With Friedrich Pukelsheim I discuss double proportional representation. Since 2006 the Canton of Zurich in Switzerland uses double proportionality to elect its 180 members of parliament. Friedrich Pukelsheim was invited to design an electoral system that would deliver on the promise of overall proportional representation in the canton while keeping the existing electoral districts since they are meaningful social and geographic entities. The complication is that some of these districts are very small (4 seats) while others are large (up to 18 seats). So the problem to be solved was to achieve proportional representation and electoral equality while honoring those very diverse districts.

The resulting electoral system was double proportionality, nicknamed “Doppelter Pukelsheim” (“Double Pukelsheim”). Friedrich Pukelsheim has become well-known across Switzerland thanks to his successful design of an electoral system that fits the Zurich's requirements. He emphasizes, however, that the system was first discovered by Michel Balinski. As of now, 8 cantons in Switzerland have adopted a double proportional representation system. 

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.

As a remark, this conversation was recorded in July 2024.

⁠⁠⁠⁠Find a full transcript and links to all material discussed in the show notes⁠⁠⁠⁠.⁠

Schedule: 00:00 Introduction / 04:03 Personal questions / 6:08 Main discussion / 52:50 Recommendations by Friedrich Pukelsheim.

Find Friedrich Pukelsheim’s research here.

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Many thanks to Ana Margarida Santos who co-produced this episode.

Please enjoy this conversation with Friedrich Pukelsheim.