Interest in dimensionality arises in both formal theory and empirical work. An important example of the theoretical results has to do with locating the optimal spatial strategy for a political candidate or party. As Anthony Downs and others have pointed out, the party seeking to win an election should move to the center of the voter distribution if, along with other conditions, the campaign is based on a single unidimensional issue continuum. Guttman scaling, factor analysis, and multidimensional scaling are among the many empirical techniques which have been devised to test unidimensionality. If these techniques indicate that attitudes on an issue are unidimensional, then the Downsian candidate should adopt the position of the median voter. Thus empirical data can be brought together with derivations from axiomatic theory to obtain optimal strategies for political parties. The empirical frequency of the paradox of voting provides another example of this combination of scaling techniques with formal theory. Duncan Black, for *University of Rochester and Ohio State University, respectively. We would like to thank Michael Coveyou for bringing to our attention one of the examples used in the paper.