A General Measure of the "Effective" Number of Parties in a Political System

This paper proposes a general measure of the effective number of parties, based on the family of generalized entropy inequality indices. This measure encompasses existing measures in the sense that these can be derived, through an appropriate configuration of parameter values, from this general measure. The proposed measure has attractive properties both in terms of interpretation and in terms of aggregation. In terms of interpretation, this measure always yields a value between 1 and N (N=the number of parties contesting) and takes one, or the other, extreme value depending on whether vote (or seats) are monopolized by a party or shared equally between the contesting parties. In terms of aggregation, it is always the case that the effective numbers of parties at sub-national levels can be aggregated to yield a national figure. The aggregation is effected through weights which, themselves, have an appealing interpretation in terms of the different sub-national contributions to overall inequality in the distribution of votes (or seats). The use of this general measure is illustrated by applying it to the results of the 1997 and 2001 Parliamentary (Westminster) elections in Northern Ireland. The central message of the paper is that the construction of indices or measures which purport to give scalar representation to vectors of distributive outcomes cannot be wholly based on "objective" considerations. This observation applies in full to the measurement of the effective number of parties in a political system.