UC Santa Barbara

The problem that incomplete election returns pose for the calculation of the effective number of parties and related statistics such as the Herfindahl-Hirschman fractionalization index is known. Over the past several decades, different measurement approaches have been proposed, all of which attempt to overcome these challenges. The approach that is chosen may have consequences for theories about party system size. However, this issue has not been rigorously empirically explored to date. Accordingly, we investigate the practical consequences of the strategy for measuring party system size using district-level election data for Ireland over a 30-year period. Our primary contribution is to show that the choice of measure of party system size matters for conclusions about its relationship to both social structure and the electoral system at the level of the electoral district. While none of the three commonly employed inexact measurement approximations (the block, omission, and method of bounds) dominates the other two as a proxy for the exact measure across all tests and situations, our results show that the method of bounds performs the best most of the time. Exceptions include when very large shares of votes or seats go to “minor” parties and independents, or when there is only one minor party or independent; researchers must exercise caution in such instances. Yet even the method of bounds leads to different conclusions in our substantive application from that obtained with complete data. An additional contribution of the paper is to show that both district magnitude and social diversity shape party system size at the district level in Ireland, although arguably not always as hypothesized.