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Elections and swings

Published online by Cambridge University Press:  01 August 2016

Colin R. Fletcher
Colin R. Fletcher*
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth SY23 3BZ
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Extract

The change from essentially two party contests to three-, or even four-cornered fights, has provided the impetus for a fresh look at both diagrammatic representations of an election outcome, and the measure of swing from one election to the next. The representation of the votes in a three-cornered contest has been considered, amongst others, by Ibbetson [1], by Hollingdale [2] and by Miller in a series of papers and books (see for example [3] and [4]). Miller puts forward three ways of describing the outcome of such a contest, the ‘box-corner’ method (three-dimensional coordinate axes), homogeneous coordinates, and the ‘rectangular coordinate derivation’, but, as he notes, these three are fundamentally the same. Miller states that ‘mathematicians will instinctively go for the homogeneous coordinate representation’, and Hollingdale kindly obliges, although Miller himself plumps for the third representation, [3].

Type
Research Article
Information
The Mathematical Gazette , Volume 71 , Issue 455 , March 1987 , pp. 1 - 7
Copyright
Copyright © Mathematical Association 1987

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References

1. Ibbetson, D., discussion, J. Roy. Stat. Soc. A 128, 54–55 (1965).Google Scholar
2. Hollingdale, S.H., Votes, swings and kites, Bull. I.M.A. 20, 54–55 (1984).Google Scholar
3. Miller, W. L., Symmetric representation of political trends in three-party systems with some properties, extensions and examples, Quality and Quantity, 11, 27–41 (1977).Google Scholar
4. Miller, W. L., The end of British politics, Oxford University Press (1981).Google Scholar
5. Butler, D. and Kavanagh, D., The British general election of 1979, Macmillan (1980).Google Scholar
6. Lewis, T., discussion, J. Roy. Stat. Soc. A 128, 54 (1965).Google Scholar