¹ Representative articles are Patterson, S. C., “Legislative Leadership and Political Ideology,” Public Opinion Quarterly, Vol. 27 (1963), pp. 399–410CrossRefGoogle Scholar; Rieselbach, L. N., “The Demography of the Congressional Vote on Foreign Aid, 1939–1958,” this Review, Vol. 58 (1964), pp. 577–588Google Scholar; G. R. Schubert, “The 1960 Term of the Supreme Court—A Psychological Analysis,” ibid., Vol. 56 (1962), pp. 90–107; H. R. Alker, Jr., “Dimensions of Conflict in the General Assembly,” ibid., Vol. 58 (1964), pp. 642–657; Munger, F. and Black-hurst, J., “Factionalism in the National Conventions, 1940–1964; An Analysis of Ideological Consistency in State Delegation Voting,” Journal of Politics, Vol. 27 (1965), pp. 375–394CrossRefGoogle Scholar.

² The term “roll call” will be used to refer to any division of legislators into two opposing groups on a political issue—including, for example, whip polls and discharge petitions. “Legislators” will refer to members of bodies (or groupings such as state delegations) analyzable in the ways proposed.

³ Beyle, H. C., Identification and Analysis of Attribute-Cluster Blocs (Chicago, 1931)CrossRefGoogle Scholar; Rice, S. A., Quantitative Methods in Politics (New York, 1928), ch. 16Google Scholar; Truman, D. B., The Congressional Party (New York, 1959)Google Scholar.

⁴ Most analyses of political data published so far, using analytic rotation by computers, to the author's knowledge, have used orthogonal rotation. Schubert's study (op. cit., pp. 96–97) is an important exception; he rotates to oblique axes based on Guttman scales, and avoids orthogonal rotation on grounds similar to those presented here. Another exception is Grumm, J. G., “A Factor Analysis of Legislative Behavior,” Mid-west Journal of Political Science, Vol. 7 (1963), pp. 336–356CrossRefGoogle Scholar.

⁵ In so doing, we no longer assume that such a set of roll calls must be restricted to a single issue. This meets to some extent the criticism of Lijp-hart, A. in “The Analysis of Bloc Voting in the General Assembly: A Critique and a Proposal,” this Review, Vol. 57 (1963), pp. 904–905Google Scholar.

⁶ For a recent example, see Rieselbach, op. cit.; for a more detailed exposition of reasoning and procedures, see MacRae, D. Jr., Dimensions of Congressional Voting, University of California Publications in Sociology and Social Institutions, Vol. 1 #3 (1958), pp. 203–333Google Scholar.

⁷ Guttman, L., “The Basis for Scalogram Analysis,” ch. 3 in Stouffer, S. A. et al. , Measurement and Prediction (Princeton, 1950)Google Scholar.

⁸ Voting systems with three alternatives (e.g., abstention) may often be analyzed by converting a trichotomy into two dichotomies. Votes for a multiplicity of unordered alternatives (as in a Presidential nominating convention) are less easily treated in this way.

⁹ In factor analysis it is conventional to form factor scores by adding the weighted contributions of items loaded on a given factor; this procedure treats items as interchangeable, in the sense considered here. Schubert, in assigning scores on cumulative scales, also uses an additive procedure (op. cit.); this may be appropriate for matching scales with factors, but it is not the procedure that we propose here.

¹⁰ MacRae, Dimensions …, op. cit., p. 228.

¹¹ Guttman, op. cit., pp. 80ff.

¹² For further treatment of the last two points see Kaplan, A., The Conduct of Inquiry (San Francisco, 1964), pp. 41, 50Google Scholar.

¹³ Toby, J. and Toby, M. L., “A Method of Selecting Dichotomous Items by Cross-Tabulation,” ch. 15 in Riley, M. W., Riley, J. W. Jr., and Toby, J., Sociological Studies in Scale Analysis (New Brunswick, 1954)Google Scholar.

¹⁴ Op. cit., p. 343. It was also required that the numbers of cases in cells a and d each be at least twice that in the “zero box.”

¹⁵ See, for example, Menzel, H., “A New Coefficient for Scale Analysis,” Public Opinion Quarterly, Vol. 17 (1953), pp, 268–280CrossRefGoogle Scholar; E. F. Borgatta, “An Error Ratio for Sealogram Analysis,” ibid., Vol. 19 (1955), pp. 96–100.

