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Things other than space and time can be projected to occupy three dimensions.
A three-dimensional graph is created by merely raising a third axis at right angles
to the conventional two, and plotting points inside that space. A '3D' graph is
not therefore what the term is commonly used to describe, a one-dimensional bar
chart, with each bar drawn as a pillar.
The three-dimensional graph used here is the natural extension of the equilat-
eral electoral triangle (see Chapter 7) developed into the logical three-dimensional
analogue of a tetrahedron, which attempts to show how the vote is shared between
as many as four parties in a large number of areas (Box 9.2). We need to be able
to do this if we are to include Scotland in our analysis of electoral composition in
Britain 8
(Figure 9.14). In Scotland, in recent years, the Scottish Nationalist Party
Box 9.2
The electoral tetrahedron
The idea of the equilateral triangle can be extended into three dimensions in
a tetrahedron to show the composition of the votes of four parties, among a
number of constituencies. Position (
on the triangle is calculated from
the Conservative ( C) , Labour ( L) , Liberal/Alliance ( A) and Nationalist ( N)
proportions of the vote as follows:
x,y,z)
C + L + A + N = 1
x = (C L 2 ,y = (A + N) 3
5
12
, z = N
2
Position in the equilateral tetrahedron
formed then gives the share of the
votes in any one constituency and
a map of them gives the distribu-
tion of all constituencies simultane-
ously. To understand the distribution
within the three-dimensional space it
must be rotated by the viewer. A two-
dimensional net of the space can be
opened out to expose some of the pat-
tern on flat paper, but a lot of the
dynamism of the graphic is lost. It
is hard to imagine how this device could be profitably extended to show
the composition of the vote among five parties. Three dimensions are hard
enough to grasp.
SNP 100%
Liberal/Alliance/SLD 100%
Conservative 100%
Labour 100%
8 In 1991 it was possible to write 'Scottish election results have recently become a truly four-way
affair'; currently (in 2012 as I make the last changes to this text) the SNP are in power in Scotland
and promise a referendum on independence. Things were changing two decades ago: 'Two-way
contests, which were far and away the most common in 1974, have declined pretty steadily and
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