View source for Social:Effective number of parties

{{Short description|Concept in political party systems}}
The '''effective number of parties''' is a concept introduced by Laakso and Taagepera (1979)<ref>{{Cite journal|last1=Laakso |first1=Markku |last2=Taagepera |first2=Rein|date=1979|title="Effective" Number of Parties: A Measure with Application to West Europe |journal=Comparative Political Studies |language=en |volume=12 |issue=1 |pages=3–27 |doi=10.1177/001041407901200101|s2cid=143250203 |issn=0010-4140|url=https://escholarship.org/uc/item/703827nv }}</ref> which provides for an adjusted number of political parties in a country's [[Social:Party system|party system]].  The idea behind this measure is to count parties and, at the same time, to [[Weight function|weight]] the count by their relative strength. The relative strength refers to their vote share ''effective number of electoral parties'' (ENEP) or seat share in the parliament ''effective number of parliamentary parties'' (ENPP). This measure is especially useful when comparing [[Social:Party system|party system]]s across countries, as is done in the field of political science.<ref>Lijphart, Arend (1999): Patterns of Democracy. New Haven/London: Yale UP</ref> The number of parties equals the effective number of parties only when all parties have equal strength. In any other case, the effective number of parties is lower than the actual number of parties. The effective number of parties is a frequent [[Philosophy:Operationalization|operationalization]] for the [[Social:Political fragmentation|political fragmentation]].

[[File:Effective Number of Parliamentary Parties in the Netherlands (1981-2017).png|thumb|Example of how the effective number of parties shows the fragmentation of the Dutch political landscape (1981–2017)]]

There are two major alternatives to the  effective number of parties-measure.<ref name="Lijphart1994">{{cite book|author=Arend Lijphart |title=Electoral Systems and Party Systems: A Study of Twenty-seven Democracies, 1945–1990 |url=https://archive.org/details/electoralsystems0000lijp |url-access=registration |date=1 January 1994 |publisher=Oxford University Press |isbn=978-0-19-827347-9 |page=[https://archive.org/details/electoralsystems0000lijp/page/69 69]|author-link=Arend Lijphart }}</ref> John K. Wildgen's index of "hyperfractionalization" accords special weight to small parties.<ref>{{cite web|url=http://cps.sagepub.com/content/4/2/233.extract |title=The Measurement of Hyperfractionalization |publisher=Cps.sagepub.com |date=1971-07-01 |accessdate=2014-01-05}}</ref> Juan Molinar's index gives special weight to the largest party.<ref>{{cite journal|jstor=1963951|title=Counting the Number of Parties: An Alternative Index|first=Juan|last=Molinar|date=1 January 1991|journal=The American Political Science Review|volume=85|issue=4|pages=1383–1391|doi=10.2307/1963951|s2cid=154924401 }}</ref> Dunleavy and Boucek provide a useful critique of the Molinar index.<ref>{{Cite journal |doi=10.1177/1354068803009003002 |title=Constructing the Number of Parties |date=2003 |last1=Dunleavy |first1=Patrick |last2=Boucek |first2=Françoise |journal=Party Politics |volume=9 |issue=3 |pages=291–315 |s2cid=33028828 |url=http://eprints.lse.ac.uk/17510/1/rv_number_of_parties_accepted_version_autumn_2002_vers_11LLL_altWord.pdf }}</ref>

The measure is essentially equivalent to the [[Finance:Herfindahl–Hirschman index|Herfindahl–Hirschman index]], a diversity index used in economics; the Simpson diversity index, which is a [[Diversity index|diversity index]] used in ecology; and the [[Physics:Purity (quantum mechanics)#Inverse Participation Ratio (IPR)|inverse participation ratio (IPR)]] in physics.

==Formulae==
According to Laakso and Taagepera (1979),  the ''effective number of parties'' is computed by the following formula:

: <math>N = \frac{1}{\sum_{i=1}^n p_i^2} </math>

where ''n'' is the number of parties with at least one vote/seat and <math> p_i^2 </math> the square of each party's proportion of all votes or seats. The proportions need to be ''normalised'' such that, for example, 50 per cent is 0.5 and 1 per cent is 0.01. This is also the formula for the [[Diversity index#Inverse Simpson index|inverse Simpson index]], or the true diversity of order 2.

