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The Theory of Party Equilibrium*

  • Gerald Garvey (a1)

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Behind most political scientists' studies of nonvoting there is, implicitly at least, a theory of passive consent. This is particularly the case where nonvoting as a result of apathy is concerned. For, it is suggested, apathy tends to increase when citizens are satisfied that their interests will not be seriously harmed, regardless of which party wins. In other words: the very reasons which underlie apathetic nonvoters' failure to participate in an election testify that their inactivity is a form of passive consent to the election's outcome.

Passive consent, however, cannot be equated to the “theory of consensus” which economists have recently contributed to political science. This “theory of consensus” deals with the “welfare economics” problem of aggregating individual citizens' preferences into a “true”—indeed, into a mathematically precise—schedule of social preferences. Thus, while it is plausible that a citizen can, by nonvoting, tacitly consent to a given electoral outcome, it is also likely that the final social decision would change, however slightly, if in fact this citizen's true preferences had been admitted through voting into the social aggregation. In this case, the final choice would have popular consent without real popular consensus.

The converse can also be true. For example, while Duncan Black's Theory of Committees and Elections and Kenneth Arrow's Social Choice and Individual Values are characterized by a most impressive formal elegance, it is also true that neither makes provision for nonvoting.

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*

This is a revised version of a paper delivered at the annual meeting of the American Political Science Association, Chicago, September, 1964. I am indebted to Mancur Olson of Princeton, Gordon Tullock of the University of Virginia, and to my former colleagues at the Air Force Academy, Charles Rollinger and Jack Freeman, for their help. I especially appreciate Duncan Black's and William Riker's detailed reviews of earlier drafts of this paper, their freely-given suggestions and their most helpful criticisms.

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1 The principal sources of this thesis are documented in Lipset, Seymour Martin, Political Man (New York: Doubleday, 1960), pp. 216219.

2 See especially Black, Duncan, The Theory of Committees and Elections (Cambridge: Cambridge Univ. Press, 1958) and Arrow, Kenneth, Social Choice and Individual Values (New York: Wiley, 1951). The other major contributors—all economists by training, as are Black and Arrow— are Downs, Anthony, An Economic Interpretation of Democracy (New York: Harper Bros., 1957) and Buchanan, James and Tullock, Gordon, The Calculus of Consent (Ann Arbor: University of Michigan, 1962). The appendices in the last-named volume contain further sources on the historical development of the theory of consensus; its bibliography is also comprehensive, as are those in Luce, Duncan and Raiffa, Howard, Games and Decisions (New York: Wiley, 1957) and Riker, William, “Voting and the Summation of Preferences,” this Review, LV (12, 1961), 900911.

3 Black, op. cit., pp. 14–19. Summaries of the Black theory appear in Luce and Raiffa, op. cit., pp. 353–56; in Riker, loc. cit., pp. 906ff; and in Section VII below. By “the strongest form” of the condition it is meant that all preference profiles are single-peaked, symmetrically descending and without plateaus. To arrive at the true “equilibrium points” of Section V below while keeping some (however slight) differentiation of parties, it is also necessary that there be an even number of voters; the theory of party equilibrium will also hold for a system with an odd number of voters. But in this case party differentiation will completely disappear at the equilibrium.

4 Continuity is a special, less restrictive case of the spectrum with which Black dealt in his Theory of Committees and Elections. Black's “spectrum” was composed of a limited number of discrete alternatives among which a relatively limited number of voters had to choose. Black's theory, developed for the harder “discrete issue” case,

thus applies to the model in these pages. Actually, therefore, continuity of the spectrum—which is a reasonable assumption when the electorate is very large, with many shades of differing opinions—is not necessary to the theory of party equilibrium that is herein broached. But it does simplify graphical representation of the argument.

5 The remainder of this paper owes much to the pioneering work of Harold Hotelling, who first suggested the use of location theory to explain party characteristics in a two-party democracy. See his Stability in Competition,” 39 The Economic Journal (1929), pp. 4157. Downs, supra, has made the most influential application of this mode of reasoning to election analysis.

6 By inspection, this equation must pass through coordinates: 0.5, 0.5. A further point can be established, thereby determining the line, by letting K N go to zero, whereupon:

This means that the K c intercept of the line will vary between the limits:

½ > K c > 0.

7 Campbell, Angus and others, The American Voter (New York: Wiley, 1960), Chapter 19.

8 Berelson, Bernard R., Lazarsfeld, Paul F., McPhee, William N., Voting (Chicago: University of Chicago, 1954), p. 312, emphasis in the original.

* This is a revised version of a paper delivered at the annual meeting of the American Political Science Association, Chicago, September, 1964. I am indebted to Mancur Olson of Princeton, Gordon Tullock of the University of Virginia, and to my former colleagues at the Air Force Academy, Charles Rollinger and Jack Freeman, for their help. I especially appreciate Duncan Black's and William Riker's detailed reviews of earlier drafts of this paper, their freely-given suggestions and their most helpful criticisms.

The Theory of Party Equilibrium*

  • Gerald Garvey (a1)

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