¹ One of the few discussions of the number of parties which takes seriously the complexity of multiparty systems is that by Sartori, Giovanni, “European Political Parties: The Case of Polarized Pluralism” in Political Parties and Political Development, ed. LaPalombara, Joseph and Weiner, Myron (Princeton: Princeton Univ. Press, 1966)Google Scholar. See also Sartori's, “The Typology of Party Systems-Proposals for Improvement,” in Mass Politics, ed. Rokkan, S. and Allardt, E. (New York: Free Press, 1970)Google Scholar.

² See Pfeiffer, David G., “The Measurement of Inter-Party Competition and Systemic Stability,” American Political Science Review, 61 (06, 1967), 457–467 CrossRefGoogle Scholar, and the references cited there. See also the provocative suggestions of Hasbrouck, Paul, Party Government in the House of Representatives (New York: Macmillan, 1927), chapter 9Google Scholar (as cited in Jones, Charles O., “Inter-Party Competition for Congressional Seats,” Western Political Quarterly, 17 [September, 1964], 464ff)CrossRefGoogle Scholar.

³ Mark Stern, for one, has also argued for a probabilistic conception of party competition: “Measuring Interparty Competition: A Proposal and a Test of a Method,” Journal of Politics, 39 (August, 1972), 889–904 Google Scholar. His method, however, is restricted to a two-party setting.

⁴ The interplay of “theoretical” and “operational” definitions is quite striking in the case of multiparty systems. Empirical findings using different measures of party competition “feedback” to clarify our intuitive understanding of competition.

⁵ Some measures of party competition rely on the difference between the winner and the loser. This is obviously a function of the same figures in two-party systems but not in multiparty systems.

⁶ For a discussion of the Indian situation, see Elkins, David J., Regional Contexts of Political Participation (Doctoral dissertation, University of California, Berkeeley, 1971), chaps. 3-5Google Scholar. Spafford, Duff, “The Electoral System of Canada,” American Political Science Review, 64 (03, 1970), 173 CrossRefGoogle Scholar, finds a similar situation in Canada: “When the number of minor-party candidates is increased, the share of seats won by a major party for a given own share of vote is augmented…. The dependence of major-party share of seats on the number of minor-party candidates explains the ability of parties to win majorities in the House of Commons with much less than a majority of the vote in their favor.”

⁷ Fragmentation and fractionalization should not be confused with the concept of fractionalization popularized by Rae, Douglas W. in The Political Consequences of Electoral Laws (New Haven: Yale Univ. Press, 1967)Google Scholar. His concept subsumes what, for present purposes, I have considered as two distinct concepts.

⁸ By party identification I mean the psychological attachment of an individual to a party; by party loyalty I mean the pattern of voting with the party (as a citizen or as an elected official in the legislature). Obviously, one of the reasons for being loyal is one's sense of identification. Other reasons for loyalty, besides psychological identification, are analyzed by Bailey, F. G. in terms of “moral” and “contract” groups in his Strategems and Spoils (Toronto: Copp Clark, 1969)Google Scholar.

⁹ It may turn out that party identification plays a lesser role in most other countries than it does in the United States. Regardless of the nature of that psychological attachment, the degree of loyalty to a party, which is surely a concept applicable everywhere, is the more important datum. Hence, when party identification is used in explaining the index below one could substitute any measure of loyalty instead—for example, caring which party wins or previous voting habits.

¹⁰ One must be clear about the setting to which measures of party competition refer. In particular, one must distinguish between competition for votes (for one seat or for all the seats) and competition for control of the government. In two-party systems, these are often the same, but not in multiparty systems. Generally this paper focuses on competition for votes for all the seats of a legislature or for an office such as the presidency.

