¹ See, for example, Campbell, A., Gurin, G., and Miller, W. E., The Voter Decides (Evanston, Ill.: Row, Peterson, 1954)Google Scholar; Campbell, A., Converse, P. E., Miller, W. E., and Stokes, D. E., The American Voter (New York: John Wiley and Sons, 1960)Google Scholar; Stokes, D. E., “Some Dynamic Elements of Contests for the Presidency,” this Review, 60 (03 1966), 19–28 Google Scholar.

² Downs, A., An Economic Theory of Democracy (New York: Harper and Brothers, 1957)Google Scholar.

³ Stokes, D. E., “Spatial Models of Party Competition,” this Review, 57 (06 1963), 368–377 Google Scholar.

⁴ Converse, P. E., “The Problem of Party Distances in Models of Voting Change,” in Jennings, M. K. and Zeigler, L. H. (eds.), The Electoral Process (Englewood Cliffs, N.J.: Prentice-Hall, 1966)Google Scholar.

⁵ The thermometer question followed the basic format devised by A. R. Clausen for previous Survey Research Center studies, but was revised by the authors to apply to candidates rather than groups and to screen out “don't know” responses. The full wording of the question is given in the appendix. For other analysis involving this question in the 1968 election study, see Converse, P. E., Miller, W. E., Rusk, J. G., and Wolfe, A. C., “Continuity and Change in American Politics,” this Review, 63 (12 1969), 1083–1105 Google Scholar.

⁶ Mean values of all the candidates were drawn closer to the break-even point of 50 on the scale because of use by some respondents of the score of 50 degrees to indicate no feeling about the candidates, a meaning which was other than the intended meaning of neutral feelings. The differential in means between Wallace and LeMay would be all but erased if this factor were corrected by removing all 50 responses while the Muskie-Humphrey difference would be dramatically reversed. If the candidates given large numbers of 50's were better known, it is possible that they would have been received in much more favorable or unfavorable terms as the public would have been better able to judge them.

⁷ The relationship between these preference orders and the vote may be of some interest. Of those voters giving different scores to the three nominees, about 94 percent voted for the candidate they ranked highest while less than one percent voted for the candidate they ranked lowest. About 97 percent of those giving the two major party nominees their highest two rankings voted for their first choice, compared to only 82 percent of those giving Wallace one of their top two scores.

⁸ These notions are based on C. H. Coombs's “unfolding analysis” discussed in his book, A Theory of Data (New York: John Wiley and Sons, 1964), pp. 80–121 Google ScholarPubMed. The assumption is that an individual choosing among alternative stimuli orders them in terms of their distance from his point of maximum preference. As a result, on a continuum from left to right ordered A, B, C, people may give only the preference orders ABC, BAC, BCA, and CBA. Preference orders with the middle scale item, B, in the third choice position would violate this model so the ACB and CAB patterns would be nonexistent under the condition of perfect unidimensionality.

⁹ An alternate explanation of the behavior of Democratic identifiers is that support for Wallace would not be considered defection from the Democratic party in the South given the peculiarities of Southern politics. This hypothesis yields the same prediction we have specified for the party identification model among Democrats. However, the evidence in favor of the prediction of the party identification model is even stronger among the Democratic North than the Democratic South, which suggests that the effects of party identification are more fundamental than are those of Southern politics. While some respondents may have viewed Wallace as a Democratic candidate because of his background, we choose, partly for ease of exposition, to regard his candidacy as separate from either major party. At a minimum there is no evidence that he was viewed together with the remaining Democratic candidates.

