¹ Davies, James C., “Toward a Theory of Revolution,” in Studies in Social Movements, ed. McLaughlin, Barry (New York: The Free Press, 1969), pp. 85–109 Google Scholar. Hardly an anthology on revolution or social movements exists without including this work. Geschwender, James A., “Explorations in the Theory of Social Movements and Revolutions,” Social Forces 47, 2 (12, 1968), 127–135 CrossRefGoogle Scholar, has attempted to elaborate the theory in terms of cognitive dissonance.

² de Tocqueville, Alexis, The Old Regime and the French Revolution, translated by Gilbert, Stuart (Garden City, N.J.: Doubleday Anchor, 1955), p. 177 Google Scholar. Tocqueville's observation that those parts of France which experienced the greatest degree of positive change also showed the greatest popular discontent is sometimes referred to as Tocqueville's paradox. Two different explanations of the paradox exist. The most common, and the one used by Davies and in this research, is the rising expectations thesis. A less well-known interpretation is referred to as “the present value of the past.” This argues that present achievement is devaluated by the perception of past costs. See, in this regard, Wolf, Charles Jr., “The Present Value of the Past,” mimeo (Santa Monica: The Rand Corporation, 1969)Google Scholar.

³ Davies, , “Toward a Theory of Revolution,” p. 86 Google Scholar.

⁴ Davies, James C., “The J-Curve of Rising and Declining Satisfactions as a Cause of Some Great Revolutions and a Contained Rebellion,” in The History of Violence in America, ed. Graham, Hugh Davis and Gurr, Ted Robert (New York: Bantam Books, 1970), pp. 690–731 Google Scholar.

⁵ In the philosophy of science this problem is sometimes alluded to as a problem in reductionism. See, for example, Brodbeck, May, “Methodological Individualism: Definition and Reduction,” in Readings in the Philosophy of the Social Sciences, ed. Brodbeck, May (New York: The MacMillian Co., 1968)Google Scholar.

⁶ Robinson, W. S., “Ecological Correlations and the Behavior of Individuals,” American Sociological Review, 15 (06, 1950), 351–357 CrossRefGoogle Scholar. See also: Goodman, L. A., “Some Alternatives to Ecological Correlation,” American Journal of Sociology, 64 (05, 1959), 610–625 CrossRefGoogle Scholar; Duncan, O. D. and Davis, B., “An Alternative to Ecological Correlation,” American Sociological Review, 18 (12, 1953), 665–666 CrossRefGoogle Scholar. Duncan, O. D., Cuzzort, R. P., and Duncan, B., Statistical Geography (Glencoe: The Free Press, 1961)Google Scholar, note, as we do, that the problem arises wherever the units of analysis are changed. The change need not be from one distinct type of unit (e.g., individual) to a different type (e.g., group).

⁷ McPhail, Clark, “Civil Disorder Participation: A Critical Examination of Recent Research,” American Sociological Review, 36 (12, 1971), 1058–1073 CrossRefGoogle ScholarPubMed.

⁸ See, in this regard, Bloombaum, Milton, “The Conditions Underlying Race Riots as Portrayed by Multidimensional Scalogram Analysis: A Reanalysis of Lieberson and Silverman's Data,” American Sociological Review, 33 (02, 1968), 76–91 CrossRefGoogle Scholar; Downes, Bryan T., “Social Characteristics of Riot Cities: A Comparative Study,” Social Science Quarterly, 49 (12, 1968), 504–520 Google Scholar; Lieberson, Stanley and Silverman, Arnold, “The Precipitants and Underlying Conditions of Race Riots,” American Sociological Review, 30 (12, 1965), 887–898 CrossRefGoogle ScholarPubMed; Spilerman, Seymour, “The Causes of Racial Disturbances: A Comparison of Alternative Explanations,” American Sociological Review, 35 (08, 1970), 627–649 CrossRefGoogle Scholar; and Wanderer, Jules, “An Index of Riot Severity and Some Correlates,” American Journal of Sociology, 74 (03, 1969), 500–505 CrossRefGoogle Scholar.

⁹ McPhail, , “Civil Disorder Participation,” p. 1064 Google Scholar.

¹⁰ Gurr, Ted Robert, “Urban Disorder: Perspectives From the Comparative Study of Civil Strife,” in Riots and Rebellion: Civil Violence in the Urban Community, ed. Mascotti, Louis H. and Bowen, Don R. (Beverly Hills: Sage Publications, 1968), p. 52 Google Scholar.

