¹ Key, V. O., “A Theory of Critical Elections,” Journal of Politics, 17 (02, 1955), 3–18 CrossRefGoogle Scholar.

² Key, V. O., “Secular Realignment and the Party System,” Journal of Politics, 21 (05, 1959), 198–210 CrossRefGoogle Scholar.

³ Phillips, Kevin, The Emerging Republican Majority (New Rochelle, New York: Arlington House, 1969)Google Scholar.

⁴ Polsby, Nelson W., “An Emerging Republican Majority? Review Essay,” The Public Interest, No. 17 (Fall, 1969), 118–126 Google Scholar.

⁵ Society, Ripon, The Lessons of Victory (New York: Dial Press, 1969)Google Scholar.

⁶ Scammon, Richard M. and Wattenberg, Ben J., The Real Majority (New York: Coward-McCann, 1970)Google Scholar.

⁷ Sellers, Charles, “The Equilibrium Cycle in Two-Party Politics,” Public Opinion Quarterly, 29 (Spring, 1965), 16–38 CrossRefGoogle Scholar.

⁸ Burnham, Walter Dean, “American Voting Behavior and the 1964 Election,” Midwest Journal of Political Science, 12 (02, 1968), 1–40 CrossRefGoogle Scholar. See also his Critical Elections (New York: Norton, 1970)Google ScholarPubMed.

⁹ Converse, Phillip E., Miller, Warren E., Rusk, Jerrold G., and Wolfe, Arthur C., “Continuity and Change in American Politics: Parties and Issues in the 1968 Election,” American Political Science Review, 53 (12, 1969), 1083–1105 CrossRefGoogle Scholar.

¹⁰ See von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior, Second ed. (Princeton: Princeton University Press, 1947)Google Scholar, and Luce, R. Duncan and Raiffa, Howard, Games and Decisions (New York: Wiley, 1957)Google Scholar.

¹¹ See Riker, William H., The Theory of Political Coalitions (New Haven: Yale University Press, 1962)Google Scholar, and Groennings, Sven, Kelley, E. W., and Leiserson, Michael, The Study of Political Coalitions (New York: Holt, Rinehart and Winston, 1970)Google Scholar.

¹² The proof involves nothing more complicated than substituting the definitions of terms for their names and cancelling whenever possible.

¹³ In calculating turnout, one counts all adults of voting age, whether or not they were eligible to vote.

¹⁴ Kemeny, John, Snell, J. Laurie, and Thompson, Gerald, Introduction to Finite Mathematics, Second ed. (Englewood Cliffs, N.J.: Prentice-Hall, 1966), pp. 116–122 Google Scholar.

¹⁵ The same formula could be used to study contributions of resources other than votes, such as financial contributions and time of volunteers. In that case, the turnout would measure the resource provided by a given group to either party, and the loyalty would measure the proportion of the resource that went to a given party.

¹⁶ The national turnout and loyalty figures are from the Statistical Abstract of the United States, 1970, pp. 354 and 368 Google Scholar. The group size figures were taken directly from the Survey Research Center's sample. The group loyalty and turnout figures were adjusted so that taken together with the group sizes they conform with the national loyalty and turnout statistics. The adjustment procedure is an iterative process by which a contingency table with given marginal distributions can be transformed into a table with specified marginal distributions while preserving the nature and strength of the association, as measured by appropriate criteria. The procedure is that developed by Mosteller, Frederick, “Association and Estimation in Contingency Tables,” Journal of the American Statistical Association, 63 (03, 1968), pp. 1–28 (see especially pp. 6–8)Google Scholar. For a similar application of this adjustment procedure see Butler, David and Stokes, Donald, Political Change in Britain (New York: St. Martin's Press, 1969), pp. 283ffGoogle Scholar. The sizes of the national survey samples were 1,899 in 1952; 1,762 in 1956; 1,181 before weighing and 1,954 after weighing in 1960; 1,571 in 1964; and 1,557 in 1968. Pairwise deletions were used with missing data to preserve sample size, which means that a person was deleted from a count only when some information relevant to that particular count was missing.

¹⁷ This definition is not very satisfactory because inflation and rising median income have changed the social meaning of any fixed income level. It does have the virture, however, of being easy to define and comprehend.

¹⁸ The magnitude of inflation in these years is indicated by the Consumer Price Index, Using 1957–59 = 100, the figures are 92.5 for 1952, 94.7 for 1956, 103.1 for 1960, 108.1 for 1964, and 121.2 for 1968. The figures were prepared by the Bureau of Labor Statistics and are reported by the Council of Economic Advisors in Supplement to Economic Indicators Historical and Descriptive Background (1964) and Economic Indicators (January, 1970).

¹⁹ This empirical generalization is substantiated by the 1968 data for the five actual segments of the Democratic coalition. It does not follow automatically from the definitions, however. In fact, the overlap hypothesis that the intersection of two loyal groups is more loyal than the average of the two groups is closely related to the cross-pressure hypothesis that a person who is a member of one Democratic group and one Republican group is likely to be less loyal to both parties than either group membership alone would predict.

²⁰ In 1968 the young contributed 13 per cent to the Democratic coalition by having a size of 18 per cent, a turnout of 47 per cent and a loyalty of 40 per cent.

²¹ Scammon and Wattenberg, Real Majority.

²² If the nation is partitioned into mutually exhaustive and nonoverlapping groups (such as income levels), the strategic equation is