An alternative formula proposed by Golosov (2010)<ref>{{Cite journal|last=Golosov|first=Grigorii V.|date=2010|title=The Effective Number of Parties: A New Approach|journal=Party Politics|language=en|volume=16|issue=2|pages=171–192|doi=10.1177/1354068809339538|s2cid=144503915|issn=1354-0688}}</ref> is

: <math>N = \sum_{i=1}^n \frac{p_i}{p_i+p_1^2-p_i^2} </math>

which is equivalent – if we only consider parties with at least one vote/seat – to

: <math>N = \sum_{i=1}^n \frac{1}{1+(p_1^2/p_i)-p_i} </math>

Here, ''n'' is the number of parties, <math> p_i^2 </math> the square of each party's proportion of all votes or seats, and <math> p_1^2 </math> is the square of the largest party's proportion of all votes or seats.

==Values==
The following table illustrates the difference between the values produced by the two formulas for eight hypothetical vote or seat constellations:
{| class="wikitable"
|-
! Constellation !! Largest component, fractional share !! Other components, fractional shares !! N, Laakso-Taagepera !! N, Golosov
|-
| A || 0.75 || 0.25 || 1.60 || 1.33
|-
| B || 0.75 || 0.1, 15 at 0.01 || 1.74 || 1.42
|-
| C || 0.55 || 0.45 || 1.98 || 1.82
|-
| D || 0.55 || 3 at 0.1, 15 at 0.01 || 2.99 || 2.24
|-
| E || 0.35 || 0.35, 0.3 || 2.99 || 2.90
|-
| F || 0.35 || 5 at 0.1, 15 at 0.01 || 5.75 || 4.49
|-
| G || 0.15 || 5 at 0.15, 0.1 || 6.90 || 6.89
|-
| H || 0.15 || 7 at 0.1, 15 at 0.01 || 10.64 || 11.85
|}

==Institutional theory==
The effective number of parties can be predicted with the seat product model<ref>Taagepera, Rein (2007). "Predicting Party Sizes". Oxford University Press</ref><ref>{{cite journal | url=https://doi.org/10.1016/j.electstud.2015.10.011 | doi=10.1016/j.electstud.2015.10.011 | title=The Seat Product Model of the effective number of parties: A case for applied political science | date=2016 | last1=Li | first1=Yuhui | last2=Shugart | first2=Matthew S. | journal=Electoral Studies | volume=41 | pages=23–34 }}</ref> as <math>N = (MS)^{1/6} </math>, where ''M'' is the district magnitude and ''S'' is the assembly size.

== Effective number of parties by country ==
For individual countries the values of effective number of number of parliamentary parties (ENPP) for the last available election is shown.<ref>{{cite web |title=Election indices dataset, Gallagher, Michael, 2021. |url=http://www.tcd.ie/Political_Science/people/michael_gallagher/ElSystems/index.php |access-date=2022-09-05 |archive-date=2022-10-06 |archive-url=https://web.archive.org/web/20221006214806/https://www.tcd.ie/Political_Science/people/michael_gallagher/ElSystems/index.php |url-status=dead }}</ref> 
Some of the highest effective number of parties are in Brazil, Belgium, and Bosnia and Herzegovina. European Parliament has an even higher effective number of parties if national parties are considered, yet a much lower effective number of parties if political groups of the European Parliament are considered.

