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The '''Penrose method''' (or '''square-root method''') is a method devised in 1946 by Professor [[Lionel Penrose]]<ref name=PenroseOriginalPaper>{{cite journal | author=L.S. Penrose | title=The elementary statistics of majority voting | journal=Journal of the Royal Statistical Society | volume=109 | pages=53–57 | year=1946 | url=http://www.ww.uni-magdeburg.de/bizecon/material/Penrose_The%20Elementary%20Statistics%20of%20Majority%20Voting_Journal%20of%20the%20Royal%20Statistical%20Society_1091)1946_53-57.pdf | doi=10.2307/2981392}}</ref> for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to the [[square root]] of the population represented by this delegation. This is justified by the fact, that due to the [[Penrose square root law|square root law of Penrose]], the a priori voting power (as defined by the [[Penrose–Banzhaf index]]) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of the size of their constituency. Proportional allocation would result in excessive voting powers for the electorates of larger constituencies.


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A precondition for the appropriateness of the method is ''en bloc'' voting of the delegations in the decision-making body: a delegation cannot split its votes; rather, each delegation has just a single vote to which weights are applied proportional to the square root of the population they represent. Another precondition is that the opinions of the people represented are statistically independent. The representativity of each delegation results from statistical fluctuations within the country, and then, according to Penrose, "small electorate are likely to obtain more representative governments than large electorates." A mathematical formulation of this idea results in the square root rule.
 
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The Penrose method is not currently being used for any notable decision-making body, but it has been proposed for apportioning representation in a [[United Nations Parliamentary Assembly]],<ref name=PenroseOriginalPaper/><ref name=INFUSA>{{cite web | title = Proposal for a United Nations Second Assembly | publisher = [[INFUSA|International Network for a UN Second Assembly]] | year = 1987 | url = http://www.earthrights.net/archives/gpa/unsa.html | accessdate = 27 April 2010}}</ref> and for [[voting in the Council of the European Union]].<ref name="Penrose Voting System and Optimal Quota">{{cite journal|author=W. Slomczynski, K. Zyczkowski|title=Penrose Voting System and Optimal Quota|journal=Acta Physica Polonica B|volume=37|pages=3133–3143|year=2006|issue=11|url=http://chaos.if.uj.edu.pl/~karol/pdf/SZapp06.pdf | format = pdf}}</ref><ref name=xyz>{{cite web | title =Maths tweak required for EU voting | publisher =[[BBC news]] | date =7 July 2004 | url =http://news.bbc.co.uk/2/hi/science/nature/3804841.stm | accessdate = 27 April 2011}}</ref> Other bodies where the Penrose method could be appropriate include the [[Electoral College (United States)|US Presidential Electoral College]] and the [[Bundesrat of Germany]].{{Citation needed |date=June 2013}}


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{{see also|Voting in the Council of the European Union}}
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{| class="wikitable" style="float:right; font-size:80%; text-align:center; valign:bottom; margin-left:1em; margin-bottom:1em;"
|+ <big>Comparison of voting weights</big><br/> ''Population in millions as of 1 January 2003 <ref>{{Cite journal | url=http://www.eds-destatis.de/en/downloads/sif/nk_04_13.pdf | title=First results of the demographic data collection for 2003 in Europe | work=Statistics in focus: Population and social conditions: 13/2004 | publisher=Joint demographic data collection the [[Council of Europe]] and [[Eurostat]] | author=François-Carlos Bovagnet | year=2004 | accessdate= 28 April 2011}}</ref>''
|- style="background: #ffebad;"
! Member state
| colspan="2" | Population
| colspan="2" | [[Treaty of Nice|Nice]]
| colspan="2" | Penrose<ref name="Penrose Voting System and Optimal Quota"/>
|-
| style="text-align:left;" | {{Flag|Germany}}
| style="background: #efefef;" | 82.54m
| 16.5%
| style="background: #efefef;" | 29
| 8.4%
| style="background: #efefef;" | 9.55%
|-
| style="text-align:left;" | {{Flag|France}}
| style="background: #efefef;" | 59.64m
| 12.9%
| style="background: #efefef;" | 29
| 8.4%
| style="background: #efefef;" | 8.11%
|-
| style="text-align:left;" | {{Flag|UK}}
| style="background: #efefef;" | 59.33m
| 12.4%
| style="background: #efefef;" | 29
| 8.4%
| style="background: #efefef;" | 8.09%
|-
| style="text-align:left;" | {{Flag|Italy}}
| style="background: #efefef;" | 57.32m
| 12.0%
| style="background: #efefef;" | 29
| 8.4%
| style="background: #efefef;" | 7.95%
|-
| style="text-align:left;" | {{Flag|Spain}}
| style="background: #efefef;" | 41.55m
| 9.0%
| style="background: #efefef;" | 27
| 7.8%
| style="background: #efefef;" | 6.78%
|-
| style="text-align:left;" | {{Flag|Poland}}
| style="background: #efefef;" | 38.22m
| 7.6%
| style="background: #efefef;" | 27
| 7.8%
| style="background: #efefef;" | 6.49%
|-
| style="text-align:left;" | {{Flag|Romania}}
| style="background: #efefef;" | 21.77m
| 4.3%
| style="background: #efefef;" | 14
| 4.1%
| style="background: #efefef;" | 4.91%
|-
| style="text-align:left;" | {{Flag|Netherlands}}
| style="background: #efefef;" | 16.19m
| 3.3%
| style="background: #efefef;" | 13
| 3.8%
| style="background: #efefef;" | 4.22%
|-
| style="text-align:left;" | {{Flag|Greece}}
| style="background: #efefef;" | 11.01m
| 2.2%
| style="background: #efefef;" | 12
| 3.5%
| style="background: #efefef;" | 3.49%
|-
| style="text-align:left;" | {{Flag|Portugal}}
| style="background: #efefef;" | 10.41m
| 2.1%
| style="background: #efefef;" | 12
| 3.5%
| style="background: #efefef;" | 3.39%
|-
| style="text-align:left;" | {{Flag|Belgium}}
| style="background: #efefef;" | 10.36m
| 2.1%
| style="background: #efefef;" | 12
| 3.5%
| style="background: #efefef;" | 3.38%
|-
| style="text-align:left;" | {{Flag|Czech Republic|name=Czech Rep.}}
| style="background: #efefef;" | 10.20m
| 2.1%
| style="background: #efefef;" | 12
| 3.5%
| style="background: #efefef;" | 3.35%
|-
| style="text-align:left;" | {{Flag|Hungary}}
| style="background: #efefef;" | 10.14m
| 2.0%
| style="background: #efefef;" | 12
| 3.5%
| style="background: #efefef;" | 3.34%
|-
| style="text-align:left;" | {{Flag|Sweden}}
| style="background: #efefef;" | 8.94m
| 1.9%
| style="background: #efefef;" | 10
| 2.9%
| style="background: #efefef;" | 3.14%
|-
| style="text-align:left;" | {{Flag|Austria}}
| style="background: #efefef;" | 8.08m
| 1.7%
| style="background: #efefef;" | 10
| 2.9%
| style="background: #efefef;" | 2.98%
|-
| style="text-align:left;" | {{Flag|Bulgaria}}
| style="background: #efefef;" | 7.85m
| 1.5%
| style="background: #efefef;" | 10
| 2.9%
| style="background: #efefef;" | 2.94%
|-
| style="text-align:left;" | {{Flag|Denmark}}
| style="background: #efefef;" | 5.38m
| 1.1%
| style="background: #efefef;" | 7
| 2.0%
| style="background: #efefef;" | 2.44%
|-
| style="text-align:left;" | {{Flag|Slovakia}}
| style="background: #efefef;" | 5.38m
| 1.1%
| style="background: #efefef;" | 7
| 2.0%
| style="background: #efefef;" | 2.44%
|-
| style="text-align:left;" | {{Flag|Finland}}
| style="background: #efefef;" | 5.21m
| 1.1%
| style="background: #efefef;" | 7
| 2.0%
| style="background: #efefef;" | 2.39%
|-
| style="text-align:left;" | {{Flag|Ireland}}
| style="background: #efefef;" | 3.96m
| 0.9%
| style="background: #efefef;" | 7
| 2.0%
| style="background: #efefef;" | 2.09%
|-
| style="text-align:left;" | {{Flag|Lithuania}}
| style="background: #efefef;" | 3.46m
| 0.7%
| style="background: #efefef;" | 7
| 2.0%
| style="background: #efefef;" | 1.95%
|-
| style="text-align:left;" | {{Flag|Latvia}}
| style="background: #efefef;" | 2.33m
| 0.5%
| style="background: #efefef;" | 4
| 1.2%
| style="background: #efefef;" | 1.61%
|-
| style="text-align:left;" | {{Flag|Slovenia}}
| style="background: #efefef;" | 2.00m
| 0.4%
| style="background: #efefef;" | 4
| 1.2%
| style="background: #efefef;" | 1.48%
|-
| style="text-align:left;" | {{Flag|Estonia}}
| style="background: #efefef;" | 1.36m
| 0.3%
| style="background: #efefef;" | 4
| 1.2%
| style="background: #efefef;" | 1.23%
|-
| style="text-align:left;" | {{Flag|Cyprus}}
| style="background: #efefef;" | 0.72m
| 0.2%
| style="background: #efefef;" | 4
| 1.2%
| style="background: #efefef;" | 0.89%
|-
| style="text-align:left;" | {{Flag|Luxembourg}}
| style="background: #efefef;" | 0.45m
| 0.1%
| style="background: #efefef;" | 4
| 1.2%
| style="background: #efefef;" | 0.70%
|-
| style="text-align:left;" | {{Flag|Malta}}
| style="background: #efefef;" | 0.40m
| 0.1%
| style="background: #efefef;" | 3
| 0.9%
| style="background: #efefef;" | 0.66%
|- style="background:#cccccc;"
| style="text-align:left;" | {{Flag|EU}}
| 484.20m
| 100%
| 345
| 100%
| 100%
|}


