# Parlamentswahlen nach dem doppelt-proportionalen Sitzzuteilungsverfahren im Lichte der territorialen Repräsentation. Eine empirische Annäherung an ein konzeptionelles Dilemma

Lüscher, Sandro (2023). Parlamentswahlen nach dem doppelt-proportionalen Sitzzuteilungsverfahren im Lichte der territorialen Repräsentation. Eine empirische Annäherung an ein konzeptionelles Dilemma. Zeitschrift für Parlamentsfragen, 54(3):571-595.

## Abstract

The “doppelter Pukelsheim”, as the biproportional divisor method with standard rounding is colloquially called, enjoys great popularity in Switzerland. For good reason: the new method of distributing parliamentary seats among the parties better reflects the will of the voters than conventional PR-based methods. However, the formula, which was used for the first time in 2007 for the cantonal elections in Zurich, has a mathematical property that works against a fair representation of local electorates. Specifically, unequal participation rates and unequal proportions of eligible voters in the constituencies subtly lead to unequal influence of the individual constituencies on the overall result. On the basis of the Zurich municipal elections 2022 and the Graubünden cantonal elections 2022, I explain why this is problematic and then show how the representation of the constituency electorates could be optimized with a minimal intervention in the calculation formula. The evaluation shows that, in both cases, seat shifts between the parties occur. This can be explained to a large extent by the different mobilization of the constituency electorates and only to a lesser extent by the different proportions of eligible voters in the constituencies. Furthermore, initial evidence suggests that these seat shifts are not random but are related to the demographics of the party electorates.

## Abstract

The “doppelter Pukelsheim”, as the biproportional divisor method with standard rounding is colloquially called, enjoys great popularity in Switzerland. For good reason: the new method of distributing parliamentary seats among the parties better reflects the will of the voters than conventional PR-based methods. However, the formula, which was used for the first time in 2007 for the cantonal elections in Zurich, has a mathematical property that works against a fair representation of local electorates. Specifically, unequal participation rates and unequal proportions of eligible voters in the constituencies subtly lead to unequal influence of the individual constituencies on the overall result. On the basis of the Zurich municipal elections 2022 and the Graubünden cantonal elections 2022, I explain why this is problematic and then show how the representation of the constituency electorates could be optimized with a minimal intervention in the calculation formula. The evaluation shows that, in both cases, seat shifts between the parties occur. This can be explained to a large extent by the different mobilization of the constituency electorates and only to a lesser extent by the different proportions of eligible voters in the constituencies. Furthermore, initial evidence suggests that these seat shifts are not random but are related to the demographics of the party electorates.

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