¹¹ Davies, , “The J-curve,” p. 717 Google Scholar.

¹² Ibid., p. 724.

¹³ McPhail, , “Civil Disorder Participation,” p. 1059 Google Scholar.

¹⁴ Dollard, John et al., Frustration and Aggression (New Haven: Yale University Press, 1939)CrossRefGoogle Scholar.

¹⁵ This statement is based on the elaboration of Dollard's work by Miller, Neal E. et al., “The Frustration-Aggression Hypothesis,” Psychological Review, 48 (07, 1941), 337–342 CrossRefGoogle Scholar. See also: Berkowitz, Leonard, Aggression: A Social Psychological Analysis (New York: McGraw Hill, 1962)Google Scholar, in Advances in Experimental Social Psychology, Volume 2, ed. Berkowitz, Leonard (New York: Academic Press, 1965)Google Scholar.

¹⁶ Gurr, , Why Men Rebel (Princeton: Princeton University Press, paperback, 1970)Google Scholar.

¹⁷ Davies, , “The J-curve,” pp. 86–87 Google Scholar.

¹⁸ Grofman, Bernard N. and Muller, Edward N., “The Strange Case of Relative Gratification and Potential for Political Violence: The V-Curve Hypothesis,” The American Political Science Review, 67 (08, 1973), 514–539 CrossRefGoogle Scholar.

¹⁹ In addition to the sociological literature noted above in footnote 8, see, for example: Feierabend, Ivo K., Feierabend, R. L., and Nesvold, B. A., “Social Change and Political Violence: Cross-National Patterns,” in Anger, Violence and Politics: Theories and Research, ed. Feierabend, Ivo K., Feierabend, Rosalind L., and Gurr, Ted Robert (Englewood Cliffs, N.J.: Prentice Hall Google Scholar, Feierabend, Ivo K., Feierabend, Rosalind L., “Aggressive Behaviors within Polities 1948–1962: A Cross-National Study,” Journal of Conflict Resolution, 10 (09, 1966), 249–271 CrossRefGoogle Scholar; Tanter, Raymond and Midlarsky, Manus, “A Theory of Revolution,” Journal of Conflict Resolution, 11 (09, 1967), 264–280 CrossRefGoogle Scholar; and Ted Robert Gurr, “A Causal Model of Civil Strife: Using New Indices,” in Anger, Violence and Politics, ed. I. K. Feierabend et al. Much to his credit, of all the authors cited, Gurr, Ibid., p. 210, is the only one to acknowledge the level-of-analysis problem.

²⁰ This latter operationalizations was suggested, in part, by Duncan, Otis D., “Discrimination Against Negroes,” in Social Intelligence for America's Future, ed. Gross, Bertram M. (Boston: Allyn and Bacon, 1969)Google Scholar. Discrimination is measured by taking the slope and intercept of the regression equation for whites and plugging in the observed independent variable (education) scores for blacks. The resultant predicted dependent variable (income) scores for blacks are subtracted from the blacks' actual score on the dependent variable. The residual [Yp (if respondent were white) – Ya] is the measure of deprivation.

A wholly individual measure, based on differences between actual and predicted income, was desired for the “differ” operationalization. Such a measure would have been very similar to the one used for the “discrim” operationalization. In the calculation of measures of association, the type of measure is feasible. In calculating summary measures for the purpose of obtaining averages for blacks, this is not possible. In the case of any individual black, the “differ” is the residual between predicted income and actual income. The average of the residuals [Σ(Ŷi–Ya)/N] however, always equals zero. The operationalization is meaningful for an individual black, but it aggregates to zero when cumulated for the group. To provide an analogous measure for the purpose of calculating an average, the average difference of predicted income for whites and blacks is calculated, given each groups' respective regression equation. Thus the average score is based on Σ Ŷi/N for blacks subtracted from Σ Ŷi/N for whites.

