Unanimous Implementation: A Case for Approval Mechanisms

We study whether approval mechanisms -- i.e. voting systems that allow subjects to vote for as many alternatives as they want -- can help a committee reach consensus. By focusing on the single-peaked domain, we prove that if an approval mechanism satisfies a set of desirable properties, then it leads to a predictable and unanimous decision (i.e. the equilibrium outcome is unique and it is approved by everyone). Moreover, we establish that the set of approval mechanisms that satisfy these properties is quite rich: essentially, for every Nash-implementable choice rule, there exists an approval mechanism that unanimously implements it.