Editing D'Hondt method (section)

== Motivation ==
Proportional representation systems aim to allocate seats to parties approximately in proportion to the number of votes received. For example, if a party wins one-third of the votes then it should gain about one-third of the seats. In general, exact proportionality is not possible because these divisions produce fractional numbers of seats. As a result, several methods, of which the D'Hondt method is one, have been devised which ensure that the parties' seat allocations, which are of whole numbers, are as proportional as possible.<ref name="gallagher">{{cite journal |last=Gallagher |first=Michael |date=1991 |title=Proportionality, disproportionality and electoral systems |url=http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElectoralStudies1991.pdf |journal=Electoral Studies |archive-url=https://web.archive.org/web/20131116104818/http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElectoralStudies1991.pdf |archive-date=November 16, 2013|volume=10 |issue=1 |pages=33–51 |doi=10.1016/0261-3794(91)90004-C |access-date=30 January 2016}}</ref> 
Although all of these methods approximate proportionality, they do so by minimizing different kinds of disproportionality. 
The D'Hondt method minimizes the largest seats-to-votes ratio.<ref name="Medzihorsky2019">{{cite journal |author=Juraj Medzihorsky |title=Rethinking the D'Hondt method |journal=Political Research Exchange |volume=1 |issue=1 |pages=1625712 |year=2019 |doi=10.1080/2474736X.2019.1625712 |doi-access=free}}</ref> Empirical studies based on other, more popular concepts of disproportionality show that the D'Hondt method is one of the least proportional among the proportional representation methods. The D'Hondt favours large [[political party|parties]] and [[Electoral coalition|coalitions]] over small parties due to [[strategic voting]].<ref name="auto">{{cite conference |first=Friedrich |last=Pukelsheim |title=Seat bias formulas in proportional representation systems |book-title=4th ECPR General Conference |url=http://www.essex.ac.uk/ecpr/events/generalconference/pisa/papers/PP996.pdf |archive-url=https://web.archive.org/web/20090207140906/http://www.essex.ac.uk/ecpr/events/generalconference/pisa/papers/PP996.pdf |archive-date=7 February 2009 |year=2007 }}</ref><ref name="Seat biases">{{cite journal |last1=Schuster |first1=Karsten |last2=Pukelsheim |first2=Friedrich |last3=Drton |first3=Mathias |last4=Draper |first4=Norman R. |date=2003 |title=Seat biases of apportionment methods for proportional representation |url=http://www.math.uni-augsburg.de/stochastik/pukelsheim/2003b.pdf |journal=Electoral Studies |volume=22 |issue=4 |pages=651–676 |doi=10.1016/S0261-3794(02)00027-6 |access-date=2016-02-02 |archive-url=https://web.archive.org/web/20160215162203/http://www.math.uni-augsburg.de/stochastik/pukelsheim/2003b.pdf |archive-date=2016-02-15 |url-status=dead }}</ref><ref>{{cite journal |last=Benoit |first=Kenneth |year=2000 |title=Which Electoral Formula Is the Most Proportional? A New Look with New Evidence |journal=Political Analysis |volume=8 |issue=4 |pages=381–388 |doi=10.1093/oxfordjournals.pan.a029822 |url=http://www.kenbenoit.net/pdfs/PA84-381-388.pdf |access-date=2016-02-11 |archive-url=https://web.archive.org/web/20180728202050/http://kenbenoit.net/pdfs/PA84-381-388.pdf |archive-date=2018-07-28 |url-status=dead }}</ref><ref>{{cite journal |last=Lijphart |first=Arend |year=1990 |title=The Political Consequences of Electoral Laws, 1945-85 |journal=The American Political Science Review |volume=84 |issue=2 |pages=481–496 |doi=10.2307/1963530|jstor=1963530 |s2cid=146438586 }}</ref> In comparison, the [[Sainte-Laguë method]] reduces the disproportional bias towards large parties and it generally has a more equal [[seats-to-votes ratio]] for different sized parties.<ref name="auto"/>

The axiomatic properties of the D'Hondt method were studied and they proved that the D'Hondt method is a consistent and monotone method that reduces [[political fragmentation]] by encouraging coalitions.<ref name=":0">{{Cite journal|last1=Balinski |last2=Young|first1=M. L. |first2=H. P.|date=1978|title=The Jefferson method of Apportionment|url=http://pure.iiasa.ac.at/597/1/PP-76-006.pdf|journal=SIAM Rev|volume=20 |issue=2|pages=278–284 |doi=10.1137/1020040|s2cid=122291481 }}</ref><ref>{{Cite journal|last1=Balinski |last2=Young |first1=M. L. |first2=H. P. |date=1979 |title=Criteria for proportional representation |journal= [[Operations Research (journal)|Operations Research]] |volume=27 |pages=80–95 |doi=10.1287/opre.27.1.80|url=http://pure.iiasa.ac.at/525/1/RR-76-020.pdf }}</ref> A method is consistent if it treats parties that received tied votes equally. Monotonicity means that the number of seats provided to any state or party will not decrease if the house size increases.