We analyze Assessment Voting, a new two-round voting procedure that can be applied to binary decisions in democratic societies. In the first round, a randomly-selected number of citizens cast their vote on one of the two alternatives at hand, thereby irrevocably exercising their right to vote. In the second round, after the results of the first round have been published, the remaining citizens decide whether to vote for one alternative or to abstain. The votes from both rounds are aggregated, and the final outcome is obtained by applying the majority rule, with ties being broken by fair randomization. Within a costly voting framework, we show that large electorates will choose the preferred alternative of the majority with high probability, and that average costs will be low. This result is in contrast with the literature on one-round voting, which predicts either higher voting costs (when voting is compulsory) or decisions that often do not represent the preferences of the majority (when voting is voluntary).