A second distinction must be made between competition for a particular office and competition over a range of offices. In this paper I assume that measuring competition for a single office or type of office must be done before one combines values for a range of offices. (See also Stern, , “Measuring Interparty Competition,” pp. 891, 896.Google Scholar)

A third distinction contrasts the degree of competition over a long period with the measurement of competition at a particular moment in time. While averaging the single-moment values over the period in question may prove acceptable, it may overlook important trends; and the way in which one measures competition determines whether the index yields different values in the long and short run. When one considers the importance of party loyalty, the long-term commitments of individuals cannot easily be separated from competitiveness in the current election.

¹¹ This is another reason why Stern's measure is unsatisfactory: it is based solely on previous election returns and not on assessments of loyalty, even though constancy of voting pattern is assumed.

¹² The best definition of “dominant party” requires that the net defection rate between the dominant party and opposition parties does not significantly change the likelihood that the dominant party will retain control of the government. In other words, dominance is a structural constraint (of undefined origin) in the party system which inhibits the development of serious contenders. It is not an explantory term at all, but a purely descriptive one; we must still look for reasons for these structural rigidities.

¹³ At the end of this paper I will show how my measure of party competition can be used to ascertain which parties are important enough to count in deciding whether the system is two-party, three-party, or more.

¹⁴ This is true even of the Wallace vote in the 1968 presidential election. Wallace had no chance of winning the presidency, as he stated; his role was intended to be that of a “spoiler.” Had he thrown the race into the Congress by deadlocking the Electoral College, we would still have no reason to reassess our estimation of the number of parties.

¹⁵ Sartori, , “European Political Parties,” pp. 157, 167ffGoogle Scholar, likewise argues that the number of actual parties is not the same as the number by which we identify the system. Thus, he says if only four of ten parties are significant, then we call it a four-party system, not a ten-party one.

¹⁶ Indeed, after the split in the Congress party, it is fair to say that a multiparty coalition controlled the Federal Government in India in 1969–71.

¹⁷ Duverger, Maurice, Political Parties (London: Methuen, 1959), pp. 206–280.Google Scholar

¹⁸ Ibid., p. 226.

¹⁹ Note the similarity between this conclusion and the reasoning about competitiveness in Downs, Anthony, An Economic Theory of Democracy (New York: Harper & Row, 1957)Google Scholar.

²⁰ Stokes, Donald E., “Party Loyalty and the Likelihood of Deviating Elections,” in Campbell, Angus, Converse, P., Miller, W., and Stokes, D., Elections and the Political Order (New York: Wiley, 1966), pp. 125–135 Google Scholar, demonstrates this for the United States.

²¹ By casting competitiveness in terms of “surprise,” that is, amount of information conveyed, one can readily see that the measure of party competition is similar to the notion of entropy. See, for example, Theil, Henri, “The Desired Political Entropy,” American Political Science Review, 63 (06, 1969), 521–525.CrossRefGoogle Scholar

²² Sartori's concept of “polarization” approaches this from a different direction. By polarization Sartori means “distance” between the parties, which in turn increases the difficulties of interchange between them. This is very close to an analysis based on the difficulty of defection. See Sartori, “European Political Parties.”

²³ In these examples, and in the empirical examples from Canadian elections in a later section, consistency is defined in terms of votes in two successive elections.

²⁴ Converse, Philip, “The Concept of a Normal Vote,” Campbell, et al., Elections and the Political Order, pp. 23, 27 Google Scholar.

²⁵ This procedure requires that we estimate party competition from survey data and not from official returns. Since we must know about party identification and intensity anyway, all procedures for measuring competition must rely on surveys.

²⁶ Although an interval level of measurement is mandatory, a ratio scale is not: first, because a zero pointy while defineable mathematically, has no empirical interpretation (unless there is only one party, there is always some chance of turnover); second, because an interval level with an arbitrary zero point is just as useful as an absolute, or natural, zero point. For example, as z-scores get very large (say>5), unity minus their associated probability approaches zero, and we can arbitrarily say that if z > 5, then there is zero competition for all practical purposes, regardless of what party system we examine.