¹⁶ It can be seen from Figure 1 that for roll call #1, p+ = (a+c)/N, and for roll call #2, p+ = (a + b)/N. The difference is (c–b)/N. If roll call #1 has the higher p+, this difference will be positive.

¹⁷ See MacRae, D. Jr., “An Exponential Model for Assessing Fourfold Tables,” Sociometry, Vol. 19 (1956), pp. 84–94CrossRefGoogle Scholar. This method was used in Dimensions …, op. cit..

¹⁸ See Yule, G. U., Introduction to the Theory of Statistics (London, 1911), p. 38CrossRefGoogle Scholar.

¹⁹ This approximation is good as long as c is much larger than b.

²⁰ See Goodman, L. A. and Kruskal, W. H., “Measures of Association for Cross Classifications,” Journal of the American Statistical Association, Vol. 49 (1954), pp. 723–764Google Scholar. An alternative line of reasoning which leads to similar formulations is put forward in Kendall, M. G., Rank Correlation Methods (London, 3d ed., 1962), pp. 3–5Google Scholar. In comparing two rankings, Kendall counts the number of pairs of elements that are ranked consistently, and the number ranked inconsistently, out of all possible such pairs. With either of these approaches, it would be possible to assess a fourfold table not only in terms of the proportional consistency of the rankings it provides (as measured by Q), but also in terms of the proportion of rankings about which a judgment of consistency may be made. If this latter proportion is low (i.e., the proportion of ties is high), as in tables with extreme values of p+, the table may be given less emphasis in interpretation.

²¹ Computer programs for carrying out this operation are discussed in Bonner, R. E., “On Some Clustering Techniques,” IBM Journal of Research and Development, Vol. 8 (1964), pp. 22–32CrossRefGoogle Scholar. A related program was written by F. K. Bamberger for the Univac I, and used in exploratory research by the author. A similar program was written for the IBM 7094 at Chicago by R. Axelrod. These programs were costly in computer time, however; the clusters reported here there-fore were obtained from the Q-matrix by paperand-pencil methods, which are believed reliable up to a matrix size of about 150 items.

²² In the House of Representatives, the votes ignored by this choice tend to include a disproportionate number of questions affecting particular areas of the country, such as the appointment of judges for a particular district, the movement of an Army installation from one place to another, or the treatment of an industry whose production and markets are highly localized.

²³ See MacRae, D. Jr., “IBM 1401 Q-Matrix and Editing Programs for Legislative Votes,” Behavioral Science, Vol. 10 (1965), p. 324Google Scholar. For each pair of roll calls, only those legislators voting on both are counted in the calculation.

²⁴ These numbers are used to identify the roll calls in the Congressional Quarterly Almanac, Vols. 11, 12 (Washington, 1955, 1956)Google Scholar.

²⁵ The actual computer printout also indicates the value of p+, and the provisional “positive” vote (yea or nay), on each roll call. This preserves all the information in the individual fourfold tables except for the distribution of non-voting.

²⁶ See R. C. Tryon and D. E. Bailey, Cluster and Factor Analysis (in preparation). Reference is made to this method in D. MacRae, Jr., "Cluster Analysis of Congressional Votes with the BC TRY System,” Western Political Quarterly (in press). See also Tryon and Bailey, “The BC TRY Computer System of Cluster and Factor Analysis,” Multivariate Behavioral Research (in press).

²⁷ More elaborate procedures of the second type are presented in Bonner, op. cit. In the procedure used here, ties between clusters of equal size are resolved in favor of the cluster with highest average Q.

²⁸ To designate roll calls by number, we precede the Congressional Quarterly number by the last digit of the year (5 or 6).

²⁹ In general, we terminate after the first six scales and ties, if all possible scales containing as few as six roll calls have been found.

³⁰ This procedure was proposed in Stouffer, S. A. et al. , “A Technique for Improving Cumulative Scales,” Public Opinion Quarterly, Vol. 16 (1952), pp. 273–291CrossRefGoogle Scholar.

