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Bernard Grofman, Samuel Merrill, Thomas L. Brunel, and William Koetzle, "The Potential Electoral Disadvantages of a Catch-all Party: Ideological Variance among Republicans and Democrats in the 50 US States," Party Politics, 5 (April 1999), 199-210.

First Paragraph:
The standard uni-dimensional Downsian model (Downs, 1957) emphasizes the importance of the median voter, but models of two-party political competition that build on Downsian insights often emphasize the importance of the median voter within each political party. For example, models of competition that incorporate the role of primaries in US political competition, such as those of Aranson and Ordeshook (1972), Coleman (1971, 1972), or Owen and Grofman (1995), give rise to the expectation that, in ideological terms, party candidates will locate somewhere between their party's median voter and the overall median,' an expectation that is empirically confirmed (Shapiro et al., 1990). Similar results are obtained for models emphasizing the importance of party activists. But if voters are choosing between two candidates located at or near each party's median, then it is possible that the smaller party will actually find its candidate closer to the overall median voter than is the candidate of the larger. Thus, ceteris paribus, sometimes the smaller but more ideologically cohesive party should be able to win state-wide elections when its share of identifiers would suggest it ought not be able to win.

Figures and Tables:
Figure 1: Typical voter distribution: mixed normal probability density
Table 1: Mean and median ideologies (NES seven-point scale) for Democrats, Republicans and independents in the nation as a whole
Table 2: State variance and medians on seven-point ideological scale
Table 3: Relative location of Republican and Democrats identifiers

Last Paragraph:
We have sought to provide new insights into the links between party and overall medians and party means and variances for two-party competition. Our theoretical results have direct and important practical implications. Our data analysis has highlighted the practical implications of our model for two-party competition in the USA. We expect that Republicans are advantaged in US electoral politics because, ceteris paribus, due to the variance effect, the Republican position can be expected to be closer to the overall median (sometimes even a lot closer) than we would expect from simply examining the relative numbers of each party's identifiers/supporters. This effect is not simply a national-level effect, but is also found in almost all states.