Rein Taagepera,
"Conservation of Balance in the Size of Parties," Party
Politics, 11 (May, 2005), 283298.
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 seatwinning
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 seatwinning 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 welldefined total is randomly divided into
a welldefined number of components. Median agreement is
good when assemblies contain 3 to 12 parties, while
deviations are marked in twoparty 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:
s_{1}p^{0.5} = 1. The worldwide median is
within 2 percent of 1.00.
