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A Note on the ‘Equilibrium’ Division of the Vote*

Published online by Cambridge University Press:  01 August 2014

Duff Spafford
Duff Spafford*
Affiliation:
University of Saskatchewan
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Extract

This research note proposes a model in which an “equilibrium” share of the vote figures as a measurable quantity. Variants of the model are fitted to election data for the U. S. House of Representatives.

Type
Articles
Information
American Political Science Review , Volume 65 , Issue 1 , March 1971 , pp. 180 - 183
Copyright
Copyright © American Political Science Association 1971

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Footnotes

*

Thanks are due to my colleague, Peter C. Dooley, and to an anonymous Review referee.

References

1 See Stokes, Donald E. and Iversen, Gudmund R., “On the Existence of Forces Restoring Party Competition,” Public Opinion Quarterly, 26 (1962), 159–171 CrossRefGoogle Scholar, and Charles Sellers, “The Equilibrium Cycle in Two-party Politics,” ibid., 29 (1965), pp. 16–38.

2 “We use the term ‘restoring’ or ‘equilibrium’ force as a generalized name for factors tending to return the party division to 50 percent in the long run” (Stokes and Iversen, op. cit., p. 161, footnote 6).

3 Chipman, John S., “The Nature and Meaning of Equilibrium in Economic Theory,” Functionalism in the Social Sciences, Martindale, Don (ed.) (Philadelphia, 1965), p. 36 Google Scholar.

4 See, e.g., Samuelson, Paul A., Economics: An Introductory Analysis (6th ed.; New York, 1964), pp. 396–398 Google Scholar.

5 For a more formal account of stability conditions, lee Appendix, item 1.

6 The reader is referred to Goldberg, Samuel, Introduction to Difference Equations (New York, 1958)Google Scholar.

7 Share of total vote was favored over share of major-party vote because of greater simplicity of interpretation. The equations also were fitted using major-party shares; such differences as arose are noted in the text.

8 This is very close to the mean Democratic share of vote (47.3 percent), the reason being that the means of the unlagged and lagged shares are very similar. If the two series had the same mean, that common mean would be equal to the equilibrium share. A regression line is constrained to pass through the point of means, ẍt = β 0 + β 1ẍt-1. Now let ẍt = ẍt-1, = ẍ; then ẍ = β 0 + β 1ẍ or ẍ = β 0/(1 — β 1); cf. equation (5).

9 A comparison of actual shares of vote won by the Democratic party in the four post-sample elections with the shares predicted by Version V may be of interest Actual percentages with predicted percentages in parentheses, are: 1962, 52.5 (52.0); 1964, 57.2 (54.4); 1966, 50.9 (53.9); 1968, 50.0 (53.8).

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