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Published online by Cambridge University Press: 27 January 2009
In recent years a considerable amount of work has been done on spatial models of party competition.1 The usual approach has been to represent the position of a voter on a given issue or issues as a point in a space of one or more dimensions, the position of a party or candidate similarly, and then to try to build models based on the distribution of voter positions and the relative positions of voters and candidates, using various criteria for party goals and strategy – e.g. maximizing votes, or maximizing plurality.
1 See for example: Davis, Otto M. and Hinich, Melvin J., ‘A Mathematical Model of Policy Formation in a Democratic Society’, in Bernd, J. L., ed., Mathematical Applications in Political Science II (Dallas: Southern Methodist University Press, 1966), 175–208Google Scholar; Davis, and Hinich, , ‘Some Results Related to a Mathematical Model of Policy Formation in a Democratic Society’, in Bernd, J. L., ed., Mathematical Applications in Political Science III (Charlottesville: University of Virginia Press, 1967), 14–38Google Scholar; Davis, and Hinich, , ‘On the Power and Importance of the Mean Preference in a Mathematical Model of Democratic Choice’, Public Choice, 5 (1968), 59–72CrossRefGoogle Scholar; Hinich, Melvin J. and Ordeshook, Peter C., ‘Abstentions and Equilibrium in the Electoral Process’, Public Choice, 7 (1969), 81–106CrossRefGoogle Scholar; Ordeshook, , ‘Extensions to a Model of the Electoral Process and Implications for the Theory of Responsible Parties’, Midwest Journal of Political Science, 14 (1970), 43–70CrossRefGoogle Scholar; Davis, , Hinich, and Ordeshook, ‘An Expository Development of a Mathematical Model of the Electoral Process’, The American Political Science Review, 64 (1970), 426–48CrossRefGoogle Scholar; Hinich, and Ordeshook, , ‘Plurality Maximization vs Vote Maximization: A Spatial Analysis with Variable Participation’, The American Political Science Review, 64 (1970), 772–91CrossRefGoogle Scholar; Garvey, Gerald, ‘The Theory of Party Equilibrium’, The American Political Science Review, 60 (1966), 29–38CrossRefGoogle Scholar; Chapman, David, ‘Models of the Working of a Two-Party Electoral System,’ Public Choice, 5 (1968), 19–37CrossRefGoogle Scholar; Chapman, , ‘Models of the Working of a two-party Electoral System – 1’, Papers on Non-market Decision Making, 3 (1967), 19–37Google Scholar; Tullock, Gordon, Toward a Mathematics of Politics (Ann Arbor: University of Michigan Press, 1967).Google Scholar
2 Taylor, Michael and Rae, Douglas W., The Analysis of Political Cleavages (New Haven: Yale University Press, 1970).Google Scholar To quote from p. 30: ‘… the model-interpretation is not meant to be a description of reality so much as a template against which to silhouette realities’.
3 Meek, B. L., ‘A Note on Uniform Election Processes as Riemann-Stieltjes Integrals’, Public Choice, 10(1971), 41–60.CrossRefGoogle Scholar
4 See Meek, ‘A Note on Uniform Election Processes’, for further discussion of this point.
5 The papers closest in approach are Hinich and Ordeshook, ‘Plurality Maximization’ and Garvey, ‘The Theory of Party Equilibrium’. In Hinich and Ordeshook ‘Plurality Maximization’ the distribution function is referred to as the probability that a randomly chosen voter will be at position x; in the view of the present author this is an unnecessarily confusing way of putting it, as it imports the idea of probability into the theory only by using the concept of ‘randomly choosing’ a voter from the population, which is irrelevant to the theory.
6 Again, see Meek, ‘A Note on Uniform Election Processes’, for further discussion.
7 The concept of ‘distance’ from such a spectrum position would still be meaningless, of course.