²⁷ Berelson, Bernard, Lazarsfeld, Paul, and McPhee, William, Voting (Chicago: Univ. of Chicago Press, 1954), p. 134.Google Scholar

²⁸ For a simple discussion of this type of “significance” testing, see Winch, Robert F. and Campbell, Donald T., “Proof? No. Evidence? Yes. The Significance of Tests of Significance,” The American Sociologist, 4 (05, 1969), 140–143 Google Scholar. For more advanced discussions, see Edgington, E. S., Statistical Inference: The Distribution-Free Approach (New York: McGraw-Hill, 1969)Google Scholar, and Chung, J. H. and Fraser, D. A. S., “Randomization Tests for a Multivariate Two-Sample Problem,” Journal of the American Statistical Association, 53 (09, 1958), 729–735 CrossRefGoogle Scholar.

²⁹ The Canadian surveys for 1965 and 1968 were kindly made available by Professor John Meisel, Queen's University, Kingston, Ontario. They may be obtained now through the Inter-University Consortium for Political Research. Some Gallup polls conducted by the Canadian Institute of Public Opinion also contain sufficient information for the computation of revalues, but the sampling frame is unstable and not as accurate as would be desirable.

³⁰ Brief histories of these parties may be found in Young, Walter D., Democracy and Discontent: Progressivism, Socialism, and Social Credit in the Canadian West (Toronto: Ryerson, 1969)Google Scholar, and Thorburn, Hugh G., ed., Party Politics in Canada (Scarborough, Ont.: Prentice-Hall, 1967)Google Scholar.

³¹ Pinard, Maurice, The Rise of a Third Party: A Study in Crisis Politics (Englewood Cliffs, N.J.: Prentice-Hall, 1971)Google Scholar.

³² See the references cited in footnote 28.

³³ In fact, it is more reasonable to say that Canada has a three-party system because by 1972 Social Credit existed solely as a regional party. Thus, a further guideline might be that no purely regional party be counted in numbering the system. If one were calculating competition scores regionally, of course, then regional parties would still figure prominently.

³⁴ Erskine, Hazel, “The Polls,” Public Opinion Quarterly, 35 (Fall 1971), 489–495 Google Scholar; and Burnham, Walter Dean, Critical Elections and the Mainsprings of American Politics (New York: Norton, 1970), chapters 5 and 6Google Scholar.

³⁵ See the provocative formalizations of this feature in William McPhee and Jack Ferguson, “Political Immunization,” and McPhee, William, Anderson, Bo, and Milholland, Harry, “Attitude Consistency,” both in Public Opinion and Congressional Elections, ed. McPhee, William and Glaser, William (New York: Free Press, 1962)Google Scholar.

³⁶ Converse, Philip, “The Concept of a Normal Vote,” in Campbell, et al., Elections and the Political Order, pp. 11-16, 18 Google Scholar.

³⁷ Ibid., pp. 28-30; that is, defection rates are inelastic with respect to turnout, at least within the range of turnout variation found in American presidential elections.

³⁸ Stokes, , “Party Loyalty and the Likelihood of Deviating Elections,” p. 128 Google Scholar.

³⁹ Stokes, Donald E. and Iversen, Gudmund R., “On the Existence of Forces Restoring Party Competition,” Public Opinion Quarterly, 26 (Summer, 1962), 159–171.CrossRefGoogle Scholar

⁴⁰ Laponce, Jean A., “An Experimental Method for Measuring the Tendency to Equibalance in a Political System,” American Political Science Review, 60 (December, 1966), 982–993 CrossRefGoogle Scholar.

⁴¹ Sellers, Charles, “The Equilibrium Cycle in Two-Party Politics,” Public Opinion Quarterly, 29 (Spring, 1965), 16–38 CrossRefGoogle Scholar.

⁴² See the references in footnote 35. Berelson et al., Voting, make the same point in less formal terms.

⁴³ The stabilizing effect of party identifications can change quickly in some cases. See for example, Cameron, David R., “Stability and Change in Patterns of French Partisanship,” Public Opinion Quarterly, 36 (Spring, 1972), 19–30 CrossRefGoogle Scholar.