The author proposes a two-round process called minority voting to allocate public projects in a polity. In the first round, a society decides by a simple majority decision whether to provide the public project. If the proposal in the first round is rejected, the process ends. Otherwise the process continues, but only the members of the minority keep agenda and voting rights for the second round, in which the financing scheme is determined. In the second round, the unanimity rule or the simple majority rule is applied. The author provides a first pass of relative welfare comparisons between minority voting and simple majority voting and outline the research program.