings for the Committee for Constitutional Affairs in Brussels in the European Parliament. So I hope they are making progress on this point. Which is also a nice topic by itself, but which we are not going to spend the next hour on time. I’m going to leave it by that. But once this particular, the composition has been settled, there is still the challenge of unifying the system by which people cast their vote because now we still have the same problem as with small districts in Swiss cantons that some of the member states, like Malta and Cyprus, are very small and some are very big and the individuals, the human beings, the people, the electorate who go and cast their vote in France and Spain have different success chances with their vote. So in that respect, the election of the European Parliament lacks equality. It is our understanding, our democratic goal to achieve equality here and there are various ways to do it. The most prominent right now is to establish transnational lists. So to have that the European political parties present a list of candidates to all of the European citizens across all 27 member states. But this would only be relevant for a subset of seats, perhaps 10% which out of 730 would be 73 or so not to all seats. And my idea which I derive from my experience here in Switzerland would be to use a double proportional system where we have, as in Switzerland, the number of seats per member state is being decided upon by this composition solution or decision. And the number of seats for the European political parties are evaluated jointly and equally across the whole of the European Union. The trouble is we do not have at this point acting European political parties that we could recognize. We have factions in the European parliament, like the European People’s Parties and the Socialists and Democrats. But legally, from a constitutional point, they are factions in parliament, “Fraktionen im Parlament”, which is not the same as a political party that presents itself to the almost 500 million European citizens. So this is the much bigger challenge to bring the domestic political parties of the 27 member states to a level that they agree to form and campaign in the election as one visible European political party.

Stephan Kyburz: So as a comparison in Switzerland, most parties are national or even in Zurich, of course, parties are present across all districts. So it’s easy to add up votes for the same party and they are present everywhere. And that would be kind of a condition to have double proportionality in Europe.

Friedrich Pukelsheim: Yes, a precondition. This has first to be achieved before you can implement double proportionality. When it comes to double proportionality for the European parliament, I’m pretty sure that I’m too old to be still alive when it should happen. But I think that’s really where I contribute as a scientist. It is a play of sorts. It is a concept which you have to develop to present in the relevant journals to discuss and it may after some while grow and find more supporters or something else may happen. It’s an option. It’s a valid option. It’s doable provided these European political parties which actually right now exist, but they exist for the sole purpose to draw some money from the union budget. But if they start to get to work with the money they get, then the situation may change, but it will certainly need more time. Nevertheless, I find it exciting and challenging to think about a possibility like that.

Stephan Kyburz: Yeah, for sure. I totally agree with that. I think we should always think about possibilities of changing institutions or adjusting them. I think that’s also why I do the podcast in the first place. Yeah, I think this is maybe a good point to end the discussion. But before we really end it, I would like to know, do you have any recommendations of books or articles for the audience? Because we knew also that some aspects are maybe also hard to really explain in a podcast. Of course, we have no visuals. So maybe some people would like to read a bit more on this topic.

Friedrich Pukelsheim: Well, a book I would certainly recommend and I’ve often recommended is by Michel Balinski, whom we mentioned in the beginning and his student Peyton Young, who now is a professor in Oxford. “Fair Representation” where he tells, they tell the story of apportioning the seats of the American US House of Representatives among the member states of the Union over there. And that’s fascinating writing. I find it’s a gem of scientific writing. Essentially, the book is 200 pages. The first 100 pages, they tell the story how it developed from the beginning of the United States, which methods were proposed, why they were proposed, with sometimes good arguments that were proposed and sometimes ridiculous arguments that were proposed. And why they were changed. I find it a thriller and it’s non-technical reading. The second half, the second 100 pages is the mathematics of it. And so this will be interesting. Many people will decide to be satisfied with the first 100 pages. But that’s really a gem of scientific writing and it has contributed a lot to the mathematical understanding of apportionment methods. And as I said, I’ve learned a lot from Michel Balinski, personally too. Well, the other book I would like to recommend, of course, is my own book on proportional representation. Of which there is a thicker version of 300 pages in English where the mathematics of double proportional systems is set out in detail which at least at some point in some publication needs to be done. There’s also a small clone of a little bit of 100 pages in German where the essence of it is described and it’s not quite so technical, but I realize that I’m a mathematician and my style of writing is not really a thriller for people from other sciences, other fields of science. Another author whom I find very intriguing is George Pólya. He is a famous mathematician. He was a famous mathematician, Hungarian by origin. He died in Stanford in California. But on his way from Hungary to California, he spent some time in Switzerland and met his wife and they both lived close to 100 years. And anyway, he married her here in Switzerland. He was a professor at the ETH and it may be, I cannot really be sure, that this is the case that for being made a Swiss citizen he had in those days, 1919, 1920 to prove his interest in this country. And as a mathematician, he may have decided to write papers on the cantonal proportional representation systems. And he did this in a very charming language in some of these Swiss journals. I can give you the reference and you can append it to the podcast. And in the beginning of one of it, he says this is a paper by a mathematician, but I want to reach other people. So I’m not writing it in a mathematical style. But to no avail, he was not received by the literature. He barely appears in any of the political sciences’ books. Although it is very convincing, very well written. And in his old papers, he also advertises the divisor method with standard rounding the method by Sainte-Laguë, which I mentioned, which is now implemented in double proportional systems. And he said this method is neutral to both sides. And this is why it’s better than the D’Hondt system, which is a similar system that is always forgetting about remainders, which is unfair to one side. So it’s all in there. It’s more than 100 years back. So append it to the podcast and then people can find it and enjoy it.

Stephan Kyburz: Yes, sounds fascinating. All three recommendations, very specific also. And yeah, I will definitely add them to the show notes of the podcast. So thanks a lot for having taken time to explain and discuss double proportionality, the double Pukelsheim and I really enjoyed it. And it was a great pleasure to have you here in Zurich.

Friedrich Pukelsheim: Well, thank you, Stephan Kyburz. It was my pleasure too to sit here face to face with you and discuss electoral problems, electoral mathematics. I find it fascinating myself and I find it very useful and rewarding. And I hope that with your podcast, you are successful and drawing masses to the subject. Good luck!

Stephan Kyburz: Thank you. I hope that too!

Outro:

Thanks for listening to this episode, I really appreciate you’ve taken the time. If you enjoyed it and you’d like to help support the podcast, please share it with others, post about it on social media, or leave a rating and review. It really helps my message to get heard.

This episode was co-produced by Ana Margarida Santos and me.

If you have suggestions for future episodes or feedback on the podcast, don’t hesitate to contact me by email at rulesofthegame.ddi@gmail.com. I’ll put my email address in the show notes.

To catch all the latest from me, you can follow me on X @skyburz and on LinkedIn. Thanks again, and I’ll see you next time!