Alternating sign matrix: Difference between revisions

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{{No footnotes|date=November 2010}}
== ' Pula slight nod ==
The '''Gallagher Index''' (or [[least squares]] index) is used to measure the disproportionality of an electoral outcome, that is the difference between the percentage of votes received and the percentage of seats a party gets in the resulting legislature. This is especially useful for comparing proportionality across [[electoral systems]]. The index involves taking the [[square root]] of half the [[sum]] of the squares of the difference between percent of vote and percent of seats for each of the [[political parties]].


: <math>\mathrm{LSq} = \sqrt{ \frac{1}{2} \sum_{i=1}^n ( V_i-S_i ) ^2}</math>{{sfn|Gallagher|1991|p=40}}<!--What are ''V''<sub>''i''</sub> and ''S''<sub>''i''</sub>?-->
Side walls extending out,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_24.htm オークリー サングラス フロッグスキン], then instantly swept Nabing stab sword, sharp thorn sword extremely tough, just barely issued a 'laugh' is heard on countless powder and then disappeared into see.<br><br>'Good!' Pula surprise shouted, 'even C2 hardness weapons are easily destroyed!'<br>What<br>behalf?<br><br>representative of a normal second-order cosmic Warrior,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_11.htm オークリー サングラス 登山], will stop this attack.<br><br>'the stronger the better.' Pula eyes shine, threw the second handle backup weapon,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_55.htm オークリー サングラス 交換レンズ], the same thorn-edged sword. These weapons are not worth ...... Standby Force is a valuable weapon, read the force of weapons.<br><br>'Chi Chi ,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_12.htm スポーツサングラス オークリー]......'<br><br>time, received three stab sword color streamer spread, slight tremors, cracked a little faint,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_71.htm 自転車 サングラス オークリー], but the damage is very slow.<br><br>'C5 level is difficult to destroy?' Pula slight nod, smile surpassed, 'Very good,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_27.htm サングラス オークリー 偏光], very good.'<br><br>a spaceship,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_44.htm テニス サングラス オークリー], the strongest attacks will not be passive aggressive entrance,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_50.htm オークリーサングラス取扱店], because
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<ul>
 
  <li>[http://www.shipingheka.com/plus/feedback.php?aid=264 http://www.shipingheka.com/plus/feedback.php?aid=264]</li>
 
  <li>[http://www.klt365.com/plus/feedback.php?aid=410 http://www.klt365.com/plus/feedback.php?aid=410]</li>
 
  <li>[http://sxmz.org/sxmz/home.php?mod=space&uid=468563 http://sxmz.org/sxmz/home.php?mod=space&uid=468563]</li>
 
</ul>


The index weighs the deviations by their own value, creating a responsive index, ranging from 0 to 100. The lower the index value the lower the disproportionality and vice versa. [[Michael Gallagher (academic)|Michael Gallagher]], who created the index, included 'other' parties as a whole category, and [[Arend Lijphart]] modified it, excluding those parties. Unlike the well-known [[Loosemore–Hanby index]], the Gallagher index is less sensitive to small discrepancies.{{sfn|Gallagher|1991|p=41}}
== only human society elites 'Warrior' aspect where they can. ==


== Example of calculating disproportionality ==
Area,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_14.htm オークリー ゴルフ サングラス], only human society elites 'Warrior' aspect where they can.<br><br>'Yes,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_39.htm オークリー サングラス ノーズパッド], my wife. turned Luofeng parents ask you,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_58.htm ロードバイク サングラス オークリー], you say ...... Luo Feng soon returned.' Chen Valley exhortations soon.<br><br>'I understand,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_21.htm スポーツサングラス オークリー].' Chen Gu wife nodded.<br><br>,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_55.htm オークリー サングラス 度付き 価格]......<br>City on<br>and base completely different atmosphere wilderness area, but also throughout Eurasia,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_65.htm 偏光サングラス オークリー], monsters gathered almost up to the city - 003 suburbs in the northern edge of the city, is undergoing a peak of the war, two and three God of War Lord monster fight!<br><br>'I have to speed up!'<br><br>'Otherwise,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_41.htm ゴルフ用サングラスオークリー], if the monster after winning return lair lord, I did not point opportunities. Ares humans win if they go to the monster lair, I also have no chance.' Luo Feng stature erratic move forward quickly,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_21.htm スポーツサングラス オークリー], 'my only chance that while they battle it out for a short time. '<br><br>parents are bases City
 
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This table uses the [[New Zealand general election, 2005|New Zealand 2005 election]] result.<ref name="General election, 2005">{{cite web |title=Official Count Results -- Electorate Status |url= http://www.electionresults.govt.nz/electionresults_2005/electoratestatus.html |publisher=[[Chief Electoral Office (New Zealand){{!}}Chief Electoral Office]] |accessdate=9 August 2013 |date=1 October 2005}}</ref> Note that since New Zealand uses the [[Mixed-member proportional representation|MMP voting system]], [[Elections in New Zealand|voters have two votes]]. This list uses the ''party vote'', which determines the proportionality of the [[New Zealand House of Representatives|House]]; the ''electorate vote'' determines the local member.
<ul>
 
