Do changes in district magnitude affect electoral fragmentation? Evidence over time at the district level

While there is a strong correlation between district magnitudes and electoral fragmentation, studies of national-level electoral system reforms provide mixed evidence that such reforms actually change levels of party system fragmentation because reforms are often endogenous to the outcomes they purport to explain. We propose that the reallocation of seats at the district level in PR systems (which hold geographic boundaries constant) provide better leverage to test how the electoral system affects the party system because these reforms are not politically manipulated in the way that national-level reforms are. We look at the effect of changing district magnitude on the effective number of parties winning seats, the number of parties running for office, and the effective number of parties winning votes in 20 countries. Adding seats increases the number of parties that run for office, the number of parties who win votes, and the number of parties who win seats in the subsequent election. The effects on electoral fragmentation is especially large in ethnically and politically divided countries. While the mechanical effect of adding seats is larger than is the psychological effects on parties or voters, these data provide strong evidence that electoral system reforms directly affect election outcomes.