Does Voter Distribution Matter in the Directional Model? A Refutation of the Original Claims

Abstract

In this paper I demonstrate that the distribution of votes influences the theoretical predictions formulated through the instrumentality of the directional model of spatial analysis, thereby refuting the claims made by Macdonald, Listhaug and Rabinowitz (1991) who argue that the distribution of voters is only relevant for proximity-based models. Further, l show that the boundary of the region of responsibility is not always the ideologically dominant position, as Rabinowitz and Macdonald (1989) originally assert, this situation appearing only as a special case, determined by the fact that the area encompassed between the graph of the voter distribution function and the X - axis is numerically higher between the boundary of the region of responsibility and the point of origin then between the most extreme point of the ideological dimension and the boundary of the region of responsibility. Finally, I improve the full proportionality theorem by specifying the necessary conditions for each position described in the theorem to become ideologically optimal.