¹⁰ The correlations measure the covariation in the ratings of candidate pairs. The average level of popularity of a candidate does not affect such co-variation nor does the degree of dispersion in the scores given to a candidate. In particular, the co-variation would not be altered by a linear transformation of the scores for a given candidate, such as a “bandwagon effect” which adds five degrees to every respondent's score for Nixon. All temporal effects need not involve simple linear transformations, but the covariation is less affected by such matters than the preference orders would be. Additionally, the use of the covariation measure may affect the distance between a pair of candidates in a spatial representation. A standard unfolding analysis would locate Nixon and Humphrey, for example, very near one another in a geometric space since large numbers of respondents rated both high. However, their correlation is actually a negative value, —.18. This indicates that the higher a respondent rated one of them, the lower he tended to rate the other; thus, the two belong in opposite parts of the space.

¹¹ See Kruskal, J. B., “Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis,” Psychometrika, 29 (03 1964), 1–27 CrossRefGoogle Scholar; Kruskal, J. B., “Nonmetric Multidimensional Scaling: A Numerical Method,” Psychometrika, 29 (06 1964), 115–130 CrossRefGoogle Scholar. Also, Guttman, L., “A General Nonmetric Technique for Finding the Smallest Coordinate Space for a Configuration of Points,” Psychometrika, 33 (12 1968), 469–506 CrossRefGoogle Scholar; Lingoes, J. C., “An IBM-7090 Program for Guttman-Lingoes Smallest Space Analysis—I,” Behavioral Science, 10 (04 1965), 183–184 Google Scholar; Shepard, R. N., “Metric Structures in Ordinal Data,” Journal of Mathematical Psychology, 3 (07 1966), 287–315 CrossRefGoogle Scholar.

¹² There are several reasons why we have more faith in the order of the correlation values than in their exact magnitudes. First, individuals tended to restrict their responses to the nine scores cited on the thermometer card rather than using the full range provided by the thermometer analogy. Ordinal correlation values on such a nine point scale did not equal the correlation values earlier obtained, but the crucial point is that the order of such values was virtually identical for the two types of coefficients (Spearman's rho = .99). Second, some respondents may have given low scores to two candidates for opposite reasons—such as one candidate being too far to the left and the other too far to the right to satisfy the respondent. Giving similar low ratings to a pair of candidates adds to their correlation, even when the respondents involved actually saw the two candidates as quite distant from one another. This has little effect on correlations of candidates near one another in the space, but it may artificially increase the correlations between distant candidates. As a result, the negative correlations and some of the low positive correlations may be higher (in the direction of +1.0) than they should be, though the order of the correlations should be substantially unaffected. Third, all respondents did not necessarily translate the same feelings toward the candidates into the same thermometer values. Individuals could have different response set tendencies—some preferring to give candidates high scores and others tending to give them low scores, a result which would give an artificial positive boost to the correlation of any particular pair of candidates. Such slippage between a person's actual feelings and his verbal scoring of the candidates makes our correlations more positive (or less negative) than they should be. (A detailed proof of this regularity is beyond the scope of this paper.) One way to correct for this effect would be to compute correlations based on each individual's deviation scores from his mean; this, however, would destroy the entire meaningfulness of the thermometer scale and its “anchors” of 0, 50, and 100 degrees. The values obtained from such an operation would be different from our correlation values, but again the order of the two sets of correlations would be essentially similar. (In fact, the Spearman rho coefficient between the original correlations and those obtained by use of such deviation scores is .96, a value which is very high but which does permit some mismatch in the ordering of correlation values for given pairings of candidates.)

An additional consideration motivating the use of a nonmetric technique over factor analysis has to do with the proven tendency of the latter to over-estimate the dimensionality of data of the type used here (C. H. Coombs, A Theory of Data, Ch. 8). Indeed some exploration with factor analysis on the thermometer data showed that it was supplying one more dimension than was uncovered by our use of a multidimensional scaling algorithm.

¹³ The terms used are those suggested by Kruskal for the evaluation of various stress values.

¹⁴ The exact details of such a solution should not be overinterpreted. Adjacent points, such as Johnson, Kennedy, and Muskie, might switch positions with one another if alternative assumptions had been made in the analysis. Thus small differences in the solution space should not be given too much credence. However, the gross features of the structure of the space—particularly clusters of points in that space—are generally invariant under the uncertainties governing this analysis.

