# Effective number of parties

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The effective number of parties (or effective number of political parties, ENP, ENPP) is a concept introduced by Laakso and Taagepera (1979)[1] which provides a measure of the number of political parties of a party system. The concept is to weight the parties by their support so as to answer how many equally-sized parties are equivalent to the number of parties observed. For instance, a party with hardly any support would only count as a fraction of an "equally sized party": a dominant party system would not be considered two-party if the second party obtains very few votes.

The ENP is analogous to diversity measures in economics, ecology, and physics. It can be calculated based on either votes for the different parties, or the number of seats they win in an assembly; when the two differ significantly, this indicates that the voting method for that assembly is not proportional.

## Formulae

### Laakso and Taagepera's measure

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 normalized such that, for example, 50 per cent is 0.5 and 1 per cent is 0.01.

### Entropy measure

Greene and Bevan provide a measure that they argue is more accurate than Laakso and Taagepera's.[2] It is based on the w:Shannon information entropy and calculated as follows:

${\displaystyle N=\exp(-\sum _{i=1}^{n}{p_{i}\log p_{i}})}$

where ${\displaystyle p}$ is defined as above.

## References

1. Laakso, Markku; Taagepera, Rein (1979). ""Effective" Number of Parties: A Measure with Application to West Europe". Comparative Political Studies. 12 (1): 3–27. doi:10.1177/001041407901200101. ISSN 0010-4140.
2. Greene, Zachary; Bevan, Shaun (2013). "How many parties? A more sensitive approach to measuring the effective number of parties" (PDF). Annual Elections, Public Opinion and Parties Conference, Lancaster, UK.