In 1998 a long-lost proposal for an election law by Gottlob Frege (1848--1925) was rediscovered in the Th\"uringer Universit\"ats- und Landesbibliothek in Jena, Germany. Frege's method for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while the elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions over time . We find that through a slight modification of the original voting method even stronger forms of proportionality can be achieved. This modified version of Frege's method can also be seen as providing a novel solution to the apportionment problem . We prove that it is distinct from all of the best-known apportionment methods, while it still possesses noteworthy proportionality properties.
In 1998 a long-lost proposal for an election law by Gottlob Frege (1848--1925) was rediscovered in the Th\"uringer Universit\"ats- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run . We find that through a slight modification of Frege's original method even stronger proportionality guarantees can be achieved. This modified version of Frege's method also provides a novel solution to the apportionment problem , which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties.
R
Frege's method
The method that Frege proposed
D
the
R
over time
in the long run
R
the original voting
Frege's original
R
forms of proportionality
proportionality guarantees
R
can also be seen as providing
also provides
R
. We prove that it
, which
R
it still possesses
still possessing