Jeffrey A. Karp and Susan A. Banducci, "Issues and Party Competition Under Alternative Electoral Systems," Party Politics, January 2002, vol. 8, no. 1, pp. 123-141

First Paragraph:
Although the spatial model of elections has been a predominant paradigm in election studies, it has been criticized because of an empirical anomaly that parties tend to take more extreme positions than those of their voters. Recent debates over the usefulness of the Downsian model to explain party and voter behaviour have highlighted alternative models that account for the disparities between voter and elite issue positions (Iversen, 1994; Macdonald and Rabinowitz, 1989; Macdonald et al., 1991; Rabinowitz et al., 1991). Whereas the proximity or Downsian model predicts that parties are likely to adopt positions that are closer to their voters, the alternative directional model predicts that parties will adopt more extreme positions in order to generate political support among an electorate that has diffuse policy interests (Macdonald and Rabinowitz, 1989; Macdonald et al., 1991; Rabinowitz et al., 1991). Each model yields different predictions under alternative electoral rules.

Figures and Tables:
Table 1. Electoral outcomes for New Zealand political parties (%)
Figure 1. Party positions under FPP and PR rules
Table 2. Proximity model: OLS estimates
Table 3. Proximity model: OLS estimates

Last Paragraph:
While we expected the directional model to be less applicable under PR, we find that it actually performs better. Parties on average took more divergent positions than they had in the past and support for these parties appears best explained by taking into account the intensity of preference. The differences in the explanatory power of the models, though, tend to be only slight. Overall, both of these issue-based models of party rankings perform better under PR than under FPP, suggesting that congruence between voters and parties on issues (however measured) improves under PR.