The power of ideologically concentrated minorities

In two-party competition, it is well known that the party whose supporters! identifiers are more ideologically concentrated can pull the overall media n in the direction of its party median, while the overall mean is essential ly simply an average of the two party means weighted by the number of suppo rters/identifiers of each party. Yet the exact nature of the relationship b etween the overall median and the party-specific medians has never, we beli eve, been fully explicated. We consider three questions relevant to unidime nsional two-party political competition: The first is 'What factors determi ne the location of the coverall median relative to the medians in each poli tical party?' The second is 'What are the factors that determine the locati on of the overall median relative to the overall mean?' The third, and pote ntially most interesting, is 'Under what circumstances, if any, will the me dian of the party with fewer supporters be closer to the overall median tha n that of the party with a preponderance of supporters?' For party distributions which sufficiently overlap, we show analytically ho w (a) degree of party support, and (b) ideological cohesion of each party's supporters trade off with one another to determine the location of the ove rall median relative to the party medians. In general, if the smaller party is more concentrated ideologically and if the disparity in dispersion betw een the two parties exceeds the disparity in the number of party identifier s, then the overall median is closer to the median of the smaller party and , ceteris paribus, the smaller party can be expected to win.