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South African Journal of Science

On-line version ISSN 1996-7489

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

 

RESEARCH ARTICLES

 

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: jgreben@csir.co.za

 

 


ABSTRACT

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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References

1. Pelzer B., Eisinga R. and Franses P.H. (2001). Estimating transition probabilities from a time series of independent cross sections. Statistica Neerlandica 55, 249-262.         [ Links ]

2. Hawkes A. (1969). An approach to the analysis of electoral swing. J. R. Statist. Soc. A 132, 68-79.         [ Links ]

3. Miller W.L. (1972). Measures of electoral change using aggregate data. J. R. Statist. Soc. A 135, 122-142.         [ Links ]

4. Greben J.M. (2005). Several methods of trend analysis applied to the South African elections. CSIR Tech. Rep. CSIR/BE/LQM/IR/2007/0100B, Pretoria.         [ Links ]

5. McCarthy C. and Ryan T.M. (1977). Estimates of voter transition probabilities from the British general elections of 1974. J. R. Statist. Soc. A140, 78-85.         [ Links ]

6. Upton G.J.G (1978). A note on the estimation of voter transition probabilities. J. R. Statist. Soc. A 141, 507-512.         [ Links ]

7. Lemon A. (2001). The general election in South Africa, June 1999. Electoral Studies 20, 305-339.         [ Links ]

8. Greben J.M., Elphinstone C.E., Holloway J., de Villiers R., Ittmann H. and Schmitz P (2005) Prediction of the 2004 national elections in South Africa. S. Afr. J. Sci. 101, 157-161.         [ Links ]

9. Lahiri A.K. and Roy P. (1984). Assessing swings in multi-party systems: the Indian experience. Electoral Studies 3, 171-189.         [ Links ]

10. Herniter J.D. (1973). An entropy model of brand purchase behaviour. J. Marketing Res. 10, 361-375.         [ Links ]

11. Greben J.M., Elphinstone C.E. and Holloway J. (2006). A model for election night forecasting applied to the 2004 South African elections. J. Operations Res. Soc. S. Afr. (ORiON) 22, 89-103.         [ Links ]

12. Kuhn H.W and Tucker A.W. (1951). Non-linear programming. Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman. University of California Press, Berkeley.         [ Links ]

13. Bernholtz B. (1963). A new derivation of the Kuhn-Tucker conditions. Opns Res. 12, 295-299.         [ Links ]

14. Kaufman L. and Rousseeuw P.J. (1990). Finding groups in data. In An Introduction to Cluster Analysis, pp. 182-185. Wiley-Interscience, New York.         [ Links ]

15. Benewick R.J., Birch, A.H., Blumler J.G. and Ewbank A.(1969). The floating voter and the liberal view of representation. Political Studies 17, 177-195.         [ Links ]

16. Bass F.M. (1974). The theory of stochastic preference and brand switching. J. Marketing Res. 11, 1-20.         [ Links ]

17. Hauser J.R. and Wisniewski K.J. (1982). Dynamic analysis of consumer response to marketing strategies. Management Sci. 28, 455-486.         [ Links ]

18. Upton G.J.G (1978). A memory model for voting transitions in British elections. J. R. Statist. Soc. A 140, 86-94.         [ Links ]

19. Upton G.J.G and Sarlvik B. (1981). A loyalty-distance model for voting change. J. R. Statist. Soc. A 144, 247-259.         [ Links ]

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