Rein Taagepera and Bernard
Grofman, "Mapping the Indices of SeatsVotes
Disproportionality and InterElection Volatility,"Party
Politics, 9 (November 2003), 659677.
First Paragraph:
Deviation from proportional representation (PR) means the
difference in party vote shares and party seat shares in
some given election (vit versus si).
Volatility of votes means the difference in party vote
shares (vi) from one election to another (vit
versus vit'); similarly, volatility of seats
means the difference in party seat shares (si) from
one election to another (s sit versus sit' How
do we best measure the proportionality/disproporrionality of
the translation of party vote shares into party seat shares
in a given election? How do we best measure the
stability/volatility of party vote shares (or party seat
shares) across elections?
Figures and Tables:
Table 1: Evaluation of indices of
disproportionality/volatility based on absolute values of
difference
Table 2: Evaluation of indices of
disproportionality/volatility based on suqare of
difference
Table 3: Evaluation of indices of
disproportionality/volatility with bases other than absolute
values of difference or square of difference
Last Paragraph:
What have we added to Monroe's (1994) and Pennisi's (1998)
earlier studies of disproportionality and malapportionment?
First, we have updated and complemented the zoo of indices
proposed and used by various researchers, pointing out
parallel developments in measuring volatility and possible
extension toward systematic measurement of vote splitting.
Second, we have composed two sets of desirable criteria
(theoretical and practical), rating each of the 19 indices
explicitly on those 12 criteria. The most widely used
indices, Gallager's Gh and LoosemoreHanby's D,
satisfy more criteria than any other, including Dp,
proposed by Monroe (1994).
Third, we have tried to
specify a constellation that would he intuitively halfway
from perfect concordance to utmost discordance; once more,
Gh and D are among the few indices that yield
50 percent for such a constellation. We have located
a dilemma when Dalton's principle of transfers is applied to
parties rather than individuals: which party is the richer
one when one has more extra seats while another is overpaid
by a larger ratio? If the number of excess seats is taken as
the preferred criterion, Gh becomes slightly
preferable to D, in view of the latter's ambiguity
when data sources lump several small parties. Finally, we
tried to devise an even better index than Gh or D
but came up short. [First two paragraphs of the
Conclusion.]
