Journal article: This paper examines the comparative properties of voting rules based on the richness of their ballot spaces, assuming a given distribution of voting rights. We focus on how well voting rules aggregate the information dispersed among voters. We consider how different voting rules affect both voters’ decisions at the voting stage and the incentives of the agenda-setter, who decides whether to put the proposal to a vote. Without agenda-setter, the voting efficiency of rules is higher when their ballot space is richer. Moreover, full-information efficiency requires full divisibility of the votes. In the presence of an agenda-setter, we uncover a novel trade-off: in some cases, rules with high voting efficiency provide worse incentives to the agenda-setter to select good proposals. This negative effect can be large enough to wash out the higher voting efficiency of even the most efficient rules.