²¹ Edelman, Murray, Politics as Symbolic Action: Mass Arousal and Quiescence (Chicago: Markham, 1971)Google Scholar; Grofman and Muller, “The Strange Case of Relative Gratification and Potential for Political Violence”; Feierabend et al., “Social Change”; Lipset, Seymour Martin, Political Man (Garden City: Anchor Books, 1963), esp., pp. 54–55 Google Scholar; Aiken, Michael et al., Economic Failure Alienation and Extremism (Ann Arbor: The University of Michigan Press, 1968)Google Scholar; Moore, Barrington Jr., “Revolution in America,” New York Review of Books, 12 (01 30, 1969), 6–12 Google Scholar.

²² Correlations of .25 in social science data are generally viewed as quite favorable. In this case, however, we have chosen to view .25 as a minimal level of acceptance because a criterion for the establishment of a valid substitute measure for different levels of analysis is being considered. Without engaging in a lengthy discourse on the philosophical issues involved in the level-of-analysis question, it is clear that such substitutions do involve an issue of validity, i.e., whether one measure is a valid substitute for another. Correlational requirements for measures of reliability and validity are far greater than for mere assertions of substantive importance. See for example, Kerlinger, Fred N., Foundations of Behavioral Research (New York: Holt, Rinehart and Winston, Inc., 1965), 444–462 Google Scholar.

²³ We wish to thank Leslie Kish and Irene Hess of the sampling section of the University of Michigan's Institute for Social Research for explaining the sampling design to us and clarifying this issue.

²⁴ The theorem is represented as follows: probability (∣f/n−p∣≥ϵ)→0 as N→∞; where f is the frequency of occurrence of event X among N trials, p is the probability of X, ϵ is some arbitrarily small positive number. It is generally assumed that good results are produced with N greater than 30. It also is at this point that the normality assumption of the Central Limit Theorem can be relaxed.

²⁵ Ted Robert Gurr informs us (Correspondence 12/27/74) that although he agrees that the linkage between future expectations and current need fulfillment is a fundamental assumption of relative deprivation theory, the relationship may vary within the social structure. In the course of yet uncompleted research (with Raymond Duvall) Gun has theorized that individuals in the middle range of attained values (need fulfillment) appear to expect more gains in the future than those at the extremes of the distributions. If Gurr is correct, this would require some critical restatement of the underlying assumptions of relative deprivation theory. Some preliminary analyses that we have undertaken demonstrate that for blacks, those at the lowest end of the continuum have the highest expectations. For example, preliminary runs from SRC's Campbell-Schuman data set indicate that young (18–35) northern, black males are most dissatisfied with their current situation and most optimistic about the future. Needless to say, the issue Professor Gurr raised is an important one that could conceivably have a major impact on relative deprivation theory.

²⁶ For a discussion of this position see Merton, Robert K., Social Theory and Social Structure (Glencoe, Ill.: The Free Press, 1957), pp. 5–11 Google Scholar.

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²⁸ Snyder, David and Tilly, Charles, “Hardship and Collective Violence in France, 1830–1960,” American Sociological Review, 37 (10, 1972), 520–532 CrossRefGoogle Scholar.

²⁹ Davies, , “Comments,” pp. 607–610 Google Scholar.

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³¹ For a discussion of causal inference in classical experimental design, see Campbell, Donald T. and Stanley, Julian C., Experimental and Quasi-Experimental Design for Research (Chicago: Rand McNally, 1963)Google Scholar.

³² Sears, David O. and McConahay, John B., The Politics of Violence (Boston: Houghton Mifflin, 1973), pp. 90–91, footnote 1Google Scholar.

³³ Gurr, Why Men Rebel.

³⁴ Davies, “The J-curve.”

³⁵ Feierabend et al., “Social Change.”

³⁶ Ibid.

³⁷ Grofman and Muller, “The Strange Case of Relative Gratification.”

³⁸ Feierabend, et al., “Social Change,” p. 637 Google Scholar.

³⁹ Grofman and Muller, p. 514.

⁴⁰ Durkheim, Emile, “Anomie and Suicide,” in Sociological Theory, ed. Coser, Lewis A. and Rosenberg, Bernard (New York: MacMillian, 1970), p. 529 Google Scholar.

⁴¹ Moore, “Revolution in America.”

⁴² Aiken et al., Economic Failure, Alienation and Extremism.

⁴³ Lipset, Political Man.

⁴⁴ Conn, Norman, The Pursuit of the Millennium (New York: Harper Torchbooks, paperback, 1961), p. 319 Google Scholar.

⁴⁵ Edelman, Politics as Symbolic Action.

⁴⁶ Ibid., pp. 20–21.