³¹ In the descending sequence of values of p₊, any interval of .10 or greater is first marked off as a division point. Then each sequence of values of p₊ between these division points, or at the end of the overall sequence, is further divided if it spans a range of p₊ greater than .15. This division is made by specifying further division points, equally spaced, with intervals as near to .10 as possible. The roll calls falling between each pair of division points then constitute a contrived (or if only one, an ordinary) item. This procedure, while useful for placing legislators, discards information provided by the distribution of p₊.

³² The detailed procedures are essentially the same as those specified in MacRae, Dimensions …, pp. 321–322.

³³ Goodman and Kruskal, op. cit., pp. 749–751.

³⁴ For an elementary discussion of gamma, how to calculate it, and its relation to Q, see Zel-ditch, M., A Basic Course in Sociological Statistics (New York, 1959), pp. 180–186Google Scholar.

³⁵ MacRae, Dimensions …, op. cit.

³⁶ This finding is consistent with the high associations between the former agriculture scale and the former welfare-state and race-relations scales (7=+.70, +.79resp.).

³⁷ This distinction was shown to be related to the rural or urban character of constituencies in Dimensions …, op. cit., pp. 266–268.

³⁸ Further evidence of this overlap arose in the process of cluster identification. A number of roll calls in Scale 1 could equally well have been placed in Cluster 5; they were simply assigned to Cluster 1 by the preference which our rules give to larger clusters. Moreover, a change in the minimum Q also transferred items from one cluster to another.

³⁹ This was also pointed out in Dimensions …, op. cit., pp. 251–252.

⁴⁰ This position was taken by Guttman when he introduced the scaling technique. See Measurement and Prediction, op. cit., pp. 72, 84, 85.

⁴¹ The two issues were not similar in this sense for the two parties combined, however; the Republicans were generally more favorable to civil rights than the Democrats.

⁴² See MacRae, D. Jr., “Intraparty Divisions and Cabinet Coalitions in the Fourth French Republic,” Comparative Studies in Society and History, Vol. 5 (1903), pp. 164–211CrossRefGoogle Scholar.

⁴³ The principal exception to this rule concerns votes on civil rights, on which the Democrats generally voted more conservatively. The polarities on civil rights roll calls were reversed before application of the rule. Scale #5 for the Republicans in the 80th Congress was assigned a polarity consistent with its higher-order cluster; the two of its four roll calls whose polarities were thus reversed were on Republican bills opposed by Democrats and conservative Republicans.

⁴⁴ The polarity of Scales #4 for the Republicans and #4 for the Democrats is reversed in Table III relative to Table II. This is because in the previous study, polarities were chosen for intra-party consistency, while they are chosen here to show the relations between internal divisions and inter-party differences.

⁴⁵ For domestic issues, this difference between the parties has also been observed in another study of this period: David R. Mayhew, “Democrats and Republicans in the U. S. House of Representatives: A Study of Intra-Party Coalition Patterns in the Postwar Period,” Ph.D. dissertation, Harvard, 1963, esp. ch. 6.

⁴⁶ This low association is partly due to the inclusion of Marcantonio and Isacson (ALP, NY) together with the Democrats; on Scale 6, they joined a small group of conservatives in opposing foreign aid.

⁴⁷ See Riddick, F. M., “The Eighty-Second Congress: First Session,” Western Political Quarterly, Vol. 5 (1952), pp. 106, 108Google Scholar; Congressional Quarterly Almanac, Vol. 8 (Washington, 1952), pp. 58–59Google Scholar.

⁴⁸ Representatives from the eleven former Confederate states.

⁴⁹ Bloc analysis of the parties in the 81st Congress also showed the Republicans to be divided into more and smaller subgroups than the Democrats. See D. B. Truman, The Congressional Party, op. cit.

⁵⁰ The proportions of roll calls in the leading scale, if the parties are combined and the same procedures followed as for a single party, are .27 for the 83d Congress and .35 for the 87th. The division between the parties at the median p+ ap-pears, however, only when the dominant scale is a domestic one.

⁵¹ Details of sampling are reported in MacRae, “Intraparty Divisions …,” op. cit. The results given here differ from those in that reference in that a minimum level of Q = .8 was used for comparability with the Congressional data presented here.

⁵² This is of course an aim of the Beyle-Rice method, as pointed out by D. B. Truman, op. cit.