Voter growth paradox

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The following consequence of seat allocation procedures, which is viewed as paradoxical , is described as the voter growth paradox (English population paradox) : Voting gains or losses of one party cause a mandate shift between two other parties.

Practical implications

An increase in the vote of a coalition party can cause a coalition partner - and thus the coalition as a whole - to lose a mandate to an opposition party. In order for this to be seen as a paradox, however, one must assume that there is such a thing as “natural coalitions”. According to the electoral law in force in the Federal Republic of Germany, one cannot elect coalitions, only the preferred party. After the election, the elected representatives decide on the formation of coalitions. The outcome of the coalition negotiations is not certain from the outset. B. could experience after the federal election in 2005 .


This problem occurs, for example, with quota procedures such as the Hare-Niemeyer procedure . This paradox does not occur with divisor methods. Examples: D'Hondt , Sainte-Laguë / Schepers , Hill-Huntington , Dean , Adams .

Differentiation from negative voting weight

In the voter growth paradox, an increase in the votes of party A leads to party B winning seats and party C to losing seats.

In the case of negative voting weight , an increase in the votes of party A leads to a loss of mandate for party A.

On this basis, the voter growth paradox and the negative voting weight are different effects that can occur in electoral systems.

In 2012, however, the Federal Constitutional Court used the term negative voting weight more generally. Accordingly, the negative voting weight exists if the number of seats of a party, contrary to expectations, correlates with the number of votes allotted to this party or a competing party . In the voter growth paradox described above, the number of seats in party B correlates, contrary to expectations, with the number of votes in competing party A. Because if party A increases in votes, no increase in seats for party B can be expected. Accordingly, the voter growth paradox is a special case of negative voting weight.


A parliament has 13 mandates for which 4 lists A, B, C and D apply. Mr. X prefers a continuation of the coalition of B and C and chooses list C. The final result of the election and the distribution of mandates according to the Hare-Niemeyer process are as follows:

list Number of votes Vote proportionally Number of mandates
A. 43 5.036 5
B. 29 3.396 3
C. 27 3.162 3
D. 12 1.405 2 (1 + 1)
total 111 13 13

(D receives the 13th mandate due to the highest decimal number 0.405)

With that, B and C with a total of 6 mandates missed an absolute majority (7 votes would be necessary).

If, on the other hand, Mr X had not participated in the election, the result would be as follows:

list Number of votes Vote proportionally Number of mandates
A. 43 5.082 5
B. 29 3.427 4 (3 + 1)
C. 26th 3.073 3
D. 12 1.418 1
total 110 13 13

(The 13th mandate is given to B due to the highest number after the decimal point 0.427)

In this case, B and C would have obtained an absolute majority with 7 seats.

Result: If one regards the vote of Mr. X for list C as one vote for (B + C) or the coalition of B and C, as it corresponds to the intention of Mr. X, then the intended effect of the vote has been exactly The opposite is wrong. This intention to vote for a coalition is, however, irrelevant in terms of electoral law. However, depending on your point of view, it can appear politically undesirable.

According to the Sainte-Laguë procedure , the following distribution of mandates would have resulted in both cases presented: A: 5, B: 4, C: 3, D: 1. From the point of view of Mr X, it would now be irrelevant whether he casts his vote or Not.

In all mandate distribution procedures, the mathematical problem of mapping a large number of images (votes) into a small target number (mandates) arises ; it can therefore in principle not be bijective . Rounding errors always occur that can be seen as paradoxical, in particular no procedure can simultaneously meet the quota condition and avoid the voter growth paradox, this is mathematically proven by the impossibility principle of Balinski and Young . It is therefore a question of evaluation as to which mistakes one is willing to accept and which ones are not.

See also

Web links

Wiktionary: voter growth paradox  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. BVerfG, 2 BvF 3/11, paragraph 85 of July 25, 2012