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South African Journal of Science

On-line version ISSN 1996-7489
Print version ISSN 0038-2353

S. Afr. j. sci. vol.103 n.5-6 Pretoria May./Jun. 2007




A theory of quantitative trend analysis and its application to South African general elections



Jan M. Greben

Logistics and Quantitative Methods, CSIR, P.O. Box 395, Pretoria 0001, South Africa. E-mail:




Trends are usually defined as progressive changes in a particular phenomenon. If the phenomenon can be characterized by one variable over time (such as the price of some item), then a trend analysis is fairly simple. Phenomena are often characterized, however, by more than one variable at particular discrete time intervals. In such cases a trend analysis becomes more complex and ambiguous. If enough data are available, however, trends between two subsequent times can be represented by so-called transition matrices. The theory of such matrices for the description of voting patterns was developed in the United Kingdom in the 1970s. South African general elections represent an ideal test case for such theories as both the number of independent results (17 000 voting districts versus about 240 three-way contested constituencies in the U.K.) and the number of parties (about 20 versus 4 in Britain) are much greater in the South African case. This paper reports such a trend analysis using extensions of previous methods, and introduces two new methods to avoid negative transition matrix elements. The applicability of the old and new methods is discussed and their results examined. Other areas of application of transition matrices to trends are briefly reviewed.



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