Rein Taagepera, "Conservation of Balance in the Size of Parties," Party Politics, 11 (May, 2005), 283-298.

First Two Paragraphs:
When changes in electoral rules or other conditions enable more parties to win seats in a representative assembly, the seat share of the largest party tends to go down. Is there some characteristic of the party system that tends to stay constant in the process? Is something conserved?

The concept of a conserved quantity is important in many areas of science. Quantities such as energy, momentum, electric charge and (under certain conditions) mass are conserved when a closed system undergoes changes. It is worthwhile asking whether any quantities tend to be conserved in the course of political processes. Absolute in macroscopic physics, the conservation principles become probabilistic at quantum level. In social relations, a stochastic element can be expected, so that conservation could be expected to apply only to the median outcomes.

Figures and Tables:
Table 1. The number of elections in the given range of the largest seat share (s1) by the number of seat-winning parties (p)
Figure 1. The median seat share of the largest party versus the number of parties in the assembly. Data from Table 1
Table 2. Distribution of index of balance b for 2 and more than 2 seat-winning parties
Table 3. Median values of index of balance for periods with same electoral rule

First Two paragraphs of Conclusion:
The concept of a conserved quantity is important in many areas of science. This study has used extensive worldwide data on the number and size of parties in assemblies to test a general rule of conservation of balance. This rule should apply whenever a well-defined total is randomly divided into a well-defined number of components. Median agreement is good when assemblies contain 3 to 12 parties, while deviations are marked in two-party assemblies and in an extremely splintered field. One may wonder whether a similar pattern arises with components different from parties, such as populations and areas of federal subunits.

Within the limits of validity thus established, the following principle of conservation of balance can now be asserted: the median product of the largest party's fractional share and the square root of the number of seatwinning parties is conserved: s₁p^0.5 = 1. The worldwide median is within 2 percent of 1.00.