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Johannes Moenius and Yuko Kasuya, "Measuring Party Linkage Across Districts: Some Party System Inflation Indices and their Properties," Party Politics, 10 (September, 2004), 543-564.

First Paragraph:
This article introduces some improved measures that gauge the degree of party linkage, defined as the extent to which parties are uniformly successful in winning votes across districts. While this issue has been relatively neglected in the literature on party politics until recently, it is of vital importance if one is trying to understand the formation of national-level party systems. The examples of the US and India illustrate this point. In both cases, the system of election for the lower chamber is a single-member district plurality system. At the district level, the effective number of parties (the number of parties seriously contesting elections) for both countries is around two. In other words, it appears that both countries have a twoparty system at the district level, on average. However, when we nationally aggregate votes and calculate the effective number of parties at the national level, a very different picture arises. While the US remains a twoparty system at the national level, India has a very fragmented national party system in which the effective number of parties is about seven. This difference stems from variation in the degree of linkage. India is an example of poor linkage, in that parties across districts have very different degrees of success in gaining votes. Thus, at the national level, the aggregate size of the party system becomes highly inflated. The case of the US, on the other hand, exhibits high linkage, in that the same set of parties competes across districts with equal strength. In high linkage cases, there is little inflation when local-level party systems are aggregated to the national level.

Figures and Tables:
Figure 1. Conceptual scheme of national party system formation
Figure 2. Degree of party linkage as a continuum
Figure 3. Iteration sequence for ëdistributed monopolyí case
Figure 4. Simulating distributed monopoly of parties (introducing competition from larger districts)
Figure 5. Simulating concentrated monopoly of parties (introducing competition from larger districts)
Figure 6. Simulating concentrated monopoly of parties (introducing competition from smaller districts)
Table 1. Comparison of inflation measures for four countries
Table 2. Comparison of Italian elections of 1987, 1992, 1994
Table 3. Regional-level party system inflation rates and effective number of parties in Italy, 1994 election
Table 4. District-level contribution to national party system inflation
Figure 7. Histogram of distribution of Ii* for Germany, India, Italy, and the US

Last Paragraph:
In this article we introduced some improved measures to gauge the degree of party linkage, which refers to the degree to which parties are uniformly successful in winning votes across districts. We built upon Coxís measure, which gauges party linkage in terms of the inflation of the national party system size in comparison to the average, district-level party system size. We first suggested an alternative party system inflation measure that is intuitive and easy to interpret. We then introduced what we believe to be a relevant weighting method to our suggested inflation measure in order to adjust for the variation in district sizes across districts. Further, we proposed what we called a local inflation measure, which enabled us to analyze which subnational areas contribute to the national party system inflation, as well as the extent of their contribution. We explored the theoretical properties of these measures, examined how they behave in numerical simulations, and finally applied these measures to the cases of India, Italy, Germany, and the US to show their usefulness in the analysis of real-world phenomena.