Apportionment paradox#Population paradox

As voters growth paradox (English population paradox ), the following referred to as paradoxical consequence of prestigious seat allocation process: Votes gains or losses of a party cause a mandate shift between two other parties.

Practical implications

An increase in votes for a coalition party may mandate a loss of / a coalition partner - and thus the coalition as a whole - cause to an opposition party. Thus one can interpret this as a paradox, however, you must assume that there is such a thing as "natural" coalitions. After the electoral law in force in the Federal Republic, however, you can not select coalitions, but only the preferred party. About the formation of coalitions decide after the election, the elected representatives, the output of the coalition negotiations is not certain from the outset, as has happened after the 2005 federal election, for example.

Occurrence

This problem occurs, for example at ratio method as the Hare - Niemeyer method. In Divisor this paradox does not occur. Examples: D' Hondt, Sainte-Laguë/Schepers, Hill - Huntington, Dean, Adams.

Demarcation to negative voting weight

When voters growth paradox lead vocal growth of Party A to Party B the mandate gains and losses mandate of the party C.

When negative voting weight lead vocal growth of a party A to mandate loss of party A.

Assuming that voters are growth paradox and the negative voting weight different effects that can occur in electoral systems.

The Federal Constitutional Court used the concept of negative voting weight in 2012 but more general. Thus, there is the negative voting weight if the number of seats a party correlated as expected unconstitutional by the amounts attributable to this or a competing party votes .. the above-described voters growth paradox correlates the number of seats the party B as expected unconstitutional with the votes of the competing party A. Because with electoral gains for the A party can not expect growth mandate for the party B. Thus, the voters growth paradox is a special case of the negative voting weight.

Example

In a Parliament 13 seats are to be awarded to the apply 4 lists A, B, C and D. Mr. X prefers a continuation of the coalition of B and C, and selects the list C. The final result of the election and the distribution of seats after the Hare - Niemeyer method are as follows:

( The 13th Mandate D due to the highest after the decimal 0.405 )

Thus, B and C have together with six mandates an absolute majority ( 7 votes would be needed ) misses.

Mr. X had not, however, participate in the election, the result would look like this:

( The 13th mandated by B due to the highest after the decimal 0,427 )

In this case, B and C were obtained with 7 mandates an absolute majority.

Results: Considering the voice of Mr. X for the list C as a voice 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 exactly the contrary wrong. However, this intention to vote for a coalition is either legally irrelevant. You can, however, depending on your view appear as politically undesirable.

After Sainte- Laguë method would have resulted in both cases illustrated, the following distribution of seats: A: 5, B: 4, C: 3, D: 1 From the perspective of Mr. X would it be now so indifferent that it is delivering his voice or do not.

For all mandate distribution process, there is the mathematical problem of mapping a large image set ( voters ) into a small target volume ( mandates); therefore it can not in principle be bijective. Always take rounding errors, which can be regarded as paradoxical, in particular, no process at the same time meet the quota condition and avoid the electoral growth paradox, this indicates the impossibility theorem of Balinski and Young to mathematically. It is thus a question of evaluation, the error can be accepted is ready and what not.