Effective number of parties

Some political scientists use the effective number of parties as a diversity index. The measure as introduced by Laakso and Rein Taagepera (1979), produces an adjusted number of political parties in a country's party system, weighted by their relative size. The measure is useful when comparing party systems across countries.

A jurisdiction's party system can be measured by either:

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 smaller than the number of actual parties. The effective number of parties is a frequent operationalization for political fragmentation. Conversely, political concentration can be seen by the share of power held large political parties.

Several common alternative methods are used to define the effective number of parties. 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.

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 ${\displaystyle p_{i}^{2}}$ 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.

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 ${\displaystyle \alpha =2}$ in information theory.

An alternative formula was proposed by Grigorii Golosov in 2010.