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Spatial Models of Party Competition

Published online by Cambridge University Press:  01 August 2014

Donald E. Stokes*
University of Michigan


The use of spatial ideas to interpret party competition is a universal phenomenon of modern politics. Such ideas are the common coin of political journalists and have extraordinary influence in the thought of political activists. Especially widespread is the conception of a liberal-conservative dimension on which parties maneuver for the support of a public that is itself distributed from left to right. This conception goes back at least to French revolutionary times and has recently gained new interest for an academic audience through its ingenious formalization by Downs and others. However, most spatial interpretations of party competition have a very poor fit with the evidence about how large-scale electorates and political leaders actually respond to politics. Indeed, the findings on this point are clear enough so that spatial ideas about party competition ought to be modified by empirical observation. I will review here evidence that the “space” in which American parties contend for electoral support is very unlike a single ideological dimension, and I will offer some suggestions toward revision of the prevailing spatial model.

Research Article
Copyright © American Political Science Association 1963

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1 For expositions of Downs's model, see Downs, Anthony, An Economic Theory of Democracy (Harper and Brothers, New York, 1957), pp. 114141Google Scholar, and An Economic Theory of Political Action in a Democracy,” Journal of Political Economy, Vol 65 (1957), pp. 135150CrossRefGoogle Scholar. For a similar model, developed independently, see MacRae, Duncan Jr., Dimensions of Congressional Voting: a Statistical Study of the House of Representatives in the Eighty-First Congress (University of California Press, Berkeley and Los Angeles, 1958), pp. 354382Google Scholar.

2 Downs's model is a little more complicated than this. Each voter has not only a most-preferred degree of government intervention (let us say his “point” on the scale); he has some amount of preference for every other degree of government intervention (the other points on the scale), the amount decreasing monotonically the farther the point is from his optimum. Hence, the preference of the electorate as a whole for a given degree of government intervention is the sum of the preferences of individual voters for that degree of intervention. Moreover, a party's position on the scale may be thought of as the sum or average of the positions it takes on a variety of particular issues.

3 Hotelling, Harold, “Stability in Competition,” Economic Journal, Vol. 39 (1929), pp. 4157CrossRefGoogle Scholar.

4 Smithies, Arthur, “Optimum Location in Spatial Competition,” Journal of Political Economy, Vol. 49 (1941), pp. 423429CrossRefGoogle Scholar.

5 Downs makes several other modifications of Hotelling's and Smithies's models in addition to treating the distribution of the public on the scale as a variable. Especially important is the assumption that one party will not “jump over” the position of another on the liberal-conservative dimension.

6 The assumption that no party can move past another on the left-right scale makes the equilibrium positions of two competing parties less well defined than it is for the competing firms of the models of Hotelling and Smithies.

7 My remarks here are directed solely to Downs's spatial model of party competition. An Economic Theory of Democracy (op. cit.) sets forth a whole collection of models, elaborated from a few central variables. All are worth detailed study. Paradoxically, the spatial model described here is likely to have great intuitive appeal for a wide audience, yet its postulates are almost certainly as radical asthose of any model in Downs'scollection.

8 Campbell, Angus, Converse, Philip E., Miller, Warren E., and Stokes, Donald E., The American Voter (John Wiley and Sons, New York, 1960), pp. 197198Google Scholar.

9 Ibid., Chapter 10, “The Formation of Issue Concepts and Partisan Change,” pp. 227-234.

10 It is a curious and interesting fact that the agrarian party of modern Norway, like the Catholic party of pre-Hitler Germany, has chosen to call itself the “Center” party, that is, to call itself by a name that refers to a dimension other than the one on which the party's main support is based. By selecting a title that is neutral in terms of a primary dimension of political conflict, the party invites potential supporters to ignore that dimension and rally to the party's special cause.

11 Downs, op. cit., 1957, p. 128.

12 A troublesome problem in applying a more general model to the real world is that of defining some kind of distance function over all pairs of points in the space. The need for such a function is less acute in the one-dimensional case, because an approximate ordering of distances between points can be derived from the strong ordering of points in the space. However, the points of a multidimensional space are no longer strongly ordered, and it may not be possible to compare the appeal of two or more parties for voters located at a given point by measuring how far from the point the parties are. Of course, if the space can be interpreted in physical terms, as Hotelling's could, this problem does not arise.

13 These terms may recall the distinction between “position issues” and “style issues” made by Berelson, Bernard R., Lazarsfeld, Paul F., and McPhee, William N., Voting (University of Chicago Press, Chicago, 1954), pp. 184198Google Scholar. If I understand their point, the difference between issues of position and style rests on a material-ideal distinction and hence tends to oppose class-related issues to all others. Their account of style issues sounds at places like the conception of valence-issues here. But many of the style issues they cite (e.g., prohibition, civil liberties) would be position-issues under the definitions I have given.

14 Because the public's evaluation of political actors is so often and so deeply influenced by valence-issues the Survey Research Center has used a model of individual electoral choice (and, by extension, of the national vote decision) that measures only the valence and intensity of the affect associated with the parties and candidates. The model is described in Stokes, Donald E., Campbell, Angus, and Miller, Warren E., “Components of Electoral Decision,” this Review, Vol. 52 (06 1958), pp. 367387Google Scholar, and Campbell, Converse, Miller, and Stokes, op. cit., pp. 68-88 and 524-531.

15 See, among others, MacRae, Duncan Jr., “The Role of the State Legislator in Massachusetts,” American Sociological Review, Vol. 19 (1954), pp. 185194CrossRefGoogle Scholar; MacRae, Duncan Jr., and Price, Hugh D., “Scale Positions and ‘Power’ in the Senate,” Behavioral Science, Vol. 4 (1959), pp. 212218CrossRefGoogle Scholar; and Belknap, George M., “A Method for Analyzing Legislative Behavior,” Midwest Journal of Political Science, Vol. 2 (11 1958), pp. 377402CrossRefGoogle Scholar.

16 In view of the ambiguity of party ideologies and the multidimensional grounds of party conflict, the necessity of agreeing upon a unidimensional seating order can itself lead to conflict in a legislative chamber that follows a left-right scheme. An interesting example of this is the attempt of the Finnish People's Party to move its seats to the left of the Agrarian Party in Finland's Eduskunta after the 1951 election.

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