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The Penrose method became revitalised within the [[European Union]] when it was proposed by Sweden in 2003 amid negotiations on the [[Amsterdam Treaty]] and by Poland June 2007 during summit on the [[Treaty of Lisbon]]. In this context, the method was proposed to compute voting weights of member states in the Council of the European Union.
 
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Currently, the voting in the Council of the EU does not follow the Penrose method. Instead, the [[Voting_in_the_Council_of_the_European_Union#Treaty_of_Nice|rules of the Nice Treaty]] are effective between 2004 and 2014, under certain conditions until 2017. The associated voting weights are compared in the table to the right along with the population data of the member states.


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Besides the voting weight, the voting power (i.e., the Penrose–Banzhaf index) of a member state also depends on the threshold percentage needed to make a decision. Smaller percentages work in favor of larger states. For example, if one state has 30% of the total voting weights while the threshold for decision making is at 29%, this state will have 100% voting power (i.e., an index of 1). For the EU-27, an optimal threshold, at which the voting powers of all citizens in any member state are almost equal, has been computed at about 61.6%.<ref name="Penrose Voting System and Optimal Quota"/> After the university of the authors of this paper, this system is referred to as the "[[Jagiellonian Compromise]]". Optimal threshold decreases with the number <math> M </math>  
    
of the member states as   <math> 1/2 +1/\sqrt{\pi M} </math>.<ref name="srvs">{{cite journal|author=K. Zyczkowski, W. Slomczynski|title=Square root voting system, optimal threshold and <math> \pi </math>|journal=preprint arXiv:1104.5213|url=http://arxiv.org/pdf/1104.5213v2.pdf | format = pdf}}</ref>
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==The UN proposal==
According to [[INFUSA]], "The square-root method is more than a pragmatic compromise between the extreme methods of world representation unrelated to population size and allocation of national quotas in direct proportion to population size; Penrose showed that in terms of statistical theory the square-root method gives to each voter in the world an equal influence on decision-making in a world assembly".<ref name=INFUSA/>


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Under the Penrose method, the relative voting weights of the most populous countries are lower than their proportion of the world population. In the table below, the countries' voting weights are computed as the square root of their year-2005 population in millions. This procedure was originally published by Penrose in 1946 based on pre-[[World War II]] population figures.<ref name=PenroseOriginalPaper/>
 
