Effective Number of Parties Calculator

Calculate the effective number of parties (Laakso–Taagepera index) from each party’s vote or seat share, entered as decimals or percentages.

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Effective Number Of Parties Formula

The following formula is used to calculate the effective number of parties for a given set of party shares.

N = (1) / (Σpᵢ²)

Variables:

N is the effective number of parties
p_i is party i’s share of the same complete vote or seat total, expressed as a decimal; all shares sum to 1

To calculate the effective number of parties, sum the squares of the party shares and then take the reciprocal of this sum.

What is the Effective Number Of Parties?

The effective number of parties is a measure used in political science to quantify the number of significant parties in a political system. Unlike a simple count of parties, this measure takes into account the relative sizes of the parties, giving more weight to larger parties and less weight to smaller ones. This provides a more accurate representation of the party system’s complexity and competitiveness. The effective number of parties can be calculated for both votes and seats, offering insights into the electoral and legislative dynamics of a political system.

How to Calculate the Effective Number Of Parties?

The following steps outline how to calculate the Effective Number Of Parties.

First, determine the shares of votes or seats for every party (p_i), using a complete distribution that sums to 1 (or 100%). Do not combine distinct parties into an “other” category.
Next, square each of these shares.
Next, sum all the squared shares.
Finally, take the reciprocal of the sum to get the Effective Number Of Parties.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Party Shares: 0.4, 0.3, 0.2, 0.1

Effective Number Of Parties Calculator screenshot