Measuring party linkage across districts: Some party system inflation indices and their properties

In this article we suggest improved measures of 'party linkage' across districts. The degree of party linkage, defined as the extent to which parties are uniformly successful in winning votes across districts, is an important but neglected issue in the party politics literature. It is particularly important in understanding the nature of national-level party system formation. Our suggested indices build on the measure of party linkage introduced by Cox (1999), which he named the party system 'inflation index' since it measures the inflation from the district-level to the national-level party system size that occurs in the process of party system aggregation. Our measures improve on Cox by making it more intuitive, introducing an appropriate weighting scheme, and suggesting a subnational-level measurement of party linkage. We examine the properties and the usefulness of our measures by numerical simulation and by empirical application to data from Italy, India, Germany, and the United States.