Triangles and three-party competition

Although we strongly support maps when visualizing data there are still opportunities for using different approaches. This first case study examines the use of triangles when

describing aspects of electoral and party competition. The approach adopts similar methods developed by Upton (Upton 1991) and by Dorling (Dorling, Pattie et al. 1993) that were discussed briefly in Chapter 3. The method that is particularly suitable for viewing the dynamics of three-party competition and was used in research that developed a new method for decomposing electoral bias (Borisyuk, Johnston et al. 2010).

Traditionally, a single straight line is used to describe some aspects of two-party competition whether it is vote share or the simple left-right continuum. In his Economic Theory of Democracy Anthony Downs (Downs 1957) used this method to show how two parties

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competed for the centre ground where the maximum number of voters were likely to be located. There was also some description using the left-right dimension to show why third parties do not do well in first past the post voting. This presentation is not as useful when trying to display three-party competition, however. In Chapter 3 we showed how Upton (Upton 1976) began to use triangles to describe three parties and this method was adopted by others (Dorling, Pattie et al. 1993; Katz and King 1999). It was a method that the Elections Centre adopted as it began to try and develop a method for decomposing electoral bias for the three party case.

The method for decomposing electoral bias was formulated by Ralph Brookes in the late 1950s and then adopted for the UK by Ron Johnston and others (Johnston, Pattie et al. 2001). The problem was that Brookes’ original formula was written for two parties and needed to be adapted to fit the three-party case. In recent times the UK has moved away from a two-party system where the combined vote and share of seats won by the Conservative and Labour parties was very large to more of a three-party system where the share of the national vote won by the third party, the Liberal Democrats since 1988, has been rising and also the party’s share of seats.

In about 2007 Johnston began to collaborate with Plymouth University as they sought to develop a revised method. Our particular interest in this research project lay in the methods the team used to develop their ideas about the underlying nature of the voting data. Because of the three-party competition it was decided that triangular graphs would be the best way to show the distribution of the three-party vote.

If we imagine a hypothetical result in a constituency where the three main parties, Conservative, Labour and Liberal Democrat, all tie in votes – i.e. the candidates all get

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exactly 33.3% of the vote share. This constituency would be located in the exact centre of the triangle. Constituencies would move around inside the triangle depending on the relative strengths of the three main parties. It was important to do this because the researchers needed to understand the shape of the vote distribution between the main parties after each general election. Figure 5.12 below shows the distribution after the 2005 general election. This clearly shows a large number of Labour/Conservative marginal seats (at the intersection marked with a dotted black line) but many fewer Labour/Liberal Democrat marginal seats. In the bottom third of the pyramid is a group of seats where the Labour vote is very low and the effective two-party competition is between Conservative and Liberal Democrat.

Figure ‎5.12: Distribution of three-party vote shares, 2005 general election

They also needed to see what happened to that distribution when they applied their new method for estimating bias. This involved running a number of simulations of what the election would have looked like if the original finishing order of the parties (e.g. ABC) had been different (e.g. ACB). The method required comparing the actual result with all possible

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combinations of the parties’ finishing order – ABC, ACB, BCA, BAC, CAB, and CBA). The resulting set of graphics is shown (Figure 5.13) below partly to demonstrate how the method works but also to show the deterioration in visualisation that occurs when there is the switch from colour to black and white – again the journal could not accept coloured graphics.

ABC BAC CAB

CBA BCA

ACB

Figure ‎5.13: Distribution of three-party vote shares:

ABC (actual), ACB, BAC, BCA, CAB, and CBA (notional elections)

The final composite picture (the amalgamation of all six elections) is revealed in Figure 5.14. It is by from this display of the data that the researchers were able to summarise the

distribution of overall bias between Conservative, Labour and Liberal Democrat parties for the 2005 general election.

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Figure ‎5.14: The superposition ABC+ACB+BAC+BCA+CAB+CBA

At stated earlier (Chapter 1) the paper format stands in the way of reporting data

visualisations properly. The Elections Centre, for example, during this research decided that a better way of watching the effects of running different election simulations was to use Matlab software to create film-like animations that would show the changing dynamic of actual party competition for a series of general elections. The two figures below are simple screen-grabs of different parts of the evolution between the 2005 and 2010 general elections in this case. Each constituency is a point beginning with the 2005 general election which then ‘migrates’ into another area of the triangle dependent upon the direction of flow of vote. If the change in share affected only two parties, e.g. Labour and Conservative then the line would run along a certain vector but if there was also a change in vote share for the Liberal Democrats then the vector would take that into account also.

The second The third

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Figure ‎5.15: screen grab1 evolution of votes 2005-2010 general election

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The first (Figure 5.15) shows the distribution of constituencies at the time of the 2005 general election (estimate seat shares because constituency boundaries changed during this period) while the second (Figure 5.16) shows the movement of each constituency in the three-party share space. The direction of each line is an indication of the flow of votes between parties during that election. Watching these animations provided us with a much clearer

understanding about flow of votes that could be obtained from tabular data that would need to split the data into categories and would be difficult to read. The animations were in fact better than the static pyramids because with these the user had to move their eyes from one to another. Unfortunately, while this method was useful for visualizing electoral change it cannot be applied when submitting papers to academic journals unless those journals publish online versions that contain hyperlinks to data, animations, graphics etc. The technology is already available but the publishers appear unwilling or unable to use it.