Editing Highest averages method (section)

==References==
{{reflist|1=30em|refs=
<ref name="Pukelsheim-2017-1">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Divisor Methods of Apportionment: Divide and Round |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=71–93  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_4 |access-date=2021-09-01 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_4 |isbn=978-3-319-64707-4}}</ref>
<ref name="Pukelsheim-2017-5">{{cite book|last=Pukelsheim |first=Friedrich |chapter=From Reals to Integers: Rounding Functions, Rounding Rules |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=59–70 |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_3 |access-date=2021-09-01 |place= |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_3 |isbn=978-3-319-64707-4}}</ref>
<ref name="Balinski-1982">{{cite book |last1=Balinski |first1=Michel L. |url=https://archive.org/details/fairrepresentati00bali |title=Fair Representation: Meeting the Ideal of One Man, One Vote |last2=Young |first2=H. Peyton |publisher=Yale University Press |year=1982 |isbn=0-300-02724-9 |location=New Haven |url-access=registration}}</ref>
<ref name="Pukelsheim-2017-7">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Securing System Consistency: Coherence and Paradoxes |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=159–183  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_9 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_9 |isbn=978-3-319-64707-4}}</ref>
<ref name="Argersinger-2012">{{Citation |title="Injustices and Inequalities": The Politics of Apportionment, 1870–1888 |date=2012 |work=Representation and Inequality in Late Nineteenth-Century America: The Politics of Apportionment |pages=8–41 |editor-last=Argersinger |editor-first=Peter H. |url=https://www.cambridge.org/core/books/representation-and-inequality-in-late-nineteenthcentury-america/injustices-and-inequalities/64C5A0FB683166BE4100230A7FFA334B |access-date=2024-08-04 |place=Cambridge |publisher=Cambridge University Press |doi=10.1017/cbo9781139149402.002 |isbn=978-1-139-14940-2 |quote=Apportionment not only determined the power of different states in Congress but, because it allocated electors as well, directly affected the election of the president. Indeed, the peculiar apportionment of 1872, adopted in violation of the prevailing law mandating the method of allocating seats, was directly responsible for the 1876 election of Rutherford B. Hayes with a popular vote minority. Had the previous method been followed, even the Electoral Commission would have been unable to place Hayes in the White House. |archive-date=2018-06-07 |archive-url=https://web.archive.org/web/20180607004155/https://www.cambridge.org/core/books/representation-and-inequality-in-late-nineteenthcentury-america/injustices-and-inequalities/64C5A0FB683166BE4100230A7FFA334B |url-status=live}}</ref>
<ref name="Gallagher-1991">{{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 |url-status=dead |journal=Electoral Studies |volume=10 |issue=1 |pages=33–51 |doi=10.1016/0261-3794(91)90004-C |archive-url=https://web.archive.org/web/20160304030108/https://www.tcd.ie/Political_Science/staff/michael_gallagher/ElectoralStudies1991.pdf |archive-date=2016-03-04 |access-date=}}</ref>
<ref name="Gallagher-1992">{{Cite journal |last=Gallagher |first=Michael |date=1992 |title=Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities |url=https://www.tcd.ie/Political_Science/people/michael_gallagher/BJPS1992.pdf |journal=British Journal of Political Science |volume=22 |issue=4 |pages=469–496 |doi=10.1017/S0007123400006499 |issn=0007-1234 |s2cid=153414497}}</ref>
<ref name="Pennisi-1998">{{Cite journal |last=Pennisi |first=Aline |date=March 1998 |title=Disproportionality indexes and robustness of proportional allocation methods |url=https://linkinghub.elsevier.com/retrieve/pii/S0261379497000528 |journal=Electoral Studies |language=en |volume=17 |issue=1 |pages=3–19 |doi=10.1016/S0261-3794(97)00052-8 |access-date=2024-05-10 |archive-date=2024-04-24 |archive-url=https://web.archive.org/web/20240424212534/https://linkinghub.elsevier.com/retrieve/pii/S0261379497000528 |url-status=live}}</ref>