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== billig New Era Caps Vibram Five Fingers Sizing ==
<div align=center>
{| class="wikitable"
|- bgcolor="#ececec" valign=top
| colspan=2 |
| '''Population<br>as of 2005'''
| '''Percent of<br>world population'''
| '''Voting weight'''
| '''Percent of<br>total weight'''
|-
|
| '''World'''
| '''6,434,577,575'''
| '''100.00%'''
| '''721.32'''
| '''100.00%'''
|- bgcolor="#ececec" valign=top
| '''Rank'''
| '''Country'''
| colspan=4 |
|-
| 1
| People's Republic of China
| 1,306,313,812
| 20.30%
| 36.14
| 5.01%
|-
| 2
| India
| 1,080,264,388
| 16.79%
| 32.87
| 4.56%
|-
| 3
| United States
| 297,200,000
| 4.62%
| 17.24
| 2.39%
|-
| 4
| Indonesia
| 241,973,879
| 3.76%
| 15.56
| 2.16%
|-
| 5
| Brazil
| 186,112,794
| 2.89%
| 13.64
| 1.89%
|-
| 6
| Pakistan
| 162,419,946
| 2.52%
| 12.74
| 1.77%
|-
| 7
| Bangladesh
| 144,319,628
| 2.24%
| 12.01
| 1.67%
|-
| 8
| Russia
| 143,420,309
| 2.23%
| 11.98
| 1.66%
|-
| 9
| Nigeria
| 128,771,988
| 2.00%
| 11.35
| 1.57%
|-
| 10
| Japan
| 127,417,244
| 1.98%
| 11.29
| 1.56%
|-
| 11
| Mexico
| 106,202,903
| 1.65%
| 10.31
| 1.43%
|-
| 12
| Philippines
| 87,857,473
| 1.37%
| 9.37
| 1.30%
|-
| 13
| Vietnam
| 83,535,576
| 1.30%
| 9.14
| 1.27%
|-
| 14
| Germany
| 82,468,000
| 1.28%
| 9.08
| 1.26%
|-
| 15
| Egypt
| 77,505,756
| 1.20%
| 8.80
| 1.22%
|-
| 16
| Ethiopia
| 73,053,286
| 1.14%
| 8.55
| 1.18%
|-
| 17
| Turkey
| 69,660,559
| 1.08%
| 8.35
| 1.16%
|-
| 18
| Iran
| 68,017,860
| 1.06%
| 8.25
| 1.14%
|-
| 19
| Thailand
| 65,444,371
| 1.02%
| 8.09
| 1.12%
|-
| 20
| France
| 60,656,178
| 0.94%
| 7.79
| 1.08%
|-
| 21
| United Kingdom
| 60,441,457
| 0.94%
| 7.77
| 1.08%
|-
| 22
| Democratic Republic of the Congo
| 60,085,804
| 0.93%
| 7.75
| 1.07%
|-
| 23
| Italy
| 58,103,033
| 0.90%
| 7.62
| 1.06%
|-
| 24
| South Korea
| 48,422,644
| 0.75%
| 6.96
| 0.96%
|-
| 25
| Ukraine
| 47,425,336
| 0.74%
| 6.89
| 0.95%
|-
| 26
| South Africa
| 44,344,136
| 0.69%
| 6.66
| 0.92%
|-
| 27
| Spain
| 43,209,511
| 0.67%
| 6.57
| 0.91%
|-
| 28
| Colombia
| 42,954,279
| 0.67%
| 6.55
| 0.91%
|-
| 29
| Myanmar
| 42,909,464
| 0.67%
| 6.55
| 0.91%
|-
| 30
| Sudan
| 40,187,486
| 0.62%
| 6.34
| 0.88%
|-
| 31
| Argentina
| 39,537,943
| 0.61%
| 6.29
| 0.87%
|-
| 32
| Poland
| 38,635,144
| 0.60%
| 6.22
| 0.86%
|-
| 33
| Tanzania
| 36,766,356
| 0.57%
| 6.06
| 0.84%
|-
| 34
| Kenya
| 33,829,590
| 0.53%
| 5.82
| 0.81%
|-
| 35
| Canada
| 32,400,000
| 0.50%
| 5.69
| 0.79%
|-
| 36
| Morocco
| 32,725,847
| 0.51%
| 5.72
| 0.79%
|-
| 37
| Algeria
| 32,531,853
| 0.51%
| 5.70
| 0.79%
|-
| 38
| Afghanistan
| 29,928,987
| 0.47%
| 5.47
| 0.76%
|-
| 39
| Peru
| 27,925,628
| 0.43%
| 5.28
| 0.73%
|-
| 40
| Nepal
| 27,676,547
| 0.43%
| 5.26
| 0.73%
|-
| 41
| Uganda
| 27,269,482
| 0.42%
| 5.22
| 0.72%
|-
| 42
| Uzbekistan
| 26,851,195
| 0.42%
| 5.18
| 0.72%
|-
| 43
| Saudi Arabia
| 26,417,599
| 0.41%
| 5.14
| 0.71%
|-
| 44
| Malaysia
| 26,207,102
| 0.41%
| 5.12
| 0.71%
|-
| 45
| Iraq
| 26,074,906
| 0.41%
| 5.11
| 0.71%
|-
| 46
| Venezuela
| 25,375,281
| 0.39%
| 5.04
| 0.70%
|-
| 47
| North Korea
| 22,912,177
| 0.36%
| 4.79
| 0.66%
|-
| 48
| Republic of China
| 22,894,384
| 0.36%
| 4.78
| 0.66%
|-
| 49
| Romania
| 22,329,977
| 0.35%
| 4.73
| 0.66%
|-
| 50
| Ghana
| 21,029,853
| 0.33%
| 4.59
| 0.64%
|-
| 51
| Yemen
| 20,727,063
| 0.32%
| 4.55
| 0.63%
|-
| 52
| Australia
| 20,229,800
| 0.31%
| 4.50
| 0.62%
|-
| 53
| Sri Lanka
| 20,064,776
| 0.31%
| 4.48
| 0.62%
|-
| 54
| Mozambique
| 19,406,703
| 0.30%
| 4.41
| 0.61%
|-
| 55
| Syria
| 18,448,752
| 0.29%
| 4.30
| 0.60%
|-
| 56
| Madagascar
| 18,040,341
| 0.28%
| 4.25
| 0.59%
|-
| 57
| Côte d'Ivoire
| 17,298,040
| 0.27%
| 4.16
| 0.58%
|-
| 58
| Netherlands
| 16,407,491
| 0.25%
| 4.05
| 0.56%
|-
| 59
| Cameroon
| 16,380,005
| 0.25%
| 4.05
| 0.56%
|-
| 60
| Chile
| 16,267,278
| 0.25%
| 4.03
| 0.56%
|-
| 61
| Kazakhstan
| 15,185,844
| 0.24%
| 3.90
| 0.54%
|-
| 62
| Guatemala
| 14,655,189
| 0.23%
| 3.83
| 0.53%
|-
| 63
| Burkina Faso
| 13,925,313
| 0.22%
| 3.73
| 0.52%
|-
| 64
| Cambodia
| 13,607,069
| 0.21%
| 3.69
| 0.51%
|-
| 65
| Ecuador
| 13,363,593
| 0.21%
| 3.66
| 0.51%
|-
| 66
| Zimbabwe
| 12,746,990
| 0.20%
| 3.57
| 0.49%
|-
| 67
| Mali
| 12,291,529
| 0.19%
| 3.51
| 0.49%
|-
| 68
| Malawi
| 12,158,924
| 0.19%
| 3.49
| 0.48%
|-
| 69
| Niger
| 11,665,937
| 0.18%
| 3.42
| 0.47%
|-
| 70
| Cuba
| 11,346,670
| 0.18%
| 3.37
| 0.47%
|-
| 71
| Zambia
| 11,261,795
| 0.18%
| 3.36
| 0.47%
|-
| 72
| Angola
| 11,190,786
| 0.17%
| 3.35
| 0.46%
|-
| 73
| Senegal
| 11,126,832
| 0.17%
| 3.34
| 0.46%
|-
| 74
| Serbia and Montenegro
| 10,829,175
| 0.17%
| 3.29
| 0.46%
|-
| 75
| Greece
| 10,668,354
| 0.17%
| 3.27
| 0.45%
|-
| 76
| Portugal
| 10,566,212
| 0.16%
| 3.25
| 0.45%
|-
| 77
| Belgium
| 10,364,388
| 0.16%
| 3.22
| 0.45%
|-
| 78
| Belarus
| 10,300,483
| 0.16%
| 3.21
| 0.44%
|-
| 79
| Czech Republic
| 10,241,138
| 0.16%
| 3.20
| 0.44%
|-
| 80
| Hungary
| 10,081,000
| 0.16%
| 3.18
| 0.44%
|-
| 81
| Tunisia
| 10,074,951
| 0.16%
| 3.17
| 0.44%
|-
| 82
| Chad
| 9,826,419
| 0.15%
| 3.13
| 0.43%
|-
| 83
| Guinea
| 9,467,866
| 0.15%
| 3.08
| 0.43%
|-
| 84
| Sweden
| 9,001,774
| 0.14%
| 3.00
| 0.42%
|-
| 85
| Dominican Republic
| 8,950,034
| 0.14%
| 2.99
| 0.41%
|-
| 86
| Bolivia
| 8,857,870
| 0.14%
| 2.98
| 0.41%
|-
| 87
| Somalia
| 8,591,629
| 0.13%
| 2.93
| 0.41%
|-
| 88
| Rwanda
| 8,440,820
| 0.13%
| 2.91
| 0.40%
|-
| 89
| Austria
| 8,184,691
| 0.13%
| 2.86
| 0.40%
|-
| 90
| Haiti
| 8,121,622
| 0.13%
| 2.85
| 0.40%
|-
| 91
| Azerbaijan
| 7,911,974
| 0.12%
| 2.81
| 0.39%
|-
| 92
| Switzerland
| 7,489,370
| 0.12%
| 2.74
| 0.38%
|-
| 93
| Benin
| 7,460,025
