Summary
It is possible to represent three-party election outcomes by a single point in a symmetric triangular diagram. This is a particularly convenient representation for displaying time trends in three-party systems. With some loss of information the diagrams can be adapted for multiparty systems, especially four-party systems.
No system of display is any better than the content of what is displayed. Some examples have been given of data and trends even in the notoriously two-party lands of Britain which in reality involve three or four parties and which are interesting enough to merit display and comment.
In this paper there has been no attempt to develop a sustained line of political reasoning using these triangular displays. For that see Miller, 1975. The purpose here is to list some of the useful properties of these elegantly simple diagrams and provide a sufficient range of examples of their use to show that they are more than a mathematically elegant toy.
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References
Butler, D. (1965). in Discussion of H.B. Berrington, “The General Election of 1964,” Journal of the Royal Statistical Society series A, V. 128, p. 17–66. Butler referred to work by G. Pyatt for the BBC (p. 55) in response to a suggestion by D. Ibbetson (p. 54–55).
Butler, D., and various co-authors. The British General Election of 19XX. (Published after each election since 1945). London: Macmillan Press.
Miller, W.L. (1975). Pathmakers in Scottish Politics: Four-way Swing in Scotland 1955–74. Paper at CPS Scottish/Norwegian Conference, Helensburgh, 1975.
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Miller, W.L. Symmetric representation of political trends in three-party systems with some properties, extensions and examples. Qual Quant 11, 27–41 (1977). https://doi.org/10.1007/BF00143985
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DOI: https://doi.org/10.1007/BF00143985