 
{| class="wikitable"
  <li>[http://222.73.18.55:10010/bbs/viewthread.php?tid=162299&extra= http://222.73.18.55:10010/bbs/viewthread.php?tid=162299&extra=]</li>
! party
 
! % of votes
  <li>[http://eastdragonuae.com/plus/feedback.php?aid=14 http://eastdragonuae.com/plus/feedback.php?aid=14]</li>
! % of seats
 
! difference
  <li>[http://www.hhhtjc.com/home.php?mod=space&uid=286290 http://www.hhhtjc.com/home.php?mod=space&uid=286290]</li>
! difference<br>squared
 
|-
</ul>
| [[New Zealand Labour Party|Labour]]
| align="right" | 41.10
| align="right" | 41.32
| align="right" | 0.22
| align="right" | 0.0484
|-
| [[New Zealand National Party|National]]
| align="right" | 39.10
| align="right" | 39.67
| align="right" | 0.57
| align="right" | 0.3249
|-
| [[New Zealand First|NZ First]]
| align="right" | 5.72
| align="right" | 5.79
| align="right" | 0.07
| align="right" | 0.0049
|-
| [[Green Party of Aotearoa New Zealand|Greens]]
| align="right" | 5.30
| align="right" | 4.96
| align="right" | 0.34
| align="right" | 0.1156
|-
| [[Māori Party|Māori]]
| align="right" | 2.12
| align="right" | 3.30
| align="right" | 1.18
| align="right" | 1.3924
|-
| [[United Future New Zealand|United Future]]
| align="right" | 2.67
| align="right" | 2.48
| align="right" | 0.19
| align="right" | 0.0361
|-
| [[ACT New Zealand|ACT]]
| align="right" | 1.51
| align="right" | 1.65
| align="right" | 0.14
| align="right" | 0.0196
|-
| [[New Zealand Progressive Party|Progressives]]
| align="right" | 1.16
| align="right" | 0.82
| align="right" | 0.34
| align="right" | 0.1156
|-
| [[Destiny New Zealand|Destiny]]
| align="right" | 0.62
| align="right" | 0
| align="right" | 0.62
| align="right" | 0.3844
|-
| [[Aotearoa Legalise Cannabis Party|Legalise Cannabis]]
| align="right" | 0.25
| align="right" | 0
| align="right" | 0.25
| align="right" | 0.0625
|-
| [[Christian Heritage New Zealand|Christian Heritage]]
| align="right" | 0.12
| align="right" | 0
| align="right" | 0.12
| align="right" | 0.0144
|-
| [[Alliance (New Zealand political party)|Alliance]]
| align="right" | 0.07
| align="right" | 0
| align="right" | 0.07
| align="right" | 0.0049
|-
| [[New Zealand Family Rights Protection Party|Family Rights]]
| align="right" | 0.05
| align="right" | 0
| align="right" | 0.05
| align="right" | 0.0025
|-
| [[New Zealand Democratic Party|Democrats]]
| align="right" | 0.05
| align="right" | 0
| align="right" | 0.05
| align="right" | 0.0025
|-
| [[Libertarianz]]
| align="right" | 0.04
| align="right" | 0
| align="right" | 0.04
| align="right" | 0.0016
|-
| [[Direct Democracy Party of New Zealand|Direct Democracy]]
| align="right" | 0.03
| align="right" | 0
| align="right" | 0.04
| align="right" | 0.0016
|-
| [[99 MP Party|99MP]]
| align="right" | 0.03
| align="right" | 0
| align="right" | 0.03
| align="right" | 0.0009
|-
| [[One New Zealand Party|OneNZ]]
| align="right" | 0.02
| align="right" | 0
| align="right" | 0.02
| align="right" | 0.0004
|-
| [[The Republic of New Zealand Party|Republicans]]
| align="right" | 0.02
| align="right" | 0
| align="right" | 0.02
| align="right" | 0.0004
|-
| align="right" colspan="4" | '''total of squares of differences'''
| align="right" | 2.5336
|-
| align="right" colspan="4" | '''total / 2'''
| align="right" | 1.2668
|-
| align="right" colspan="4" | '''square root of (total / 2)'''
| align="right" | '''1.13'''
|}
 
Thus the disproportionality of the 2005 New Zealand election is 1.13, which is very low by international standards.<ref>{{cite web |last=Gallagher |first=Michael |title=Election indices |url= http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf |publisher=[[Trinity College, Dublin]] |accessdate=9 August 2013|authorlink=Michael Gallagher (academic) |format=PDF |year=2013}}</ref>
 
Note that the Māori Party has the highest difference, which is significantly above the others. This is due to New Zealand's system of [[Māori electorates|reserved seats for Māori]]. The Māori seats are allocated by votes on a separate electoral roll, and while any party can contest these seats, they are generally won by either the Māori Party, the Labour Party, or New Zealand First.
 
