Effective number of parties
The effective number of parties is a concept which provides for an adjusted number of political parties
Political Parties
Political Parties: A Sociological Study of the Oligarchical Tendencies of Modern Democracy is a book by sociologist Robert Michels, published in 1911 , and first introducing the concept of iron law of oligarchy...

 in a country's party system
Party system
A party system is a concept in comparative political science concerning the system of government by political parties in a democratic country. The idea is that political parties have basic similarities: they control the government, have a stable base of mass popular support, and create internal...

. The idea behind this measure is to count parties and, at the same time, to weight
Weight function
A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more "weight" or influence on the result than other elements in the same set. They occur frequently in statistics and analysis, and are closely related to the concept of a...

 the count by their relative strength. The relative strength refers to their vote share ("effective number of electoral parties") or seat share in the parliament ("effective number of parliamentary parties"). This measure is especially useful when comparing electoral systems across countries, as is done in the field of political science
Political science
Political Science is a social science discipline concerned with the study of the state, government and politics. Aristotle defined it as the study of the state. It deals extensively with the theory and practice of politics, and the analysis of political systems and political behavior...

. 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 fragmentation of a party system.

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


According to Laakso and Taagepera
Rein Taagepera
Rein Taagepera is an Estonian political scientist and politician.- Education :Born in Tartu, Estonia, Taagepera fled from occupied Estonia in 1944. Taagepera graduated from high school in Marrakech, Morocco and then studied physics in Canada and the United States. He received a Ph.D. from the...

(1979) the effective number of parties is computed by 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.

An alternative formula proposed by Golosov (2010) is

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.


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

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