¹ We view a political (as against a psychological or sociological) theory as one in which the initial preferences of political actors are known and implications are then drawn as a function of the institutional framework. This viewpoint is akin to that of formal economics, in which “utilities” are taken as given. While the study of preference formation is certainly worthwhile, it is beyond the scope of this essay.

² This project is being conducted jointly by a French group headed by Professor Georges Dupeux and by the Graduate School of Industrial Administration, Carnegie-Mellon University.

³ In legislative elections in the French Fifth Republic, deputies are elected from single-member districts. To win on the first ballot, a candidate must obtain a majority of the votes cast (blancs et nuls, excluded) and the votes of at least one-fourth of the total registered voters. All candidates receiving less than 10 per cent (5 per cent until 1967) are automatically eliminated from the second ballot, if it is necessary. Other candidates may elect to eliminate themselves. No new candidates may enter the contest for the second ballot, which is held one week after the first. Candidates eliminated from the second ballot may, and usually do, counsel their first-ballot supporters about which candidate to support on the second ballot. A plurality wins the second ballot. Our analysis applies to all metropolitan districts with second ballots, Corsica excepted.

⁴ Riker, William H. and Ordeshook, Peter C., “A Theory of the Calculus of Voting”, American Political Science Review, 62 (03, 1968), 25–42CrossRefGoogle Scholar; McKelvey, Richard and Ordeshook, Peter C., “A General Theory of the Calculus of Voting,” in Mathematical Applications in Political Science, VI, ed. Herndon, J. F. (forthcoming).Google Scholar

⁵ We omit, to simplify exposition, the addition of a stochastic term to equation (1.2) and later equations for Pr (NV)_ij.

⁶ In other words, f^k_i, throughout its domain, is either monotonically increasing or constant.

⁷ 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 (06, 1970), 426–448CrossRefGoogle Scholar, (contains references to prior work in spatial models); Hinich, and Ordeshook, , “Abstentions and Equilibrium in the Electoral Process,” Public Choice, 7 (Fall, 1969), 81–106.CrossRefGoogle Scholar For an application of the theoretical structure to empirical data, see Shapiro, Michael J., “Rational Political Man: A Synthesis of Economic and Social Psychological Perspectives,” American Political Science Review, 53 (12, 1969), 1106–1119.CrossRefGoogle Scholar

⁸ Hinich, Meivin J., Ledyard, John O., and Ordeshook, Peter C., “Nonvoting and the Existence of Equilibrium Under Majority Rule,” Journal of Economic Theory, 4 (04, 1972), 144–153.CrossRefGoogle Scholar

⁹ For detailed discussions of the assumptions underlying regression estimation of individual behavior parameters from aggregate data, see Goodman, Leo A., “Some Alternatives to Ecological Correlation,” American Journal of Sociology, 64 (05, 1959), 610–625CrossRefGoogle Scholar; Rosenthal, Howard, “Aggregate Data,” in Handbook of Communications, ed. Sola Pool, Ithiel de, Schramm, Wilbur, Frey, Frederick W., Maccoby, Nathan and Parker, Edwin B. (Chicago: Rand-McNally, forthcoming)Google Scholar; Geisel, Martin S., Kies, Naomi, McGuire, Timothy W., and Rosenthal, Howard, “A Simultaneous Equations Model of Split Ticket Voting in Israeli Elections,” 1970 Proceedings of the Social Statistics Section of the American Statistical Association, (Washington: American Statistical Association, 1971), 71–80.Google Scholar

¹⁰ In using OLS, we incur possible costs in bias or inefficiency as consequences of:

a. Spatial (in a geographic sense) autocorrelation in our cross-section (i.e., the “errors” for adjacent geographic areas will be correlated).

b. The correlation of errors from the abstention and blank ballot regressions (although in this case OLS will be efficient as long as the two models include the same set of explanatory variables.)

c. Heteroscedasticity of the errors, a condition likely to be present given the “bounded” nature of voting variables.

We intend to consider these limitations in a later paper.

¹¹ We acknowledge that for many voters the relevant proportions will differ, taking into account the expected vote transfers from supporters of eliminated candidates. Unfortunately, we do not have a method to handle these more sophisticated expectations.

¹² Converse, Phillip E., “The Problem of Party Distances in Models of Voting Change,” in the Electoral Process, ed. Jennings, M. Kent and Ziegler, L. H. (Englewood Cliffs: Prentice-Hall, 1966), 175–207Google Scholar; Pierce, Roy and Barnes, Samuel H., “Public Opinion and Political Preferences in France and Italy” (unpublished manuscript, University of Michigan, 1970).Google Scholar For U.S. candidate spaces, see Weisberg, Herbert F. and Rusk, Jerrold, “Dimensions of Candidate Evaluation,” American Political Science Review, 64 (12, 1970), 1167–1185.CrossRefGoogle Scholar

¹³ Stokes, Donald, “Spatial Models of Party Competition,” American Political Science Review, 57 (06, 1963), 368–377.CrossRefGoogle Scholar

¹⁴ See Rosenthal, “Aggregate Data,” for further discussion of these alternative models.