== Other indices ==
 
The [[Sainte–Laguë Index]] is considered by Gallagher to be ''probably the soundest of all the measures''. This is closely related to the [[Pearson's chi-squared test]] which has better statistical underpinning.
:<math>\mathrm{SLI} = \sum {(S-V)^2 \over V}</math>
 
==Notes==
{{Portal|Politics}}
{{Reflist}}
 
== References ==
* {{cite journal |ref=harv |last1=Benoit |first1= Kenneth |year= 2000 |title=Which Electoral Formula Is the Most Proportional? A New Look with New Evidence |journal=Political Analysis |volume=8 |pages=381–388 |url= http://pan.oxfordjournals.org/content/8/4/381.short |accessdate=10 August 2013}}
* {{cite journal |ref=harv |last1= Gallagher |first1= Michael |authorlink=Michael Gallagher (academic) |year=1991 |title=Proportionality, Disproportionality and Electoral Systems |journal=Electoral Studies |volume= 10 |pages=33–51}}
* {{cite journal |ref=harv |last1= Gallagher |first1= Michael |authorlink=Michael Gallagher (academic) |year=1992 |title=Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities |journal=British Journal of Political Science |volume= 22 |pages=469–496}}
* {{cite book |ref=harv |editor-last1= Gallagher |editor-first1= Michael |editor1-link=Michael Gallagher (academic) |editor-last2=Mitchell |editor-first2=P |year=2005 |title=The Politics of Electoral Systems | location= [[Oxford]] | publisher= [[Oxford University Press]] |at= Appendix B |isbn =0-19-925756-6}}
* {{cite journal |ref=harv |last1= Kestelman |first1= Philip |date=March 1999 |title=Quantifying Representativity |journal=Voting matters |volume= 10 |url = http://www.votingmatters.org.uk/ISSUE10/P6.HTM |accessdate=10 August 2013}}
 
== External links ==
* [[:Image:Aus07Gallagher.PNG|Gallagher Index of the results]] of the [[Australian federal election, 2007|Australian 2007 federal election]]
 
[[Category:Voting systems]]
[[Category:Psephology]]
[[Category:Statistical terminology]]

Latest revision as of 16:38, 13 October 2014

' Pula slight nod

Side walls extending out,オークリー サングラス フロッグスキン, then instantly swept Nabing stab sword, sharp thorn sword extremely tough, just barely issued a 'laugh' is heard on countless powder and then disappeared into see.

'Good!' Pula surprise shouted, 'even C2 hardness weapons are easily destroyed!'
What
behalf?

representative of a normal second-order cosmic Warrior,オークリー サングラス 登山, will stop this attack.

'the stronger the better.' Pula eyes shine, threw the second handle backup weapon,オークリー サングラス 交換レンズ, the same thorn-edged sword. These weapons are not worth ...... Standby Force is a valuable weapon, read the force of weapons.

'Chi Chi ,スポーツサングラス オークリー......'

time, received three stab sword color streamer spread, slight tremors, cracked a little faint,自転車 サングラス オークリー, but the damage is very slow.

'C5 level is difficult to destroy?' Pula slight nod, smile surpassed, 'Very good,サングラス オークリー 偏光, very good.'

a spaceship,テニス サングラス オークリー, the strongest attacks will not be passive aggressive entrance,オークリーサングラス取扱店, because 相关的主题文章:

only human society elites 'Warrior' aspect where they can.

Area,オークリー ゴルフ サングラス, only human society elites 'Warrior' aspect where they can.

'Yes,オークリー サングラス ノーズパッド, my wife. turned Luofeng parents ask you,ロードバイク サングラス オークリー, you say ...... Luo Feng soon returned.' Chen Valley exhortations soon.

'I understand,スポーツサングラス オークリー.' Chen Gu wife nodded.

,オークリー サングラス 度付き 価格......
City on
and base completely different atmosphere wilderness area, but also throughout Eurasia,偏光サングラス オークリー, monsters gathered almost up to the city - 003 suburbs in the northern edge of the city, is undergoing a peak of the war, two and three God of War Lord monster fight!

'I have to speed up!'

'Otherwise,ゴルフ用サングラスオークリー, if the monster after winning return lair lord, I did not point opportunities. Ares humans win if they go to the monster lair, I also have no chance.' Luo Feng stature erratic move forward quickly,スポーツサングラス オークリー, 'my only chance that while they battle it out for a short time. '

parents are bases City 相关的主题文章: