Effective number of parties

The effective number of parties is a frequent operationalization for political fragmentation.

[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.

This is also the formula for the inverse Simpson index, or the true diversity of order 2.

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

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: The effective number of parties can be predicted with the seat product model[10][11] as

[12] Some of the highest effective number of parties are in Brazil, Belgium, and Bosnia and Herzegovina.