¹⁵ In technical terms, we have employed a varimax rotation around the centroid of the space in order to approximate a simple structure solution. Multidimensional scaling solutions can be rotated freely because the choice of axes in the multidimensional space is arbitrary. The arbitrary determination of the axes sviggests that the overall structure of the space should be given the most emphasis or, alternatively, the relation of the candidate items to validating attitude items located in the same space should be stressed.

¹⁶ The solution in Figure 2 still portrays the relationships between the parties more accurately than it portrays those within the parties. In particular it understates the distance between McCarthy and Johnson. The three dimensional solution resolves these remaining discrepancies, with the third dimension providing separation within each party. This dimension divides Johnson from Kennedy and McCarthy among the Democrats and divides Nixon and Agnew from Rockefeller, Romney, and Reagan. In each case it separates the “middle-of-the-road” candidates in the party from the more liberal and conservative candidates. Those controlling their parties' organizations are divided from those who opposed their parties' establishments. While the three dimensional solution provides ah “excellent” fit to the data (stress = .018), this third dimension yields very little explanatory power so we shall not consider it further.

¹⁷ Approximately three-quarters of the electorate listed one of these as the major problem facing the government when asked just before the 1968 election. See also Converse, et al., “Continuity and Change in American Politics.”

¹⁸ Campbell, Converse, Miller, and Stokes, The, American Voter, Ch. 9.

¹⁹ The questions on urban unrest and Vietnam analyzed here and in Tables 6 and 7 below were devised by R. A. Brody, B. I. Page, S. Verba, and J. Laulicht.

²⁰ The associated stress value is .106, indicating some difficulty in satisfying the monotonic constraints. The need to satisfy the additional relationships between the attitude items and the candidate ratings has affected somewhat the structure of the candidate space embedded in Figure 3, though we would regard this candidate space as being essentially similar to that of Figure 2. The attitude items were included in both their original and reflected forms in order to facilitate comparisons of their locations with respect to both liberal and conservative candidates. While the candidate ratings have a natural direction, the scoring of these attitude items is arbitrary. Therefore it makes sense to consider both possible directions for each item. Unlike some other analysis procedures, the multidimensional scaling model does not force the two poles of an item to be exactly opposite one another in the space, though we find this to be approximately true. If an item is related to a given axis, its alternative scorings would be at opposite ends of that axis. Both poles of an item unrelated to a dimension would project on approximately the same place on that dimension.

²¹ Campbell, Converse, Miller, , and Stokes, , The American Voter, pp. 128–131 Google Scholar.

²² Converse, P. E. and Dupeux, G., “De Gaulle and Eisenhower: The Public Image of the Victorious General,” translated in Campbell, A., Converse, P. E., Miller, W. E., and Stokes, D. E., Elections and the Political Order (New York: John Wiley and Sons, 1966), pp. 292–345 Google Scholar.

²³ Ibid., p. 325.

²⁴ The seven point scales on this and the next issue were collapsed into five point scales by combining the two extreme positions at each end.

²⁵ In order to gauge the relative importance of these effects, it is necessary to consider the slopes, the distribution of cases on the issue and party variables, and the curvilinear tendencies for some of the candidates. The eta coefficient takes all of these matters into account and, hence, forms the basis for our judgments of relative importance. When squared, it relates the proportion of variance in a candidate's ratings explained by a given factor. Eta values for two variables can be compared to ascertain which factor, issue or party is the more important for the candidate of concern.

²⁶ Stokes, D. E., “Spatial Models of Party Competition,” p. 376 Google Scholar. “Position-dimensions” involve dimensions of conflict on which political actors—voters and parties—can and do take different policy stands.

²⁷ Ibid.

²⁸ A classification of elections in terms of maintaining, deviating, and realigning elections is given in Campbell, Converse, Miller, , and Stokes, , The American Voter, pp. 531–538 Google Scholar.