<ref name="Balinski-1980">{{Cite journal |last1=Balinski |first1=M. L. |last2=Young |first2=H. P. |date=January 1980 |title=The Sainte-Laguë method of apportionment |journal=Proceedings of the National Academy of Sciences |language=en |volume=77 |issue=1 |pages=1–4 |doi=10.1073/pnas.77.1.1 |doi-access=free |issn=0027-8424 |pmc=348194 |pmid=16592744|bibcode=1980PNAS...77....1B}}</ref>
<ref name="Pukelsheim-2017-8">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Tracing Peculiarities: Vote Thresholds and Majority Clauses |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=207–223  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_11 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_11 |isbn=978-3-319-64707-4}}</ref>
<ref name="Pukelsheim-2017-2">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Favoring Some at the Expense of Others: Seat Biases |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=127–147  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_7 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_7 |isbn=978-3-319-64707-4}}</ref>
<ref name="Ernst-1994">{{Cite journal |last=Ernst |first=Lawrence R. |date=1994 |title=Apportionment Methods for the House of Representatives and the Court Challenges |url=https://www.jstor.org/stable/2661618 |journal=Management Science |volume=40 |issue=10 |pages=1207–1227 |doi=10.1287/mnsc.40.10.1207 |jstor=2661618 |issn=0025-1909 |access-date=2024-02-10 |archive-date=2024-05-10 |archive-url=https://web.archive.org/web/20240510004655/https://www.jstor.org/stable/2661618 |url-status=live}}</ref>
<ref name="Pukelsheim-2017-4">{{cite book|last=Pukelsheim |first=Friedrich |chapter=From Reals to Integers: Rounding Functions and Rounding Rules |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=59–70  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_3 |access-date=2021-09-01 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_3 |isbn=978-3-319-64707-4}}</ref>
<ref name="Balinski-1975">{{Cite journal |last1=Balinski |first1=M. L. |last2=Young |first2=H. P. |date=1975-08-01 |title=The Quota Method of Apportionment |url=https://doi.org/10.1080/00029890.1975.11993911 |journal=The American Mathematical Monthly |volume=82 |issue=7 |pages=701–730 |doi=10.1080/00029890.1975.11993911 |issn=0002-9890}}</ref>
<ref name="Ricca-2017">{{Cite book |last1=Ricca |first1=Federica |url=https://dl.acm.org/doi/book/10.5555/3180776 |title=Trends in Computational Social Choice |last2=Scozzari |first2=Andrea |last3=Serafini |first3=Paola |publisher=Lulu.com |year=2017 |isbn=978-1-326-91209-3 |editor-last=Endriss |editor-first=Ulle |pages=49–68 |chapter=A Guided Tour of the Mathematics of Seat Allocation and Political Districting |access-date=2024-10-08 |archive-date=2024-10-08 |archive-url=https://web.archive.org/web/20241008025430/https://dl.acm.org/doi/book/10.5555/3180776 |url-status=live}}</ref>
<ref name="Dancisin-2017">{{Cite journal |last=Dančišin |first=Vladimír |date=2017-01-01 |title=No-show paradox in Slovak party-list proportional system |url=https://www.degruyter.com/document/doi/10.1515/humaff-2017-0002/html?lang=en |journal=Human Affairs |language=en |volume=27 |issue=1 |pages=15–21 |doi=10.1515/humaff-2017-0002 |issn=1337-401X}}</ref>
<ref name="Pukelsheim-2017-0">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Exposing Methods: The 2014 European Parliament Elections |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=1–40  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_1 |access-date=2024-07-03 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_1 |isbn=978-3-319-64707-4}}</ref>
<ref name="Caulfield-2012">{{Cite journal |last=Caulfield |first=Michael J. |date=2012 |title=What If? How Apportionment Methods Choose Our Presidents |url=https://www.jstor.org/stable/10.5951/mathteacher.106.3.0178 |journal=The Mathematics Teacher |volume=106 |issue=3 |pages=178–183 |doi=10.5951/mathteacher.106.3.0178 |jstor=10.5951/mathteacher.106.3.0178 |issn=0025-5769}}</ref>
<ref name="Pukelsheim-2017-3">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Targeting the House Size: Discrepancy Distribution |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=107–125  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_6 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_6 |isbn=978-3-319-64707-4}}</ref>
