The Laakso-Taagepera Index in A Mean and Variance Framework

The Laakso–Taagepera index (Laakso and Taagepera, 1979) has become the most commonly used measure to specify the ‘effective’ number of political parties in a party system where parties vary substantially in their vote and/or seat shares. It is well known that the Laakso–Taagepera index is the inverse of the even more widely used Herfindahl–Hirschman index of concentration (Hirschman, 1945; Herfindahl, 1950; cf. Taagepera and Grofman, 1981). Drawing on little known work by Feld and Grofman (1977, 1980) on the so called ‘class-size paradox’, it can also be shown that both indices may be re-expressed as simple functions of a distribution’s mean and variance. As far as we can judge, these latter relationships appear to be unknown in the party and electoral systems literatures. By expressing the Herfindahl–Hirschman index and the Laakso–Taagepera index in terms of means and variances we can see that each index has a ‘natural’ interpretation in terms of well known statistical parameters which allows their fundamental mathematical properties to be more clearly revealed.