{| class="wikitable sortable"
! Country !! Year !! Effective number of parties
|-
| {{flaglist|Albania}}	||	2021	||	2.18
|-
| {{flaglist|Andorra}}	||	2019	||	2.99
|-
| {{flaglist|Antigua and Barbuda}} 	||	2023	||	2.33
|-
| {{flaglist|Argentina}}	||	2021	||	2.57
|-
| {{flaglist|Armenia}}	||	2021	||	1.93
|-
| {{flaglist|Australia}}	||	2022	||	3.15
|-
| {{flaglist|Austria}}	||	2019	||	3.94
|-
| {{flaglist|Bahamas}}	||	2021	||	1.42
|-
| {{flaglist|Barbados}}	||	2022	||	1.00
|-
| {{flaglist|Belgium}}	||	2019	||	9.70
|-
| {{flaglist|Belize}}	||	2020	||	1.37
|-
| {{flaglist|Bermuda}}	||	2020	||	1.38
|-
| {{flaglist|Bhutan}}	||	2018	||	1.86
|-
| {{flaglist|Bolivia}}	||	2020	||	2.28
|-
| {{flaglist|Bosnia and Herzegovina}}	||	2022	||	9.00
|-
| {{flaglist|Botswana}}	||	2019	||	1.94
|-
| {{flaglist|Brazil}}	||	2022||	9.91
|-
| {{flaglist|Bulgaria}}	||	2022	||	5.49
|-
| {{flaglist|Burkina Faso}}	||	2020	||	4.11
|-
| {{flaglist|Cabo Verde}}	||	2021	||	2.20
|-
| {{flaglist|Canada}}	||	2021	||	2.76
|-
| {{flaglist|Chile}}	||	2021	||	4.13
|-
| {{flaglist|Colombia}} 	||	2022	||	8.74
|-
| {{flaglist|Costa Rica}}	||	2018	||	4.73
|-
| {{flaglist|Croatia}}	||	2020	||	3.19
|-
| {{flaglist|Cyprus}}	||	2021	||	4.81
|-
| {{flaglist|Czechia}}	||	2021	||	3.34
|-
| {{flaglist|Denmark}}	||	2022	||	7.24
|-
| {{flaglist|Dominican Republic}}	||	2020	||	2.75
|-
| {{flaglist|El Salvador}}	||	2021	||	2.99
|-
| {{flaglist|Estonia}}	||	2023||	5.52
|-
| {{flaglist|Faeroe Islands}}	||	2022||	5.31
|-
| {{flaglist|Fiji}}	||	2022	||	2.63
|-
| {{flaglist|Finland}}	||	2023||	6.65
|-
| {{flaglist|France}}	||	2022	||	3.72
|-
| {{flaglist|Gambia}}	||	2022	||	4.80
|-
| {{flaglist|Georgia}}	||	2020	||	2.37
|-
| {{flaglist|Germany}}	||	2021	||	5.51
|-
| {{flaglist|Ghana}}	||	2020	||	2.01
|-
| {{flaglist|Greece}}	||	2019	||	2.71
|-
| {{flaglist|Greenland}}	||	2021	||	3.52
|-
| {{flaglist|Grenada}}	||	2022	||	1.92
|-
| {{flaglist|Guatemala}}	||	2019	||	6.73
|-
| {{flaglist|Guinea}}	||	2020	||	2.06
|-
| {{flaglist|Guinea-Bissau}}	||	2019	||	3.05
|-
| {{flaglist|Guyana}}	||	2020	||	2.06
|-
| {{flaglist|Honduras}}	||	2021	||	3.16
|-
| {{flaglist|Hungary}}	||	2022	||	1.84
|-
| {{flaglist|Iceland}}	||	2021	||	6.29
|-
| {{flaglist|India}}	||	2019	||	2.17
|-
| {{flaglist|Indonesia}}	||	2019	||	7.47
|-
| {{flaglist|Iraq}}	||	2010	||	4.35
|-
| {{flaglist|Ireland}}	||	2020	||	5.98
|-
| {{flaglist|Israel}}	||	2022	||	6.51
|-
| {{flaglist|Italy}}	||	2022	||	2.40
|-
| {{flaglist|Jamaica}}	||	2020	||	1.53
|-
| {{flaglist|Japan}}	||	2021	||	2.69
|-
| {{flaglist|Kosovo}}	||	2021	||	3.49
|-
| {{flaglist|Kenya}}	||	2013	||	5.16
|-
| {{flaglist|Kyrgyzstan}}	||	2015	||	4.82
|-
| {{flaglist|Latvia}}	||	2022	||	6.14
|-
| {{flaglist|Lesotho}}	||	2022	||	3.93
|-
| {{flaglist|Liberia}}	||	2017	||	5.81
|-
| {{flaglist|Liechtenstein}}	||	2021	||	2.93
|-
| {{flaglist|Lithuania}}	||	2020	||	4.84
|-
| {{flaglist|Luxembourg}}	||	2018	||	4.56
|-
| {{flaglist|Malaysia}}	||	2022	||	7.72
|-
| {{flaglist|Malawi}}	||	2019	||	5.19
|-
| {{flaglist|Malta}}	||	2022	||	1.97
|-
| {{flaglist|Mauritius}}	||	2019	||	2.29
|-
| {{flaglist|Mexico}}	||	2021	||	2.21
|-
| {{flaglist|Moldova}}	||	2021	||	2.03
|-
| {{flaglist|Monaco}}	||	2018	||	1.29
|-
| {{flaglist|Montenegro}}	||	2020	||	3.71
|-
| {{flaglist|Morocco}}	||	2021	||	5.68
|-
| {{flaglist|Mozambique}}	||	2019	||  1.57
|-
| {{flaglist|Namibia}}	||	2019	||	2.16
|-
| {{flaglist|Nepal}}	||	2022	||	4.75
|-
| {{flaglist|Netherlands}}	||	2021	||	8.54
|-
