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]
Example of how the effective number of parties shows the fragmentation of the Dutch political landscape (1981–2017)
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:
where n is the number of parties with at least one vote/seat and 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.
which is equivalent – if we only consider parties with at least one vote/seat – to
Here, n is the number of parties, the square of each party's proportion of all votes or seats, and 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[9][10] as , where M is the district magnitude and S is the assembly size.
For individual countries the values of effective number of number of parliamentary parties (ENPP) for the last available election is shown.[11] 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.
^Lijphart, Arend (1999): Patterns of Democracy. New Haven/London: Yale UP
^Avila-Cano, Antonio; Triguero-Ruiz, Francisco (2024). "Concentration of political power: Can we improve its measurement?". Comparative European Politics. 22 (3): 389–407. doi:10.1057/s41295-023-00365-1. ISSN1472-4790.
^Molinar, Juan (1 January 1991). "Counting the Number of Parties: An Alternative Index". The American Political Science Review. 85 (4): 1383–1391. doi:10.2307/1963951. JSTOR1963951. S2CID154924401.
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