Sainte-Laguë method: Difference between revisions
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{{Wikipedia}}
The Webster/Sainte-Laguë Method is a [[Highest averages method]] used for allocating seats [[Proportionate representation | proportionally]] for representative assemblies with [[Party-list proportional representation|party list]] [[voting systems]]. It works like [[D'Hondt method]], except that you use divisors 1, 3, 5, 7, ... instead of 1, 2, 3, 4, ...
In the modified Sainte-Laguë method, the first divisor is modified to 1.4. The sequence of divisors is then 1.4, 3, 5, 7, ... The modified Sainte-Laguë method is used for elections to the Danish parliament.
== Allocation ==
After all the votes have been tallied, successive [[quota]]s are calculated for each party. The formula for the quotient is <ref name="lijphart">{{citation|contribution=Degrees of proportionality of proportional representation formulas|first=Arend|last=Lijphart|authorlink=Arend Lijphart|pages=170–179|title=Electoral Laws and Their Political Consequences|volume=1|series=Agathon series on representation|editor1-first=Bernard|editor1-last=Grofman|editor2-first=Arend|editor2-last=Lijphart|publisher=Algora Publishing|year=2003|isbn=9780875862675}}. See in particular the section "Sainte-Lague", [https://books.google.com/books?id=o1dqas0m8kIC&pg=PA174 pp. 174–175].</ref>
:: <math>\text{quotient} = \frac V {2s+1}</math>
where:
* ''V'' is the total number of votes that party received, and
* ''s'' is the number of seats that have been allocated so far to that party, initially 0 for all parties.
Whichever party has the highest quotient gets the next seat allocated, and their quotient is recalculated. The process is repeated until all seats have been allocated.
The Webster/Sainte-Laguë method does not ensure that a party receiving more than half the votes will win at least half the seats; nor does its modified form.<ref>{{citation|contribution=Election inversions under proportional representation|url=http://userpages.umbc.edu/~nmiller/RESEARCH/NRMILLER.PCS2013.pdf|first=Nicholas R.|last=Miller|date=February 2013|title=Annual Meeting of the Public Choice Society, New Orleans, March 8-10, 2013}}.</ref>
== Extensions of theory ==
Several [[cardinal PR]] methods reduce to Sainte-Laguë if certain divisors are used. Some of which are:
* [[Sequential proportional approval voting]]
* [[Single distributed vote]]
* [[Reweighted Range Voting]]
== Notes ==
Webster, unlike D'Hondt, doesn't guarantee that a majority of voters will get at least half of the seats.<ref name="Miller pp. 4–25">{{cite journal | last=Miller | first=Nicholas R. | title=Election Inversions under Proportional Representation | journal=Scandinavian Political Studies | publisher=Wiley | volume=38 | issue=1 | date=2014-12-05 | issn=0080-6757 | doi=10.1111/1467-9477.12038 | pages=4–25|url=https://userpages.umbc.edu/~nmiller/RESEARCH/NRMILLER.PCS2013.pdf|access-date=2020-03-24}}</ref>
{| class="wikitable"
|+35-seat example
!Party
!Votes
!Votes %
!2nd-to-last round seats
!2nd-to-last round divisors
!Final seats
!Final divisors
!Seats %
|-
|A
|'''503'''
|'''50.3%'''
|16
|15.2424 (503/33)
|17
|14.3714 (503/35)
|'''48.57%'''
|-
|B
|304
|30.4%
|10
|14.4762 (304/21)
|11
|13.2174 (304/23)
|31.43%
|-
|C
|193
|19.3%
|6
|14.8461 (193/15)
|7
|12.8666 (193/15)
|20%
|-
|Total seats awarded
|
|
|32
|
|35
|
|
|}
If D'Hondt had been used, the final divisor would've been 27.944, with (results calculated by rounding down to the nearest number) Party A getting 18 seats out of 35, a 51.42% majority (503/27.944), B 10 seats (304/27.944), and C 6 seats.
== References ==
<references />
[[Category:Party list theory]]
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