<ref name="MAA-2020">{{Cite web |title=Apportioning Representatives in the United States Congress - Adams' Method of Apportionment {{!}} Mathematical Association of America |url=https://www.maa.org/press/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-adams-method-of-apportionment |archive-url=https://web.archive.org/web/20240609062338/https://maa.org/press/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-adams-method-of-apportionment |website=www.maa.org|archive-date=9 June 2024 }}</ref>
<ref name="Ichimori-2010">{{Cite journal |last=Ichimori |first=Tetsuo |date=2010 |title=New apportionment methods and their quota property |journal=JSIAM Letters |volume=2 |pages=33–36 |doi=10.14495/jsiaml.2.33 |issn=1883-0617 |doi-access=free}}</ref>
<ref name="EU-2011">{{Cite report |date=2011 |title=The allocation between the EU Member States of the seats in the European Parliament |url=https://www.europarl.europa.eu/RegData/etudes/note/join/2011/432760/IPOL-AFCO_NT(2011)432760_EN.pdf |publisher=European Parliament |access-date=2024-01-26 |archive-date=2024-05-12 |archive-url=https://web.archive.org/web/20240512205358/https://www.europarl.europa.eu/RegData/etudes/note/join/2011/432760/IPOL-AFCO_NT(2011)432760_EN.pdf |url-status=live}}</ref>
<ref name="Sainte-2024">Webster, André. [http://www.numdam.org/item/10.24033/asens.627.pdf "La représentation proportionnelle et la méthode des moindres carrés."] {{Webarchive|url=https://web.archive.org/web/20240515222106/http://www.numdam.org/item/10.24033/asens.627.pdf |date=2024-05-15}} ''Annales scientifiques de l'école Normale Supérieure.'' Vol. 27. 1910.</ref>
<ref name="Pukelsheim-2017-9">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Truncating Seat Ranges: Minimum-Maximum Restrictions |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=225–245  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_12 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_12 |isbn=978-3-319-64707-4}}</ref>
<ref name="Huntington-1929">{{Cite journal |last=Huntington |first=Edward V. |date=1929 |title=The Report of the National Academy of Sciences on Reapportionment |url=https://www.jstor.org/stable/1653304 |journal=Science |volume=69 |issue=1792 |pages=471–473 |doi=10.1126/science.69.1792.471 |jstor=1653304 |pmid=17750282 |bibcode=1929Sci....69..471H |issn=0036-8075}}</ref>
<ref name="Pukelsheim-2017-6">{{cite book|last=Pukelsheim |first=Friedrich |chapter=Quota Methods of Apportionment: Divide and Rank |date=2017 |title=Proportional Representation: Apportionment Methods and Their Applications |pages=95–105  |chapter-url=https://doi.org/10.1007/978-3-319-64707-4_5 |access-date=2024-05-10 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-64707-4_5 |isbn=978-3-319-64707-4}}</ref>
<ref name="Denmark-2016">{{Cite web |title=The Parliamentary Electoral System in Denmark |url=http://www.thedanishparliament.dk/Democracy/Elections_and_referendums/~/media/PDF/publikationer/English/The%20Parliamentary%20System%20of%20Denmark_2011.ashx |url-status=dead |archive-url=https://web.archive.org/web/20160828185107/http://www.thedanishparliament.dk/Democracy/Elections_and_referendums/~/media/PDF/publikationer/English/The%20Parliamentary%20System%20of%20Denmark_2011.ashx |archive-date=2016-08-28}}</ref>
<ref name="Lauwers-2008">{{Cite journal |last1=Lauwers |first1=Luc |last2=Van Puyenbroeck |first2=Tom |date=2008 |title=Minimally Disproportional Representation: Generalized Entropy and Stolarsky Mean-Divisor Methods of Apportionment |url=http://dx.doi.org/10.2139/ssrn.1304628 |journal=SSRN Electronic Journal |doi=10.2139/ssrn.1304628 |s2cid=124797897 |issn=1556-5068}}</ref>
<ref name="Wada-2012">{{Cite journal |last=Wada |first=Junichiro |date=2012-05-01 |title=A divisor apportionment method based on the Kolm–Atkinson social welfare function and generalized entropy |url=https://www.sciencedirect.com/science/article/pii/S0165489612000194 |journal=Mathematical Social Sciences |volume=63 |issue=3 |pages=243–247 |doi=10.1016/j.mathsocsci.2012.02.002 |issn=0165-4896}}</ref>
<ref name="Agnew-2008">{{Cite journal |last=Agnew |first=Robert A. |date=April 2008 |title=Optimal Congressional Apportionment |url=https://www.tandfonline.com/doi/full/10.1080/00029890.2008.11920530 |journal=The American Mathematical Monthly |language=en |volume=115 |issue=4 |pages=297–303 |doi=10.1080/00029890.2008.11920530 |s2cid=14596741 |issn=0002-9890}}</ref>
}}

{{voting systems}}

[[Category:Party-list proportional representation]]
[[Category:Apportionment methods]]