| {{flaglist|New Zealand}}	||	2020	||	2.61
|-
| {{flaglist|Nicaragua}}	||	2021||	1.78
|-
| {{flaglist|Niger}}	||	2020	||	3.85
|-
| {{flaglist|North Macedonia}}	||	2020	||	3.25
|-
| {{flaglist|Northern Cyprus}}	||	2022	||	2.71
|-
| {{flaglist|Northern Ireland}}	||	2022	||	4.52
|-
| {{flaglist|Norway}}	||	2021	||	5.56
|-
| {{flaglist|Palestine}}	||	2006	||	2.32
|-
| {{flaglist|Panama}}	||	2019	||	3.07
|-
| {{flaglist|Paraguay}}	||	2018	||	2.86
|-
| {{flaglist|Peru}}	||	2021	||	6.20
|-
|{{flaglist|Philippines}}
|2022
|8.73
|-
| {{flaglist|Poland}}	||	2019	||	2.76
|-
| {{flaglist|Portugal}}	||	2022	||	2.66
|-
| {{flaglist|Romania}}	||	2020	||	4.30
|-
| {{flaglist|Saint Kitts and Nevis}}|| 2022 ||   2.5
|-
| {{flaglist|Saint Lucia}}	||	2021	||	1.65
|-
| {{flaglist|Saint Vincent and the Grenadines}}	||2020||1.92
|-
| {{flaglist|San Marino}}	||	2019	||	4.63
|-
| {{flaglist|Sao Tome and Principe}}	||	2022	||	2.41
|-
| {{flaglist|Scotland}}	||	2021	||	2.96
|-
| {{flaglist|Senegal}}	||	2022	||	2.61
|-
| {{flaglist|Serbia}}	||	2022	||	3.58
|-
| {{flaglist|Seychelles}}	||	2020	||	1.69
|-
| {{flaglist|Sierra Leone}}	||	2018	||	2.45
|-
| {{flaglist|Singapore}}	||	2020	||	1.24
|-
| {{flaglist|Slovakia}}	||	2020	||	4.37
|-
| {{flaglist|Slovenia}}	||	2022	||	3.04
|-
| {{flaglist|South Africa}}	||	2019	||	2.57
|-
| {{flaglist|South Korea}}	||	2020	||	2.09
|-
| {{flaglist|Spain}}	||	2019	||	4.68
|-
| {{flaglist|Sri Lanka}}	||	2020	||	2.10
|-
| {{flaglist|Suriname}}	||	2020	||	3.53
|-
| {{flaglist|Sweden}}	||	2022	||	5.18
|-
| {{flaglist|Switzerland}}	||	2023	||	5.13
|-
| {{flaglist|Taiwan}}	||	2020	||	2.45
|-
| {{flaglist|Tanzania}}	||	2015	||	1.75
|-
| {{flaglist|Thailand}}	||	2019	||	5.64
|-
| {{flaglist|Timor-Leste}}	||	2018	||	2.46
|-
| {{flaglist|Togo}}	||	2013	||	1.95
|-
| {{flaglist|Trinidad and Tobago}}	||2020||	1.99
|-
| {{flaglist|Tunisia}}	||	2014	||	3.69
|-
| {{flaglist|Turkey}}	||	2018	||	2.27
|-
| {{flaglist|Uganda}}	||	2021	||	2.34
|-
| {{flaglist|Ukraine}}	||	2019	||	2.64
|-
| {{flaglist|United Kingdom}}	||	2019	||	2.39
|-
| {{flaglist|United States}}	||	2020	||	2.00
|-
| {{flaglist|Uruguay}}	||	2019	||	3.31
|-
| {{flaglist|Venezuela}}	||	2020	||	1.17
|-
| {{flaglist|Wales}}	||	2021	||	2.71
|-
| {{flaglist|Zambia}}	||	2021	||	2.35
|}

==See also==
* {{annotated link|Social:Majoritarian representation}}
* {{annotated link|Social:Multi-party system}}
* {{annotated link|Social:One-party state}}
* {{annotated link|Social:Proportional representation}}
* {{annotated link|Social:Two-party system}}

==References==
<references />

==External links==
* [http://www.tcd.ie/Political_Science/people/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf Michael Gallagher providing data on the Laakso-Taagepera effective number of parties for over 900 elections in over 100 countries]
* Average effective number of parties (Golosov) for 183 democratic party systems and non-systems, 1792–2009, reported in Golosov, Grigorii V., [http://ppq.sagepub.com/content/19/1/122.abstract "Towards a Classification of the World's Democratic Party Systems, Step 1: Identifying the Units"], Party Politics, Vol. 19, No. 1, January 2013, pp.&nbsp;134–138.
* [http://golosovpubs.ucoz.com/index/indices_of_the_effective_number_of_parties_and_party_system_nationalization_in_excel/0-13 How to compute Golosov’s effective number of parties in Excel]


{{DEFAULTSORT:Effective Number Of Parties}}
[[Category:Electoral systems]]

{{Sourceattribution|Effective number of parties}}