Apportionment methods are used to translate a set of positive natural numbers into a set of smaller natural numbers while keeping the proportions between the numbers very similar. The methods are used to allocate seats in a chamber proportionally to the number of votes for a party in an election or proportionally to regional populations. In this article, we describe six apportionment methods and the user-written egen function apport(), which implements these methods.
BalinskiM. L., and YoungH. P.1982. Fair Representation: Meeting the Ideal of One Man, One Vote.New Haven, London: Yale University Press.
2.
KohlerU.2011. Estimating the potential impact of nonvoters on outcomes of parliamentary elections in proportional systems with an application to German national elections from 1949 to 2009. Electoral Studies30: 497–509.
MarshallA. W., OlkinI., and PukelsheimF.2002. A majorization comparison of apportionment methods in proportional representation. Social Choice and Welfare19: 885–900.
6.
NohlenD., GrotzF., KrennerichM., and ThibautB.2000. Appendix: Electoral systems in independent countries. InInternational Encyclopedia of Elections, ed. RoseR., 353–379. Washington, DC: Congressional Quarterly.
7.
PukelsheimF.2000. Mandatszuteilungen bei Verhältniswahlen: Vertretungsgewichte der Mandate. Kritische Vierteljahresschrift für Gesetzgebung und Rechtswissenschaft83: 76–103. http://www.uni-augsburg.de/pukelsheim/2000b.html.
SchusterK., PukelsheimF., DrtonM., and DraperN. R.2003. Seat biases of apportionment methods for proportional representation. Electoral Studies22: 651–676.
10.
SchwingenschlöglU., and PukelsheimF.2006. Seat biases in proportional representation systems with thresholds. Social Choice and Welfare27: 189–193.
11.
Statistisches Bundesamt. 2005. Wahl zum 16. Deutschen Bundestag am 18. September 2005. Heft 1: Ergebnisse und Vergleichszahlen früherer Bundestags-, Europa-und Landtagswahlen sowie Strukturdaten für die Bundestagswahlkreise.Stuttgart: Metzler-Poeschel.