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How do large-magnitude proportional systems affect invalid voting? We evaluate a Chilean electoral system reform that introduced proportionality. Voting is voluntary, and legislative and presidential elections are held concurrently. We compare the invalid votes between different types of elections before and after the reform using various difference-in-differences strategies. We find that invalid voting increased in legislative compared to presidential elections (pre-trends were parallel). The increase in invalid voting is greater in post-reform districts with higher magnitude and is not due to pre-reform district characteristics. The results of heterogeneity analyses and a survey experiment suggest the mechanism behind these findings is the cognitive burden associated with a longer ballot. This research highlights an understudied aspect of electoral systems: higher district magnitudes may be demobilizing in terms of valid voting for citizens who are more vulnerable to cognitive burden, even among those motivated enough to vote in the first-order election.
Cox et al. (Fri,) studied this question.