Duverger’s Law in mixed legislative systems: The impact of national electoral rules on district competition TIMOTHY S. RICH Western Kentucky University, USA Abstract. How do institutional factors shape district competition in mixed legislative systems? Preliminary evidence suggests the distinction between sub-types of mixed systems alone poorly explains variation in district results. Consistent with the contamination thesis, this analysis suggests three additional national- level factors at play: fused ballots, the electoral threshold for proportional representation seats, and the existence of compulsory voting laws. Regression analysis on an original dataset covering 90 mixed system elections in 23 countries (1990–2012) finds that while mixed member majoritarian systems correlate with fewer district candidates, these three often overlooked factors are also statistically significant.This analysis highlights the complexity of mixed systems and suggests why many of them diverge from Duverger’s Law. Keywords: district competition; mixed legislative systems; Duverger’s Law; contamination thesis Introduction How do institutional factors shape election outcomes? A large literature tackles this ques- tion in majoritarian and proportional systems (e.g., Rokkan 1970; Lijphart 1977; Taagepera & Shugart 1989; Norris 2004) and provides clear expectations on the number of parties. While a growing literature similarly addresses institutional effects in mixed legislative systems that combine single member districts (SMDs) with seats filled by proportional representation (PR), few cross-national studies tackle district competition. This level is a more direct means to address Duverger’s Law, which expects two-party competition under SMDs and multiparty competition under PR. Duverger’s Law inherently remains a district- level theory (Sartori 1986; Cox 1997) and where aggregation to the country level potentially masks underlying trends. Considering the popularity of the mixed system electoral design among a diverse range of countries and historical experiences, a greater understanding of the correlates of district competition offers insight as to why these systems often fail to meet initial expectations. Such disconnect between expectations and reality has broad ramifications – for example, failure to conform to Duverger’s Law may produce non-Condorcet winners (Colomer 2001) and further alienate supporters of parties who fail to achieve representation (Duch & Palmer 2002; Tavits & Annus 2006). Cross-national studies often compare mixed systems directly to pure majoritarian or proportional systems, where outputs such as the number of parties are found to diverge (e.g., Herron & Nishikawa 2001; Kostadinova 2002). A common distinction is made between mixed member proportional (MMP) versus mixed member majoritarian (MMM), with some scholars often characterising the former as a subcategory of traditional PR 182 European Journal of Political Research 54: 182–196, 2015 doi: 10.1111/1475-6765.12067 © 2014 European Consortium for Political Research Published by John Wiley & Sons Ltd