¹⁵ The logarithmic transformation was used for two reasons: (a) the R², values were often substantially higher, especially for blank ballots, (b) denoting y_pred and y_act as the predicted and actual values for the untransformed dependent variables, In(y)_pred and In(y)_act as the similar values for the transformed values, then

was generally less than for blank ballots.

¹⁶ Lancelot, Alain, L'Abstentionnisme Electoral en France, (Paris: Colin, 1968).Google Scholar This book is an excellent introduction to the study of nonvoting in France.

¹⁷ It has been noted, however, that blank ballots take on a definite pattern in referenda in which important provincial newspapers campaign for a blank. See Goguel, François, ed., Le Référendum du 8 avril 1962, (Paris: Colin, 1963), 137–141.Google Scholar

¹⁸ The dependence results from the fact that all proportions must sum to 1.0. Although this condition does not hold when we use the logarithms of the nonvoting proportions, one party is always dropped, since the full set of variables is highly collinear.

¹⁹ For French applications, see: Mendès-France, B. and Laumonier, L., “Une application des méthodes de l'analyse statistique à l'estimation des déplacements de voix entre les deux tours des élections présidentielles de 1965,” Revue Française de Science Politique, 17 (02, 1967), 110–114Google Scholar; and Lancelot, Alain and Weill, Pierre, “Les transferts de voix du premier au second tour des élections de Mars 1967; une analyse de regression,” in Centre d'Etude de la Vie Politique Française, Les Elections Législatives de Mars 1967 (Paris: Colin, 1970), pp. 374–388.Google Scholar

²⁰ Rosenthal, Howard, “Political Coalition: Elements of a Model and the Study of French Legislative Elections” in Calcul et Formalisation dans le Sciences de l'Homme (Proceedings of the 1966 Rome Conference on Mathematical Methods in the Social Sciences), (Paris; Editions du C.N.R.S., 1968), pp. 269–282, esp. 281–282.Google Scholar

²¹ Rosenthal, Howard and Sen, Subrata, “Participation électorale et conjoncture politique,” Revue Française de Science Politique, 20 (06, 1970), 545–556.CrossRefGoogle Scholar The 1962 results here differ slightly from those published earlier because the earlier publication eliminated some districts for ad hoc reasons.

²² In formulating the heuristic model, we owe much to the viewpoints of March, James G. and Simon, Herbert, Organizations (New York: Wiley, 1958)Google Scholar, and Schelling, Thomas C., The Strategy of Conflict (Cambridge, Mass.: Harvard, 1960).Google Scholar

²³ Downs, Anthony, An Economic Theory of Democracy (New York: Harper, 1957).Google Scholar

²⁴ Lazarsfeld, Paul F., Berelson, Bernard, and Gaudet, Hazel, The People's Choice (New York: Duell, Sloan, and Pearce, 1944).Google Scholar

²⁵ Sola Pool, Ithiel de, Abelson, Robert, and Popkin, Samuel, Candidates, Issues, and Strategies: A Computer Simulation of the 1960 Presidential Election (Cambridge, Mass.: M.I.T. Press, 1964).Google Scholar

²⁶ Lancelot, , L'Abstentionnisme Electoral en France. pp. 95–119.Google Scholar

²⁷ For large values of N ², although alienation is low, simple indifference is large. The indifference could promote large numbers of blank ballots. Thus, blank ballots may be a monotonic function of N ₂ only for small values of N ², As N ² is only 2, 3, or 4 for our data, this condition is satisfied. We note that in computing N ₂ we excluded those rare “candidates” who obtained less than a thousand votes on the second ballot. These “candidates” nearly always are individuals who have withdrawn, but too late to eliminate their ballots from the polling places.

²⁸ The particular classifications used were those found in the 1962, 1967, and 1968 Elections Legislatives publications of the French government. The 1958 classifications are those of the SOFRES polling organization. Both classifications are subject to question, but we wished to use an independent source for the initial estimates. Future analysis could attempt to use other classifications, split the 1967 F.G.D.S. into its constituent parties, etc.

²⁹ The reasons for the choice of these particular regions are stated in an earlier study which shows the importance of these regions to the analysis of public opinion regarding General de Gaulle in the 18 months preceding the 1962 elections. Cf. Rosenthal, Howard, “The Popularity of Charles de Gaulle: Findings from Archive-Based Research,” Public Opinion Quarterly, 31 (Fall, 1967), 381–398.CrossRefGoogle Scholar

³⁰ Rosenthal, and Sen, , “Participation électorale et conjoncture politique,” pp. 549–552.Google Scholar

³¹ If the standard normal test is used, the null hypothesis that the difference between the two coefficients is zero is rejected at the .0005 level. The t-statistic is 5.02.

³² Rosenthal and Sen, pp. 553–554.

³³ The blank ballot probability will be equal to [0.009 + (0.173) (5.000 — 1.148)] 0.675.