Editing Quota method (section)

== Pros and cons ==
It is easy for a voter to understand how the largest remainder method allocates seats. Moreover, the largest remainder method satisfies the [[quota rule]] (each party's seats are equal to its ideal share of seats, either rounded up or rounded down) and was designed to satisfy that criterion. However, this comes at the cost of greater inequalities in the [[seats-to-votes ratio]], which can violate the principle of [[one man, one vote]].

However, a greater concern for social choice theorists, and the primary cause behind its abandonment in many countries, is the tendency of such rules to produce erratic or irrational behaviors called [[Apportionment paradox|apportionment paradoxes]]:

* ''Increasing'' the number of seats in a legislature can ''decrease'' a party's apportionment of seats, called the [[Alabama paradox]].
* Adding more parties to the legislature can cause a bizarre kind of [[spoiler effect]] called the [[New states paradox|new state paradox]].
** When Congress first admitted [[Oklahoma]] to the Union, the House was expanded by 5 seats, equal to Oklahoma's apportionment, to ensure it would not affect the seats for any existing states. However, when the full apportionment was recalculated, the House was stunned to learn Oklahoma's entry had caused New York to lose a seat to Maine, despite there being no change in either state's population.<ref name="Caulfield22">{{cite journal |last=Caulfield |first=Michael J. |date=November 2010 |title=Apportioning Representatives in the United States Congress – Paradoxes of Apportionment |url=http://www.maa.org/publications/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-paradoxes-of-apportionment |journal=Convergence |publisher=Mathematical Association of America |doi=10.4169/loci003163|doi-broken-date=29 December 2024 }}</ref><ref name="Stein200822">{{cite book |last=Stein |first=James D. |title=How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics |publisher=Smithsonian Books |year=2008 |isbn=9780061241765 |location=New York}}</ref>{{rp|232–233}}
** By the same token, apportionments may depend on the precise order in which the apportionment is calculated. For example, identifying winning independents first and electing them, then apportioning the remaining seats, will produce a different result from treating each independent as if they were their own party and then computing a single overall apportionment.<ref name=":52" />

Such paradoxes also have the additional drawback of making it difficult or impossible to generalize  procedure to more complex apportionment problems such as [[Biproportional apportionment|biproportional apportionments]] or [[Vote linkage|partial vote linkage]]. This is in part responsible for the extreme complexity of administering elections by quota-based rules like the single transferable vote (see [[counting single transferable votes]]).

=== Alabama paradox ===
The [[Alabama paradox]] is when an ''increase'' in the total number of seats leads to a ''decrease'' in the number of seats allocated to a certain party. In the example below, when the number of seats to be allocated is increased from 25 to 26, parties D and E end up with fewer seats, despite their entitlements increasing.

With 25 seats, the results are:
{| class="wikitable"
!Party
!A
!B
!C
!D
!E
!F
!Total
|-
!Votes
|1500
|1500
|900
|500
|500
|200
|5100
|-
!Quotas received
|7.35
|7.35
|4.41
|2.45
|2.45
|0.98
|25
|-
!Automatic seats
|7
|7
|4
|2
|2
|0
|22
|-
!Remainder
|0.35
|0.35
|0.41
|0.45
|0.45
|0.98
|
|-
!Surplus seats
|0
|0
|0
|1
|1
|1
|3
|-
!Total seats
|7
|7
|4
|'''''3'''''
|'''''3'''''
|1
|25
|}
With 26 seats, the results are:
{| class="wikitable"
!Party
!A
!B
!C
!D
!E
!F
!Total
|-
!Votes
|1500
|1500
|900
|500
|500
|200
|5100
|-
!Quotas received
|7.65
|7.65
|4.59
|2.55
|2.55
|1.02
|26
|-
!Automatic seats
|7
|7
|4
|2
|2
|1
|23
|-
!Remainder
|0.65
|0.65
|0.59
|0.55
|0.55
|0.02
|
|-
!Surplus seats
|1
|1
|1
|0
|0
|0
|3
|-
!Total seats
|8
|8
|5
|'''''2'''''
|'''''2'''''
|1
|26
|}