| 0.12%
| 2.73
| 0.38%
|-
| 94
| Bulgaria
| 7,450,349
| 0.12%
| 2.73
| 0.38%
|-
| 95
| Tajikistan
| 7,163,506
| 0.11%
| 2.68
| 0.37%
|-
| 96
| Honduras
| 6,975,204
| 0.11%
| 2.64
| 0.37%
|-
| 97
| Israel
| 6,955,000
| 0.11%
| 2.64
| 0.37%
|-
| 98
| El Salvador
| 6,704,932
| 0.10%
| 2.59
| 0.36%
|-
| 99
| Burundi
| 6,370,609
| 0.10%
| 2.52
| 0.35%
|-
| 100
| Paraguay
| 6,347,884
| 0.10%
| 2.52
| 0.35%
|-
| 101
| Laos
| 6,217,141
| 0.10%
| 2.49
| 0.35%
|-
| 102
| Sierra Leone
| 6,017,643
| 0.09%
| 2.45
| 0.34%
|-
| 103
| Libya
| 5,765,563
| 0.09%
| 2.40
| 0.33%
|-
| 104
| Jordan
| 5,759,732
| 0.09%
| 2.40
| 0.33%
|-
| 105
| Togo
| 5,681,519
| 0.09%
| 2.38
| 0.33%
|-
| 106
| Papua New Guinea
| 5,545,268
| 0.09%
| 2.35
| 0.33%
|-
| 107
| Nicaragua
| 5,465,100
| 0.08%
| 2.34
| 0.32%
|-
| 108
| Denmark
| 5,432,335
| 0.08%
| 2.33
| 0.32%
|-
| 109
| Slovakia
| 5,431,363
| 0.08%
| 2.33
| 0.32%
|-
| 110
| Finland
| 5,223,442
| 0.08%
| 2.29
| 0.32%
|-
| 111
| Kyrgyzstan
| 5,146,281
| 0.08%
| 2.27
| 0.31%
|-
| 112
| Turkmenistan
| 4,952,081
| 0.08%
| 2.23
| 0.31%
|-
| 113
| Georgia
| 4,677,401
| 0.07%
| 2.16
| 0.30%
|-
| 114
| Norway
| 4,593,041
| 0.07%
| 2.14
| 0.30%
|-
| 115
| Eritrea
| 4,561,599
| 0.07%
| 2.14
| 0.30%
|-
| 116
| Croatia
| 4,495,904
| 0.07%
| 2.12
| 0.29%
|-
| 117
| Moldova
| 4,455,421
| 0.07%
| 2.11
| 0.29%
|-
| 118
| Singapore
| 4,425,720
| 0.07%
| 2.10
| 0.29%
|-
| 119
| Ireland
| 4,130,700
| 0.06%
| 2.03
| 0.28%
|-
| 120
| New Zealand
| 4,098,200
| 0.06%
| 2.02
| 0.28%
|-
| 121
| Bosnia and Herzegovina
| 4,025,476
| 0.06%
| 2.01
| 0.28%
|-
| 122
| Costa Rica
| 4,016,173
| 0.06%
| 2.00
| 0.28%
|-
| 123
| Lebanon
| 3,826,018
| 0.06%
| 1.96
| 0.27%
|-
| 124
| Central African Republic
| 3,799,897
| 0.06%
| 1.95
| 0.27%
|-
| 125
| Lithuania
| 3,596,617
| 0.06%
| 1.90
| 0.26%
|-
| 126
| Albania
| 3,563,112
| 0.06%
| 1.89
| 0.26%
|-
| 127
| Liberia
| 3,482,211
| 0.05%
| 1.87
| 0.26%
|-
| 128
| Uruguay
| 3,415,920
| 0.05%
| 1.85
| 0.26%
|-
| 129
| Mauritania
| 3,086,859
| 0.05%
| 1.76
| 0.24%
|-
| 130
| Panama
| 3,039,150
| 0.05%
| 1.74
| 0.24%
|-
| 131
| Republic of the Congo
| 3,039,126
| 0.05%
| 1.74
| 0.24%
|-
| 132
| Oman
| 3,001,583
| 0.05%
| 1.73
| 0.24%
|-
| 133
| Armenia
| 2,982,904
| 0.05%
| 1.73
| 0.24%
|-
| 134
| Mongolia
| 2,791,272
| 0.04%
| 1.67
| 0.23%
|-
| 135
| Jamaica
| 2,731,832
| 0.04%
| 1.65
| 0.23%
|-
| 136
| United Arab Emirates
| 2,563,212
| 0.04%
| 1.60
| 0.22%
|-
| 137
| Kuwait
| 2,335,648
| 0.04%
| 1.53
| 0.21%
|-
| 138
| Latvia
| 2,290,237
| 0.04%
| 1.51
| 0.21%
|-
| 139
| Bhutan
| 2,232,291
| 0.03%
| 1.49
| 0.21%
|-
| 140
| Macedonia
| 2,045,262
| 0.03%
| 1.43
| 0.20%
|-
| 141
| Namibia
| 2,030,692
| 0.03%
| 1.43
| 0.20%
|-
| 142
| Slovenia
| 2,011,070
| 0.03%
| 1.42
| 0.20%
|-
| 143
| Lesotho
| 1,867,035
| 0.03%
| 1.37
| 0.19%
|-
| 144
| Botswana
| 1,640,115
| 0.03%
| 1.28
| 0.18%
|-
| 145
| The Gambia
| 1,593,256
| 0.02%
| 1.26
| 0.17%
|-
| 146
| Guinea-Bissau
| 1,416,027
| 0.02%
| 1.19
| 0.16%
|-
| 147
| Gabon
| 1,389,201
| 0.02%
| 1.18
| 0.16%
|-
| 148
| Estonia
| 1,332,893
| 0.02%
| 1.15
| 0.16%
|-
| 149
| Mauritius
| 1,230,602
| 0.02%
| 1.11
| 0.15%
|-
| 150
| Swaziland
| 1,173,900
| 0.02%
| 1.08
| 0.15%
|-
| 151
| Trinidad and Tobago
| 1,088,644
| 0.02%
| 1.04
| 0.14%
|-
| 152
| East Timor
| 1,040,880
| 0.02%
| 1.02
| 0.14%
|-
| 153
| Fiji
| 893,354
| 0.01%
| 0.95
| 0.13%
|-
| 154
| Qatar
| 863,051
| 0.01%
| 0.93
| 0.13%
|-
| 155
| Cyprus
| 780,133
| 0.01%
| 0.88
| 0.12%
|-
| 156
| Guyana
| 765,283
| 0.01%
| 0.87
| 0.12%
|-
| 157
| Bahrain
| 688,345
| 0.01%
| 0.83
| 0.12%
|-
| 158
| Comoros
| 671,247
| 0.01%
| 0.82
| 0.11%
|-
| 159
| Solomon Islands
| 538,032
| 0.01%
| 0.73
| 0.10%
|-
| 160
| Equatorial Guinea
| 535,881
| 0.01%
| 0.73
| 0.10%
|-
| 161
| Djibouti
| 476,703
| 0.01%
| 0.69
| 0.10%
|-
| 162
| Luxembourg
| 468,571
| 0.01%
| 0.68
| 0.09%
|-
| 163
| Suriname
| 438,144
| 0.01%
| 0.66
| 0.09%
|-
| 164
| Cape Verde
| 418,224
| 0.01%
| 0.65
| 0.09%
|-
| 165
| Malta
| 398,534
| 0.01%
| 0.63
| 0.09%
|-
| 166
| Brunei
| 372,361
| 0.01%
| 0.61
| 0.08%
|-
| 167
| Maldives
| 349,106
| 0.01%
| 0.59
| 0.08%
|-
| 168
| The Bahamas
| 301,790
| 0.005%
| 0.55
| 0.08%
|-
| 169
| Iceland
| 296,737
| 0.005%
| 0.54
| 0.08%
|-
| 170
| Belize
| 279,457
| 0.004%
| 0.53
| 0.07%
|-
| 171
| Barbados
| 279,254
| 0.004%
| 0.53
| 0.07%
|-
| 172
| Vanuatu
| 205,754
| 0.003%
| 0.45
| 0.06%
|-
| 173
| São Tomé and Príncipe
| 187,410
| 0.003%
| 0.43
| 0.06%
|-
| 174
| Samoa
| 177,287
| 0.003%
| 0.42
| 0.06%
|-
| 175
| Saint Lucia
| 166,312
| 0.003%
| 0.41
| 0.06%
|-
| 176
| Saint Vincent and the Grenadines
| 117,534
| 0.002%
| 0.34
| 0.05%
|-
| 177
| Tonga
| 112,422
| 0.002%
| 0.34
| 0.05%
|-
| 178
| Federated States of Micronesia
| 108,105
| 0.002%
| 0.33
| 0.05%
|-
| 179
| Kiribati
| 103,092
| 0.002%
| 0.32
| 0.04%
|-
| 180
| Grenada
| 89,502
| 0.001%
| 0.30
| 0.04%
|-
| 181
| Seychelles
| 81,188
| 0.001%
| 0.28
| 0.04%
|-
| 182
| Andorra
| 70,549
| 0.001%
| 0.27
| 0.04%
|-
| 183
| Dominica
| 69,029
| 0.001%
| 0.26
| 0.04%
|-
| 184
| Antigua and Barbuda
| 68,722
| 0.001%
| 0.26
| 0.04%
|-
| 185
| Marshall Islands
| 59,071
| 0.001%
| 0.24
| 0.03%
|-
| 186
| Saint Kitts and Nevis
| 38,958
| 0.001%
| 0.20
| 0.03%
|-
| 187
| Liechtenstein
| 33,717
| 0.001%
| 0.18
| 0.03%
|-
| 188
| Monaco
| 32,409
| 0.001%
| 0.18
| 0.02%
|-
| 189
| San Marino
| 28,880
| 0.0004%
| 0.17
| 0.02%
|-
| 190
| Palau
| 20,303
| 0.0003%
| 0.14
| 0.02%
|-
| 191
| Nauru
| 13,048
| 0.0002%
| 0.11
| 0.02%
|-
| 192
| Tuvalu
| 11,636
| 0.0002%
| 0.11
| 0.01%
|-
| 193
| Vatican City
| 921
| 0.00001%
| 0.03
| 0.004%
|-
|}</div>


