We introduce a procedurally fair rule to study a situation where people disagree about the value of three alternatives in the way captured by the voting paradox. The rule allows people to select a final collective ranking by submitting a bid vector with six components (the six possible rankings of the three alternatives). In a laboratory experiment we test the robustness of the rule to the introduction of subsidies and taxes. We have two main results. First, in all treatments, the most frequently chosen ranking is the socially efficient one. Second, subsidies slightly enhance overbidding. Furthermore, an analysis of individual bid vectors reveals interesting behavioral regularities.