Are voters sophisticated? Rational choice theories of voting assume they are. Students of voting behaviour are more doubtful. This article examines voting in a particularly demanding setting: direct democratic elections in which two competing proposals are on the ballot. It develops a spatial model of voting and proposal qualification with competing proposals. If voters are naïve, then competing proposals can be used to block the direct democratic route to change, but, if voters vote strategically, competing proposals can bring outcomes closer to the median voter. Voting intention data from California polls provide evidence that some votes are cast strategically even in these demanding circumstances. However, the level of strategic voting appears to be affected by the nature of the election campaign.