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==Criticisms==
 
It has been claimed that the Penrose method is restricted to votes for which public opinion is equally divided for and against.<ref name=GelmanWeb>{{cite web | last=Gelman | first =Andrew | authorlink = Andrew Gelman | title =Why the square-root rule for vote allocation is a bad idea | work =Statistical Modeling, Causal Inference, and Social Science | publisher =[[Columbia University]] website | date =9 October 2007 | url =http://www.stat.columbia.edu/~cook/movabletype/archives/2007/10/why_the_squarer.html | accessdate =30 April 2011 }}</ref><ref name="Gelman">{{cite journal|author=Gelman, Katz and Bafumi|title=Standard Voting Power Indexes Do Not Work: An Empirical Analysis|journal=British Journal of Political Science|volume=34|pages=657–674|year=2004|url=http://www.stat.columbia.edu/~gelman/research/published/gelmankatzbafumi.pdf}}</ref><ref name="on the j comp">[http://www.inference.phy.cam.ac.uk/ear23/voting/voting.pdf On the "Jagiellonian compromise"]</ref> A study of various elections has shown that this equally-divided scenario is not typical; these elections suggested that voting weights should be distributed according to the 0.9 power of the number of voters represented (in contrast to the 0.5 power used in the Penrose method).<ref name="Gelman"/>
  <li>[http://www.sudiauto.com/forum.php?mod=viewthread&tid=230908&extra= http://www.sudiauto.com/forum.php?mod=viewthread&tid=230908&extra=]</li>
 
