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In political science, the effective number of parties is a diversity index introduced by Laakso and Rein Taagepera (1979),^[1] which provides for an adjusted number of political parties in a country's party system, weighted by their relative size. The measure is especially useful when comparing party systems across countries.^[2]

The size of a party can be measured by either:

The effective number of electoral parties (ENEP) weights parties by their share of the vote.
The effective number of parliamentary parties (ENPP) weights parties by their share of seats in the legislature.

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 political fragmentation. Political concentration can seen as the share of power of large political parties.^[3]

There are several common alternatives for how to define the effective number of parties.^[4] John K. Wildgen's index of "hyperfractionalization" accords special weight to small parties.^[5] Juan Molinar's index gives special weight to the largest party.^[6] Dunleavy and Boucek provide a useful critique of the Molinar index.^[7]

Measures

Quadratic

Laakso and Taagepera (1979) were the first to define the effective number of parties using the following formula:

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

where n is the number of parties with at least one vote/seat and $p_{i}^{2}$ the square of each party's proportion of all votes or seats. This is also the formula for the inverse Simpson index, or the true diversity of order 2. This definition is still the most commonly-used in political science.

This measure is equivalent to the Herfindahl–Hirschman index, used in economics; the Simpson diversity index in ecology; the inverse participation ratio (IPR) in physics; and the Rényi entropy of order $\alpha =2$ in information theory.^[8]

Alternatives

An alternative formula was proposed by Grigorii Golosov in 2010.^[9]

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

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

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

Seat product model

The effective number of parties can be predicted with the seat product model^[10]^[11] as $N=(MS)^{1/6}$ , 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.^[12] 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
Barbados	2022	1.00
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
Canada	2021	2.76
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
El Salvador	2021	2.99
Estonia	2023	4.52
Ethiopia	2021	1.07
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
Grenada	2022	1.92
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	2024	7.26
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
Mongolia	2024	2.45
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
Pakistan	2024	4.13
Panama	2019	3.07
Paraguay	2023	2.68
Peru	2021	6.20
Poland	2023	3.13
Portugal	2022	2.66
Romania	2020	4.30
Russia	2021	1.85
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
Trinidad and Tobago	2020	1.99
Turkey	2023	2.35
Uganda	2021	2.34
Ukraine	2019	2.64
United Kingdom	2024	2.23
United States	2022	2.00
Uruguay	2019	3.31
Uzbekistan	2024	3.73
Wales	2021	2.71
Zambia	2021	2.35