Largest remainder method

The Hare - Niemeyer method ( in Austria only " Hare'sches procedures," Anglo-Saxon " Hamiltonian method ", nor "quota method with residual compensation after the largest fraction ") is a seat allocation process. There is for example the case of elections to the distribution principle of proportional representation (see proportional representation ) is used to convert votes into mandates deputies.

History

The method has been propagated by the U.S. politician Alexander Hamilton before the first U.S. census in 1790 in order to distribute the seats in the U.S. House of Representatives in proportion to the population of the individual states. However, it could not prevail against using the D' Hondt method in the process. According to the census in 1840 it was finally on the method of Hamilton over and used it for the last time in the census in 1890.

The method has been applied since the election in 1987 until the election of 2005 for the calculation of the distribution of seats in the Bundestag. The name used in Germany is derived from the London lawyer Thomas Hare and the German mathematician F. Horst Niemeyer.

By order of the Federal Parliament of 24 January 2008, the Hare - Niemeyer method has since been replaced by the Sainte-Laguë/Schepers in federal elections.

Method of calculation

Or, in other words:

The second form makes it clear that the share of votes equal to the seat portion, said seat number, of course, according to the largest remainder rounded up or down. Practically, this looks as follows:

Each party are first allocated seats in proportion to their rounded quota. The still remaining seats are allocated in order of highest Nachkommareste of quotas. In the same high Nachkommaresten to be drawn from the Returning Officer by lot. It takes into account, where appropriate, only the votes of parties that do not fall under a restrictive clause.

An example: To forgive are 100 seats on four parties (A, B, C and D) are to be distributed. A total of 580 votes were cast, broken down as indicated in the table. This results in the following distribution of seats: In the first round gets 37 Party A, Party B 53, Party C and Party D 3 5 seats. Due to the Nachkommareste the remaining two seats at C and D are awarded.

Properties

The Hare - Niemeyer method is neutral with respect to the size of the parties, since the voting share (percentage of own votes of the total votes ) is equal to the seat share (percentage of own seats from the total number of seats ). Thus, it ensures compliance with the principle of equal suffrage. In contrast, other methods favor larger parties and discriminate against small (especially D' Hondt method, in Switzerland Hagenbach -Bischoff method ) or vice versa (especially Adams methods ).

The Hare - Niemeyer method is - as all quota procedures - by the inviolability of the rate condition from: After that, no Party may get more seats than they have been rounded up to the nearest whole number ratio. At the same time, no party received fewer seats than they have been rounded to the nearest whole number ratio. This advantage is not given in the Divisor.

The disadvantage of the method is the resulting from the Quota condition inconsistency; it can occur following paradoxes:

• The Alabama paradox and the losses resulting directly from him blocking clause paradox and compensatory mandate paradox
• The electoral growth paradox, which is, however, no peculiarity of the Hare - Niemeyer method, but can occur in all quota procedures.