Abstract
Can fewer votes win more seats? In the 2008 local elections in the German State of Bavaria the trick worked, thirty-six times. The year 2009 invites party officials in the German States of Rhineland-Palatia, the Saarland, and Thuringia to play the game. The name of the game is list apparentements. We show what it is about.
This paper has been published in Essays in Honor of Hannu Nurmi, Volume I (Homo Oeconomicus 26: 489–500), 2009. We would like to thank M. Holler, Hamburg, and B. Torsney, Glasgow, for valuable comments. The authors’ articles quoted in the sequel may be retrieved from the Internet at www.uni-augsburg.de/pukelsheim/publikationen.html. A German version of the present paper has been published in Stadtforschung und Statistik, 2/2009.
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- 1.
The French term "apparentement" is also used in English, see Gallagher and Mitchell (2005), p. 631.
- 2.
We use the term community as a generic synonym for political entities where voters elect a local council, such as cities, counties, townships, villages, and the like, as in Pukelsheim et al. (2009).
- 3.
We get 456 × 1 + 191 × 2 + 21 × 3 = 901.
- 4.
- 5.
AGS = Amtlicher Gemeindeschlüssel = official community key. The key defines a standard order for German communities. It may also be used to retrieve some basic statistical information about the community via www.destatis.de/gv/.
- 6.
Our counts neglect the borderline cases (1) “everyone stands alone” (1, 2,…, ℓ−1, ℓ) and there is no sub-apportionment, and (2) “all join together” (1 + 2+… + “ℓ−1” + ℓ) and there is no super-apportionment.
- 7.
The formulas from Table 2 yield \( {\text{D}}^{\prime}\text{H} (j\,|\,L_{1} , \ldots ,L_{k} ) - {\text{D}}^{\prime\prime}\text{H} (j) = - (\ell - k)\,\,s(j)\,/\,2 < 0, \) assuming that List j remains alone while other lists enter into an apparentement of two or more partners (\( k < \ell \)).
- 8.
The formulas give \( {\text{D}}^{\prime}\text{H} (j\,|\,V;\,\,\{ \,i\,\} ,\,i \notin V) - {\text{D}}^{\prime\prime}\text{H} (j) = \,(1 - s(V))\,(p - 1)\,s(j)\,/(2\,s(V)) > 0 \), assuming List j is one of p partners of the (sole) list apparentement V, the other \( \ell - p \) lists running by themselves.
- 9.
Vote counts reflect council sizes, as every voter has as many votes as there are council seats to fill.
- 10.
The German Federal Constitutional Court shares a critical stand on list apparentements: Every list apparentement [leads] to a violation of the principle of electoral equality, since votes are assigned unequal weights without justifying the deviation from equality by a forceful, substantive argument, see BVerfGE 82 (1991) 322–352 [345]. The decision concerned the by-passing of the five-percent hurdle in the first all-German elections in 1990, not the role of list apparentements in local elections.
References
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Xyz (2002). List 1 paid a major portion of the bill, its bonus shrank by a third of a seat (0.548−0.914 = −0.366). List 6 benefitted most, gaining close to half a seat (0.202− (−0.227) = 0.429). In the 2002 election, List 6 won two seats, and thus got ahead of List 5 who had to resign themselves to just one seat.
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Pukelsheim, F., Leutgäb, P. (2013). List Apparentements in Local Elections: A Lottery. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_7
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