Conservation of balance in the size of parties

Abstract

For parties of unequal seat shares (si), the widely used effective number of parties (N = 1/Σsi2) offers an equivalent in equal-sized parties, but it needs a supplement to express the imbalance in actual shares. This is akin to supplementing the mean with the standard deviation. A suitable 'index of balance' is b = -log s1/log p, where S1 is the largest share and p is the number of seat-winning parties. It can range from 0 (utter imbalance) to 1 (perfect equality of all parties). In most individual countries, the median balance is between 0.4 and 0.6, and the worldwide median balance is close to 0.50 for any number of seat-winning parties except 2, in line with a simple logical model. Independent of electoral systems used, a rule of conservation emerges: the median product of the largest party's fractional share and the square root of the number of seat-winning parties is conserved: s1p0.5 = 1. The worldwide median for 603 elections is within 2 percent of 1.00. © 2005 SAGE Publications.