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</ul>


== October 22nd Longchamp Shop Australia ==
In practice, the theoretical possibility of the decisiveness of a single vote is questionable. Elections results that come close to a tie are likely to be legally challenged, as was the case in the US presidential election in [[United States presidential election in Florida, 2000|Florida in 2000]]. After this experience, it appears naive to think that a single vote can be pivotal.<ref name="Gelman"/>


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In addition, a minor technical issues is that the theoretical argument for allocation of voting weight is based on the possibility that an individual has a deciding vote in each representative's area. This scenario is only possible when each representative has an odd number of voters in their area.<ref name="on the j comp"/>
 
 
  <li>[http://cerisier.info/spip.php?article20/ http://cerisier.info/spip.php?article20/]</li>
==See also==
 
* [[List of countries by population]]
  <li>[http://general.assembly.codesria.org/spip.php?article87&lang=pt/ http://general.assembly.codesria.org/spip.php?article87&lang=pt/]</li>
* [[Penrose square root law]]
 
 
  <li>[http://www.metransparent.net/spip.php?article2&lang=ar&id_forum=8554/ http://www.metransparent.net/spip.php?article2&lang=ar&id_forum=8554/]</li>
== References ==
 
<references/>
  <li>[http://www.proyectoalba.com.ar/spip.php?article66/ http://www.proyectoalba.com.ar/spip.php?article66/]</li>
 
 
==External links==
</ul>
*[http://ideas.repec.org/p/wrk/warwec/824.html The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union : an Appraisal Using Voting Power Analysis], D. Leech and H. Aziz, University of Warwick (2007).
 
*Many more references at the web page of American Mathematical Society [http://www.ams.org/featurecolumn/archive/weighted6.html here].
 
[[Category:Voting systems]]

Revision as of 04:48, 13 December 2013

The Penrose method (or square-root method) is a method devised in 1946 by Professor Lionel Penrose[1] for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to the square root of the population represented by this delegation. This is justified by the fact, that due to the square root law of Penrose, the a priori voting power (as defined by the Penrose–Banzhaf index) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of the size of their constituency. Proportional allocation would result in excessive voting powers for the electorates of larger constituencies.

A precondition for the appropriateness of the method is en bloc voting of the delegations in the decision-making body: a delegation cannot split its votes; rather, each delegation has just a single vote to which weights are applied proportional to the square root of the population they represent. Another precondition is that the opinions of the people represented are statistically independent. The representativity of each delegation results from statistical fluctuations within the country, and then, according to Penrose, "small electorate are likely to obtain more representative governments than large electorates." A mathematical formulation of this idea results in the square root rule.

The Penrose method is not currently being used for any notable decision-making body, but it has been proposed for apportioning representation in a United Nations Parliamentary Assembly,[1][2] and for voting in the Council of the European Union.[3][4] Other bodies where the Penrose method could be appropriate include the US Presidential Electoral College and the Bundesrat of Germany.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

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Comparison of voting weights
Population in millions as of 1 January 2003 [5]
Member state Population Nice Penrose[3]
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my blog: Hosgator review 		59.64m 12.9% 29 8.4% 8.11%
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my blog: Hosgator review 		59.33m 12.4% 29 8.4% 8.09%
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my blog: Hosgator review 		57.32m 12.0% 29 8.4% 7.95%
Hi there! :) My name is Nannette, I'm a student studying Graduate School from Luzein, Switzerland.

my blog: Hosgator review 		41.55m 9.0% 27 7.8% 6.78%
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my blog: Hosgator review 		38.22m 7.6% 27 7.8% 6.49%
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my blog: Hosgator review 		21.77m 4.3% 14 4.1% 4.91%
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my blog: Hosgator review 		16.19m 3.3% 13 3.8% 4.22%
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my blog: Hosgator review 		484.20m 100% 345 100% 100%

The Penrose method became revitalised within the European Union when it was proposed by Sweden in 2003 amid negotiations on the Amsterdam Treaty and by Poland June 2007 during summit on the Treaty of Lisbon. In this context, the method was proposed to compute voting weights of member states in the Council of the European Union.

Currently, the voting in the Council of the EU does not follow the Penrose method. Instead, the rules of the Nice Treaty are effective between 2004 and 2014, under certain conditions until 2017. The associated voting weights are compared in the table to the right along with the population data of the member states.

Besides the voting weight, the voting power (i.e., the Penrose–Banzhaf index) of a member state also depends on the threshold percentage needed to make a decision. Smaller percentages work in favor of larger states. For example, if one state has 30% of the total voting weights while the threshold for decision making is at 29%, this state will have 100% voting power (i.e., an index of 1). For the EU-27, an optimal threshold, at which the voting powers of all citizens in any member state are almost equal, has been computed at about 61.6%.[3] After the university of the authors of this paper, this system is referred to as the "Jagiellonian Compromise". Optimal threshold decreases with the number M of the member states as 1/2+1/πM.[6]

The UN proposal

According to INFUSA, "The square-root method is more than a pragmatic compromise between the extreme methods of world representation unrelated to population size and allocation of national quotas in direct proportion to population size; Penrose showed that in terms of statistical theory the square-root method gives to each voter in the world an equal influence on decision-making in a world assembly".[2]

Under the Penrose method, the relative voting weights of the most populous countries are lower than their proportion of the world population. In the table below, the countries' voting weights are computed as the square root of their year-2005 population in millions. This procedure was originally published by Penrose in 1946 based on pre-World War II population figures.[1]

