Patrick Dunleavy and Rekha
Diwakar, "Analysing multiparty competition in plurality rule
elections," Party Politics, 19 (November 2013),
855-886. [Available at http://ppq.sagepub.com/content/vol19/issue6/
In the comparative analysis of elections and party systems
we have yet to develop logically acceptable ways to chart
the district-level outcomes of multiparty elections, and to
assess the clustering or patterning of outcomes in
systematic ways. In this article, we show that the Nagayama
or 'all possibilities' triangle has major defects, but can
be reformulated and re-applied in two new ways. The first
captures the 'layer cake' character of general election
outcomes in a reductionist fashion, showing how the number
of observable parties competing for votes at district level
influences outcomes. An alternative variant (the crown
diagram) gives a more holistic picture of outcomes, shifting
attention to the performance of the top two parties or blocs
linked to the predominant political--ideological dimension
in a political system. We link this second innovation to a
tentative logic of evolutionary development applicable to
plurality rule election systems.
- Figures and
- Figure 1. The simplex representation of a three-party
- Figure 2. The 'all possibilities' triangle display
(after Grofman et al.).
- Figure 3. Flipping and rotating the APT.
- Figure 4. The size and shape of the ECS area at 3, 10
and 50 observable parties.
- Table 1. The mechanical and psychological impacts of
plurality rule elections on party competition, according
- Table 2. The percentage of all election districts
with different numbers of 'observable' parties in the UK,
India and US elections in the mid-2000s.
- Figure 5. The 2006 U.S. House of Representatives
election outcomes at district level.
- Figure 6. The 2004 Indian general election outcomes
for districts with different numbers of observable
- Figure 7. The 2005 general election outcomes in Great
Britain for districts with different numbers of
- Figure 8. The 'crown' within the double APT
- Figure 9. The seats outcomes in the U.S. House of
Representatives election, 2006.
- Figure 10. The seats outcomes in the Indian general
election of 2004.
- Figure 11. The seats outcomes in the 2005 general
election in Great Britain.
- Figure 12. The seats outcomes in the 1955 general
election in Great Britain.
- Figure 13. Hypothesized ideal-type stages in the
evolution of the UK's plurality rule system over
- Figure 14. Regional patterns of party competition in
four British regions at the 2010 general election.
- Figure 15. The outcomes of the European Parliament
elections in Great Britain in 1999, 2004 and 2009 using
regional list PR systems.
(First paragraph of Conclusions) Within plurality rule
election systems, the district-level comparison of general
election outcomes has been increasingly central in the
debate about competing Duvergerian expectations and opposing
mechanisms favouring party fragmentation (such as the
'invulnerable majority' effect). A few earlier analysts have
accumulated election data covering many separate district
contests (some 58,000 results in the case of Chhibber and
Kollman, 2004: ch. 2), yet confined their analysis to means
and standard deviations, presenting little of the richness
of outcomes patterning that can be accessed by better
methods of charting. We have demonstrated that it is helpful
to visually chart both a reductionist picture of V1V2
competition in races with different numbers of parties in
competition, shown in the ECS view, and giving insights into
the aggregated, layer-cake nature of general election
outcomes; and information about how district outcomes relate
to the most important basis for political alignments and how
the holistic patterns vary across election outcome, shown in
the crown diagram. A careful analyst will always consider