Direct democracy may impose significant information demands on voters, especially when individual propositions are highly complex. Yet, it remains theoretically ambiguous how proposition complexity affects referendum outcomes. To explore this question, I use a novel dataset on 153 Swiss federal referendums that took place between 1978 and 2010. The dataset includes hand‐collected data on the number of subjects per proposition based on official pre‐referendum information booklets as a measure of complexity. My estimation results suggest that the relationship between proposition complexity and the share of yes‐votes follows an inverse U‐shape. Using micro‐data from representative post‐referendum surveys, I provide evidence for two opposing channels. More complex propositions are supported by a more diverse group of voters. On the other hand, voters find it more difficult to estimate the personal consequences of complex propositions and are therefore more likely to reject them.