Population
as of 2005 		Percent of
world population 		Voting weight Percent of
total weight
World 6,434,577,575 100.00% 721.32 100.00%
Rank Country
1 People's Republic of China 1,306,313,812 20.30% 36.14 5.01%
2 India 1,080,264,388 16.79% 32.87 4.56%
3 United States 297,200,000 4.62% 17.24 2.39%
4 Indonesia 241,973,879 3.76% 15.56 2.16%
5 Brazil 186,112,794 2.89% 13.64 1.89%
6 Pakistan 162,419,946 2.52% 12.74 1.77%
7 Bangladesh 144,319,628 2.24% 12.01 1.67%
8 Russia 143,420,309 2.23% 11.98 1.66%
9 Nigeria 128,771,988 2.00% 11.35 1.57%
10 Japan 127,417,244 1.98% 11.29 1.56%
11 Mexico 106,202,903 1.65% 10.31 1.43%
12 Philippines 87,857,473 1.37% 9.37 1.30%
13 Vietnam 83,535,576 1.30% 9.14 1.27%
14 Germany 82,468,000 1.28% 9.08 1.26%
15 Egypt 77,505,756 1.20% 8.80 1.22%
16 Ethiopia 73,053,286 1.14% 8.55 1.18%
17 Turkey 69,660,559 1.08% 8.35 1.16%
18 Iran 68,017,860 1.06% 8.25 1.14%
19 Thailand 65,444,371 1.02% 8.09 1.12%
20 France 60,656,178 0.94% 7.79 1.08%
21 United Kingdom 60,441,457 0.94% 7.77 1.08%
22 Democratic Republic of the Congo 60,085,804 0.93% 7.75 1.07%
23 Italy 58,103,033 0.90% 7.62 1.06%
24 South Korea 48,422,644 0.75% 6.96 0.96%
25 Ukraine 47,425,336 0.74% 6.89 0.95%
26 South Africa 44,344,136 0.69% 6.66 0.92%
27 Spain 43,209,511 0.67% 6.57 0.91%
28 Colombia 42,954,279 0.67% 6.55 0.91%
29 Myanmar 42,909,464 0.67% 6.55 0.91%
30 Sudan 40,187,486 0.62% 6.34 0.88%
31 Argentina 39,537,943 0.61% 6.29 0.87%
32 Poland 38,635,144 0.60% 6.22 0.86%
33 Tanzania 36,766,356 0.57% 6.06 0.84%
34 Kenya 33,829,590 0.53% 5.82 0.81%
35 Canada 32,400,000 0.50% 5.69 0.79%
36 Morocco 32,725,847 0.51% 5.72 0.79%
37 Algeria 32,531,853 0.51% 5.70 0.79%
38 Afghanistan 29,928,987 0.47% 5.47 0.76%
39 Peru 27,925,628 0.43% 5.28 0.73%
40 Nepal 27,676,547 0.43% 5.26 0.73%
41 Uganda 27,269,482 0.42% 5.22 0.72%
42 Uzbekistan 26,851,195 0.42% 5.18 0.72%
43 Saudi Arabia 26,417,599 0.41% 5.14 0.71%
44 Malaysia 26,207,102 0.41% 5.12 0.71%
45 Iraq 26,074,906 0.41% 5.11 0.71%
46 Venezuela 25,375,281 0.39% 5.04 0.70%
47 North Korea 22,912,177 0.36% 4.79 0.66%
48 Republic of China 22,894,384 0.36% 4.78 0.66%
49 Romania 22,329,977 0.35% 4.73 0.66%
50 Ghana 21,029,853 0.33% 4.59 0.64%
51 Yemen 20,727,063 0.32% 4.55 0.63%
52 Australia 20,229,800 0.31% 4.50 0.62%
53 Sri Lanka 20,064,776 0.31% 4.48 0.62%
54 Mozambique 19,406,703 0.30% 4.41 0.61%
55 Syria 18,448,752 0.29% 4.30 0.60%
56 Madagascar 18,040,341 0.28% 4.25 0.59%
57 Côte d'Ivoire 17,298,040 0.27% 4.16 0.58%
58 Netherlands 16,407,491 0.25% 4.05 0.56%
59 Cameroon 16,380,005 0.25% 4.05 0.56%
60 Chile 16,267,278 0.25% 4.03 0.56%
61 Kazakhstan 15,185,844 0.24% 3.90 0.54%
62 Guatemala 14,655,189 0.23% 3.83 0.53%
63 Burkina Faso 13,925,313 0.22% 3.73 0.52%
64 Cambodia 13,607,069 0.21% 3.69 0.51%
65 Ecuador 13,363,593 0.21% 3.66 0.51%
66 Zimbabwe 12,746,990 0.20% 3.57 0.49%
67 Mali 12,291,529 0.19% 3.51 0.49%
68 Malawi 12,158,924 0.19% 3.49 0.48%
69 Niger 11,665,937 0.18% 3.42 0.47%
70 Cuba 11,346,670 0.18% 3.37 0.47%
71 Zambia 11,261,795 0.18% 3.36 0.47%
72 Angola 11,190,786 0.17% 3.35 0.46%
73 Senegal 11,126,832 0.17% 3.34 0.46%
74 Serbia and Montenegro 10,829,175 0.17% 3.29 0.46%
75 Greece 10,668,354 0.17% 3.27 0.45%
76 Portugal 10,566,212 0.16% 3.25 0.45%
77 Belgium 10,364,388 0.16% 3.22 0.45%
78 Belarus 10,300,483 0.16% 3.21 0.44%
79 Czech Republic 10,241,138 0.16% 3.20 0.44%
80 Hungary 10,081,000 0.16% 3.18 0.44%
81 Tunisia 10,074,951 0.16% 3.17 0.44%
82 Chad 9,826,419 0.15% 3.13 0.43%
83 Guinea 9,467,866 0.15% 3.08 0.43%
84 Sweden 9,001,774 0.14% 3.00 0.42%
85 Dominican Republic 8,950,034 0.14% 2.99 0.41%
86 Bolivia 8,857,870 0.14% 2.98 0.41%
87 Somalia 8,591,629 0.13% 2.93 0.41%
88 Rwanda 8,440,820 0.13% 2.91 0.40%
89 Austria 8,184,691 0.13% 2.86 0.40%
90 Haiti 8,121,622 0.13% 2.85 0.40%
91 Azerbaijan 7,911,974 0.12% 2.81 0.39%
92 Switzerland 7,489,370 0.12% 2.74 0.38%
93 Benin 7,460,025 0.12% 2.73 0.38%
94 Bulgaria 7,450,349 0.12% 2.73 0.38%
95 Tajikistan 7,163,506 0.11% 2.68 0.37%
96 Honduras 6,975,204 0.11% 2.64 0.37%
97 Israel 6,955,000 0.11% 2.64 0.37%
98 El Salvador 6,704,932 0.10% 2.59 0.36%
99 Burundi 6,370,609 0.10% 2.52 0.35%
100 Paraguay 6,347,884 0.10% 2.52 0.35%
101 Laos 6,217,141 0.10% 2.49 0.35%
102 Sierra Leone 6,017,643 0.09% 2.45 0.34%
103 Libya 5,765,563 0.09% 2.40 0.33%
104 Jordan 5,759,732 0.09% 2.40 0.33%
105 Togo 5,681,519 0.09% 2.38 0.33%
106 Papua New Guinea 5,545,268 0.09% 2.35 0.33%
107 Nicaragua 5,465,100 0.08% 2.34 0.32%
108 Denmark 5,432,335 0.08% 2.33 0.32%
109 Slovakia 5,431,363 0.08% 2.33 0.32%
110 Finland 5,223,442 0.08% 2.29 0.32%
111 Kyrgyzstan 5,146,281 0.08% 2.27 0.31%
112 Turkmenistan 4,952,081 0.08% 2.23 0.31%
113 Georgia 4,677,401 0.07% 2.16 0.30%
114 Norway 4,593,041 0.07% 2.14 0.30%
115 Eritrea 4,561,599 0.07% 2.14 0.30%
116 Croatia 4,495,904 0.07% 2.12 0.29%
117 Moldova 4,455,421 0.07% 2.11 0.29%
