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A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections

  • John H. Aldrich (a1) and Richard D. McKelvey (a2)


A method of scaling is proposed to estimate the positions of candidates and voters on a common issue dimension. The scaling model assumes that candidates occupy true positions in an issue space and that individual level perceptual data arise from this in a two step process. The first step consists of a stochastic component, satisfying the standard Gauss Markov assumptions, which reflects true misperception. The second step consists of a linear distortion which is introduced in the survey situation. Estimates of the parameters of the model are developed by applying the least squares criterion, and distributions of the estimates are investigated by Monte Carlo methods.

The scaling technique is applied to the seven-point issue scales asked in the 1968 and 1972 SRC survey. The resulting ideal point estimates are related to candidate positions in 1968 to test a simple Downsian voting model.



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1 See Kessel, John H., “Comment: The Issues in Issue Voting,” American Political Science Review, 66 (June, 1972), 459465, for an extensive bibliography of the literature.

2 See Davis, Otto A., Hinich, Melvin J., and Ordeshook, Peter C., “An Expository Development of a Mathematical Model of the Electoral Process,” American Political Science Review, 64 (June, 1970), 426448, foi a review of this literature.

3 See Green, Paul E. and Carmone, Frank J., Multidimensional Scaling and Related Techniques in Marketing Analysis (Boston: Allyn and Bacon, Inc., 1970) for a review of this literature. Applications of these methods to the 1968 and 1972 presidential elections can be found in Rusk, Jerrold G. and Weisberg, Herbert F., “Perceptions of Presidential Candidates: Implications for Electoral Change,” Midwest Journal of Political Science, 16 (August, 1972), 338410, Weisberg, Herbert F. and Rusk, Jerrold G., “Dimensions of Candidate Evaluation,” American Political Science Review, 64 (December, 1970), 11671185, and Mauser, Gary A., “A Structural Approach to Predicting Patterns of Electoral Substitution,” in Multidimensional Scaling: Theory and Applications in the Behavioral Sciences, Vol. II, Applications, ed. Shepard, Roger al. (New York: Seminar Press, 1972), pp. 245287.

4 These particular data have been analyzed by Page, Benjamin I. and Brody, Richard A., “Policy Voting and the Electoral Process: The Vietnam War Issue,” American Political Science Review, 66 (September 1972), 979995, and by Aldrich, John H., “Some Results about the 1968 Election Based on the Theory of the Spatial Model of Party Competition” (paper delivered at the 1973 Annual Meetings of the American Political Science Association).

5 The scaling model we develop here rests on Gauss Markov type assumptions. There is good reason to question some of these assumptions, and hence attempt to extend the basic results to cover some of these potential violations. One assumption is that of “homoscedasticity” or constant error variance for each respondent and each candidate/stimulus. It may be more reasonable to expect some respondents to have greater perceptual error than others, and some stimuli to have lesser ambiguity in their positioning on issues than others. Another assumption is that of “no covariance” among an individual's perception of different candidates. It may be more realistic to assume that a respondent might identify certain candidates so that a change in perceived position of one candidate carries over to other candidates. A more general model incorporating these objections, would assume that there is a known stochastic variance/covariance matrix for each respondent:

6 See Harman, Harry H., Modern Factor Analysis (Chicago: The University of Chicago Press, 1967), for a more complete development of the factor-analytic model.

7 See e.g., Lawley, D. N. and Maxwell, A. E., Factor Analysis as a Statistical Method (London: Butter-worths, 1963) for a discussion of this point.

8 The issue scales were asked on the postelection wave of the 1968 survey. Only 1384 individuals responded to this wave, down from an original N of 1557 in the initial, self-weighting, cross-sectional sample. Fifty citizens saw no differences between the candidates on Vietnam, while 14 (including 7 of the original 50) were no variance respondents on urban unrest.

9 These graphs were drawn to scale by determining the individual frequency distributions of Yj. The scaling dimension was divided into 16 categories, each spanning a range of .25, and the proportion of Yj in each category determined. This is the same procedure as used in the Monte Carlo experiment.

10 See Repass, David E., “Issue Salience and Party Choice,” A merican Political Science Review, 65 (June, 1971), 389400.

A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections

  • John H. Aldrich (a1) and Richard D. McKelvey (a2)


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