Effective number of parties

The effective number of parties is a concept introduced by Laakso and Taagepera (1979)[1] which provides for an adjusted number of political parties in a country's party system. The idea behind this measure is to count parties and, at the same time, to 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 party systems across countries, as is done in the field of political science.[2] 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 operationalization for the political fragmentation.

There are two major alternatives to the effective number of parties-measure.[3] John K. Wildgen's index of "hyperfractionalization" accords special weight to small parties.[4] Juan Molinar's index gives special weight to the largest party.[5] Dunleavy and Boucek provide a useful critique of the Molinar index.[6]

The measure is essentially equivalent to the Herfindahl–Hirschman index, a diversity index used in economics; the Simpson diversity index, which is a diversity index used in ecology; and the inverse participation ratio (IPR) in physics.

Formulae

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

${\displaystyle N={\frac {1}{\sum _{i=1}^{n}p_{i}^{2}}}}$

where n is the number of parties with at least one vote/seat and ${\displaystyle p_{i}^{2}}$ 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 inverse Simpson index, or the true diversity of order 2.

An alternative formula was proposed by Grigorii Golosov in 2010.[7]

${\displaystyle N=\sum _{i=1}^{n}{\frac {p_{i}}{p_{i}+p_{1}^{2}-p_{i}^{2}}}}$

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

${\displaystyle N=\sum _{i=1}^{n}{\frac {1}{1+(p_{1}^{2}/p_{i})-p_{i}}}}$

Here, n is the number of parties, ${\displaystyle p_{i}^{2}}$ the square of each party's proportion of all votes or seats, and ${\displaystyle p_{1}^{2}}$ 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:

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[8][9] as ${\displaystyle N=(MS)^{1/6}}$, 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.[10] 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.

Country Year Effective number of parties
Albania 2021 2.18
Andorra 2023 2.36
Angola 2022 2.06
Antigua and Barbuda 2023 2.43
Argentina 2023 3.04
Armenia 2021 1.93
Australia 2022 3.15
Austria 2019 3.94
Bahamas 2021 1.42
Belgium 2019 9.70
Belize 2020 1.37
Bermuda 2020 1.38
Bhutan 2023-24 1.86
Bolivia 2020 2.28
Bosnia and Herzegovina 2022 9.00
Botswana 2019 1.94
Brazil 2022 9.91
Bulgaria 2023 4.73
Burkina Faso 2020 4.11
Cabo Verde 2021 2.20
Chile 2021 4.13
Colombia 2022 8.74
Costa Rica 2022 4.90
Croatia 2020 3.19
Cyprus 2021 4.81
Czech Republic 2021 3.34
Denmark 2022 7.24
Dominica 2022 1.21
Dominican Republic 2020 2.75
Estonia 2023 4.52
Faeroe Islands 2019 5.26
Fiji 2022 2.63
Finland 2023 5.56
France 2022 3.72
Gambia 2022 4.80
Georgia 2020 2.37
Germany 2021 5.51
Ghana 2020 2.01
Gibraltar 2019 3.04
Greece 2023 3.09
Greenland 2021 3.52
Guatemala 2023 7.26
Guinea 2020 2.06
Guinea-Bissau 2023 2.64
Guyana 2020 2.06
Honduras 2021 3.26
Hungary 2022 1.84
Iceland 2021 6.29
India 2019 2.17
Indonesia 2019 7.47
Ireland 2020 5.98
Israel 2022 6.51
Italy 2022 2.40
Jamaica 2020 1.53
Japan 2021 2.69
Kosovo 2021 3.49
Latvia 2022 6.14
Lesotho 2022 3.42
Liberia 2023 6.44
Liechtenstein 2021 2.93
Lithuania 2020 4.84
Luxembourg 2023 4.43
Malawi 2019 5.19
Malaysia 2022 7.72
Malta 2022 1.97
Mauritius 2019 2.29
Mexico 2021 2.13
Moldova 2021 2.03
Monaco 2023 1.00
Montenegro 2023 4.85
Morocco 2021 5.68
Mozambique 2019 1.67
Namibia 2019 2.16
Nepal 2022 4.75
Netherlands 2023 7.03
New Zealand 2023 3.81
Niger 2020-21 3.85
North Cyprus 2022 2.71
North Macedonia 2020 3.25
Northern Ireland 2022 4.52
Norway 2021 5.56
Panama 2019 3.07
Paraguay 2023 2.68
Peru 2021 6.20
Poland 2023 3.13
Portugal 2022 2.66
Romania 2020 4.30
Saint Kitts and Nevis 2022 2.57
Saint Lucia 2021 1.65
Saint Vincent and the Grenadines 2020 1.92
San Marino 2019 4.63
Sao Tome and Principe 2022 2.41
Scotland 2021 2.96
Senegal 2022 2.61
Serbia 2023 2.90
Seychelles 2020 1.69
Sierra Leone 2023 1.92
Singapore 2020 1.24
Slovakia 2023 5.44
Slovenia 2022 3.04
South Africa 2019 2.57
South Korea 2020 2.09
Spain 2023 3.44
Sri Lanka 2020 2.10
Suriname 2020 3.53
Sweden 2022 5.18
Switzerland 2023 5.13
Taiwan 2024 2.38
Thailand 2023 4.86
Timor-Leste 2023 3.02
Turkey 2023 2.35
Uganda 2021 2.34
Ukraine 2019 2.64
United Kingdom 2019 2.39
United States 2022 2.00
Uruguay 2019 3.31
Wales 2021 2.71
Zambia 2021 2.35