118 Singapore 4,425,720 0.07% 2.10 0.29%
119 Ireland 4,130,700 0.06% 2.03 0.28%
120 New Zealand 4,098,200 0.06% 2.02 0.28%
121 Bosnia and Herzegovina 4,025,476 0.06% 2.01 0.28%
122 Costa Rica 4,016,173 0.06% 2.00 0.28%
123 Lebanon 3,826,018 0.06% 1.96 0.27%
124 Central African Republic 3,799,897 0.06% 1.95 0.27%
125 Lithuania 3,596,617 0.06% 1.90 0.26%
126 Albania 3,563,112 0.06% 1.89 0.26%
127 Liberia 3,482,211 0.05% 1.87 0.26%
128 Uruguay 3,415,920 0.05% 1.85 0.26%
129 Mauritania 3,086,859 0.05% 1.76 0.24%
130 Panama 3,039,150 0.05% 1.74 0.24%
131 Republic of the Congo 3,039,126 0.05% 1.74 0.24%
132 Oman 3,001,583 0.05% 1.73 0.24%
133 Armenia 2,982,904 0.05% 1.73 0.24%
134 Mongolia 2,791,272 0.04% 1.67 0.23%
135 Jamaica 2,731,832 0.04% 1.65 0.23%
136 United Arab Emirates 2,563,212 0.04% 1.60 0.22%
137 Kuwait 2,335,648 0.04% 1.53 0.21%
138 Latvia 2,290,237 0.04% 1.51 0.21%
139 Bhutan 2,232,291 0.03% 1.49 0.21%
140 Macedonia 2,045,262 0.03% 1.43 0.20%
141 Namibia 2,030,692 0.03% 1.43 0.20%
142 Slovenia 2,011,070 0.03% 1.42 0.20%
143 Lesotho 1,867,035 0.03% 1.37 0.19%
144 Botswana 1,640,115 0.03% 1.28 0.18%
145 The Gambia 1,593,256 0.02% 1.26 0.17%
146 Guinea-Bissau 1,416,027 0.02% 1.19 0.16%
147 Gabon 1,389,201 0.02% 1.18 0.16%
148 Estonia 1,332,893 0.02% 1.15 0.16%
149 Mauritius 1,230,602 0.02% 1.11 0.15%
150 Swaziland 1,173,900 0.02% 1.08 0.15%
151 Trinidad and Tobago 1,088,644 0.02% 1.04 0.14%
152 East Timor 1,040,880 0.02% 1.02 0.14%
153 Fiji 893,354 0.01% 0.95 0.13%
154 Qatar 863,051 0.01% 0.93 0.13%
155 Cyprus 780,133 0.01% 0.88 0.12%
156 Guyana 765,283 0.01% 0.87 0.12%
157 Bahrain 688,345 0.01% 0.83 0.12%
158 Comoros 671,247 0.01% 0.82 0.11%
159 Solomon Islands 538,032 0.01% 0.73 0.10%
160 Equatorial Guinea 535,881 0.01% 0.73 0.10%
161 Djibouti 476,703 0.01% 0.69 0.10%
162 Luxembourg 468,571 0.01% 0.68 0.09%
163 Suriname 438,144 0.01% 0.66 0.09%
164 Cape Verde 418,224 0.01% 0.65 0.09%
165 Malta 398,534 0.01% 0.63 0.09%
166 Brunei 372,361 0.01% 0.61 0.08%
167 Maldives 349,106 0.01% 0.59 0.08%
168 The Bahamas 301,790 0.005% 0.55 0.08%
169 Iceland 296,737 0.005% 0.54 0.08%
170 Belize 279,457 0.004% 0.53 0.07%
171 Barbados 279,254 0.004% 0.53 0.07%
172 Vanuatu 205,754 0.003% 0.45 0.06%
173 São Tomé and Príncipe 187,410 0.003% 0.43 0.06%
174 Samoa 177,287 0.003% 0.42 0.06%
175 Saint Lucia 166,312 0.003% 0.41 0.06%
176 Saint Vincent and the Grenadines 117,534 0.002% 0.34 0.05%
177 Tonga 112,422 0.002% 0.34 0.05%
178 Federated States of Micronesia 108,105 0.002% 0.33 0.05%
179 Kiribati 103,092 0.002% 0.32 0.04%
180 Grenada 89,502 0.001% 0.30 0.04%
181 Seychelles 81,188 0.001% 0.28 0.04%
182 Andorra 70,549 0.001% 0.27 0.04%
183 Dominica 69,029 0.001% 0.26 0.04%
184 Antigua and Barbuda 68,722 0.001% 0.26 0.04%
185 Marshall Islands 59,071 0.001% 0.24 0.03%
186 Saint Kitts and Nevis 38,958 0.001% 0.20 0.03%
187 Liechtenstein 33,717 0.001% 0.18 0.03%
188 Monaco 32,409 0.001% 0.18 0.02%
189 San Marino 28,880 0.0004% 0.17 0.02%
190 Palau 20,303 0.0003% 0.14 0.02%
191 Nauru 13,048 0.0002% 0.11 0.02%
192 Tuvalu 11,636 0.0002% 0.11 0.01%
193 Vatican City 921 0.00001% 0.03 0.004%

Criticisms

It has been claimed that the Penrose method is restricted to votes for which public opinion is equally divided for and against.[7][8][9] A study of various elections has shown that this equally-divided scenario is not typical; these elections suggested that voting weights should be distributed according to the 0.9 power of the number of voters represented (in contrast to the 0.5 power used in the Penrose method).[8]

In practice, the theoretical possibility of the decisiveness of a single vote is questionable. Elections results that come close to a tie are likely to be legally challenged, as was the case in the US presidential election in Florida in 2000. After this experience, it appears naive to think that a single vote can be pivotal.[8]

In addition, a minor technical issues is that the theoretical argument for allocation of voting weight is based on the possibility that an individual has a deciding vote in each representative's area. This scenario is only possible when each representative has an odd number of voters in their area.[9]

See also

References

  1. ↑ 1.0 1.1 1.2 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  2. ↑ 2.0 2.1 Template:Cite web
  3. ↑ 3.0 3.1 3.2 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  4. ↑ Template:Cite web
  5. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  6. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  7. ↑ Template:Cite web
  8. ↑ 8.0 8.1 8.2 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  9. ↑ 9.0 9.1 On the "Jagiellonian compromise"

External links

  • Many more references at the web page of American Mathematical Society here.
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